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diff --git a/conductor/tracks/video_analysis_entropy_epiplexity_20260621/artifacts/frames/frame_00213.jpg b/conductor/tracks/video_analysis_entropy_epiplexity_20260621/artifacts/frames/frame_00213.jpg
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Binary files /dev/null and b/conductor/tracks/video_analysis_entropy_epiplexity_20260621/artifacts/frames/frame_00213.jpg differ
diff --git a/conductor/tracks/video_analysis_entropy_epiplexity_20260621/artifacts/ocr.md b/conductor/tracks/video_analysis_entropy_epiplexity_20260621/artifacts/ocr.md
new file mode 100644
index 00000000..265e9fdb
--- /dev/null
+++ b/conductor/tracks/video_analysis_entropy_epiplexity_20260621/artifacts/ocr.md
@@ -0,0 +1,1808 @@
+# OCR Results
+
+## frame_00001.jpg
+
+```
+What
+is random?
+Is this white noise?
+2/18
+```
+
+## frame_00002.jpg
+
+```
+What
+Page 3 of 18
+is random?
+Look for longer... does it still seem random?
+3/18
+```
+
+## frame_00003.jpg
+
+```
+Page 4 of 18
+What is random?
+Whether or not something appears random depends on the available
+computation.
+Pseudorandom numbers are indistinguishable from actual random numbers
+with only polynomial time computation.
+EPIPLEXITY
+4/18
+```
+
+## frame_00004.jpg
+
+```
+Page 5 of 18
+Three Paradoxes of Information
+Accounting for computational constraints is central to understanding modern deep
+learning. We present three apparent paradoxes of information theory: statements
+that can be justified mathematically, but are in tension with reality.
+Paradox 1: Information cannot be increased by deterministic processes.
+Yet synthetic data and pseudorandom numbereeneration are ubiquitous,
+AlphaZero learns sophisticated strategies from games...
+Paradox 2: Information is independent of factorization order. Yet LLMs
+learn more from English text ordered left to right, picking out an arrow of time.
+Paradox 3: Likelihood modelling is merely distribution matching. Yet there
+are emergent phenomena, where models go beyond the data generating process.
+These paradoxes arise in part because information theory assumes unlimited
+computation and fails to target useful information content.
+5/18
+```
+
+## frame_00005.jpg
+
+```
+Page 6 of 18
+What is the description length of AlphaZero?
+Rules of Chess: 500 Bytes
+Training Algorithm: 10KB
+Seed: 32 Bytes
+Total: < 12KB
+1
+The description length of the entire system is quite small. Since information cannot
+be created, what did AlphaGo learn?
+AlphaZero
+TRAINING PROCEDURE
+(RuxHn
+('ETS
+RULES OF nc GAME
+GQ
+GAME PLAYING
+Overview of AJphaZero Training Pipeline
+6/18
+```
+
+## frame_00006.jpg
+
+```
+Page 7 of 18
+Noise or Structure?
+Classical information theory says that these have same amount of
+information
+Initial Seed
+tt.t.•j,
+Evolution Rules
+7/18
+```
+
+## frame_00007.jpg
+
+```
+andrewepiplexitymotivation.pdf
+Page 7 of 18
+RULES
+GQ
+Overview of AJphaZero
+Noise or Structure?
+o
+Q
+Q
+6/18
+Classical information theory says that these have same amount of
+information
+Initial Seed
+Evolution Rules
+```
+
+## frame_00008.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00010.jpg
+
+```
+epiplexity_encrypted_only_optimized2 (l).mpa
+00:40
+```
+
+## frame_00011.jpg
+
+```
+epiplexity_encrypted_only_optimized2 (l).mpa
+00:10
+00:40
+```
+
+## frame_00012.jpg
+
+```
+epiplexity_encrypted_only_optimized2 (1).mp4
+```
+
+## frame_00013.jpg
+
+```
+epiplexity_encrypted_only_optimized2 (1).mp4
+00:11
+00•.40
+```
+
+## frame_00014.jpg
+
+```
+epiplexity_encrypted_only_optimized2 (1).mp4 v
+```
+
+## frame_00015.jpg
+
+```
+epiplexity_encrypted_only_optimized2 (1).mp4 v
+: 12
+oo:ao
+```
+
+## frame_00016.jpg
+
+```
+epiplexity_encrypted_only_optimized2 (1).mp4
+```
+
+## frame_00017.jpg
+
+```
+epiplexity_encrypted_only_optimized2 (1).mp4
+.4
+00440
+```
+
+## frame_00018.jpg
+
+```
+epiplexity_encrypted_only_optimized2 (1).mp4
+00:14
+00:40
+```
+
+## frame_00019.jpg
+
+```
+epiplexity_encrypted_only_optimized2 (1).mp4
+00:14
+ootao
+```
+
+## frame_00020.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00021.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00022.jpg
+
+```
+1
+```
+
+## frame_00023.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00024.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00025.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00026.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00027.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00028.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00029.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00030.jpg
+
+```
+(l).mpa
+```
+
+## frame_00031.jpg
+
+```
+epiplexity_encrypted_only_optimized2 (1) .mpa
+0040
+1
+```
+
+## frame_00032.jpg
+
+```
+Q eoælexj:y v_ovLmized2
+```
+
+## frame_00033.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00034.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00035.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00036.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00037.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00038.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:07
+00:40
+```
+
+## frame_00039.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:08
+00:40
+```
+
+## frame_00040.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:08
+00:40
+```
+
+## frame_00041.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:08
+00:40
+```
+
+## frame_00042.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:08
+00:40
+```
+
+## frame_00043.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:09
+00:40
+```
+
+## frame_00044.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:09
+00:40
+```
+
+## frame_00045.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:09
+00:40
+```
+
+## frame_00046.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:10
+```
+
+## frame_00047.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:10
+oo:ao
+```
+
+## frame_00048.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:10
+oo:co
+```
+
+## frame_00049.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:11
+oo:co
+```
+
+## frame_00050.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00051.jpg
+
+```
+1
+```
+
+## frame_00052.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00053.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00054.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00055.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00056.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00057.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00058.jpg
+
+```
+1
+```
+
+## frame_00059.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00060.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00062.jpg
+
+```
+rug-
+```
+
+## frame_00063.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00064.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00065.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00066.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00067.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00069.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00071.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00072.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:18
+00:40
+```
+
+## frame_00073.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:18
+00:40
+```
+
+## frame_00074.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00075.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00076.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00078.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:24
+00:40
+```
+
+## frame_00079.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:24
+o@
+00:40
+```
+
+## frame_00080.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:25
+o@
+00:40
+```
+
+## frame_00081.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:25
+o@
+00:40
+```
+
+## frame_00082.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:25
+o@
+00:40
+```
+
+## frame_00083.jpg
+
+```
+00:25
+epiplexity_swapped_optimized2.mp4
+o@
+00:40
+```
+
+## frame_00084.jpg
+
+```
+00:26
+epiplexity_swapped_optimized2.mp4
+o@
+00:40
+```
+
+## frame_00085.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:26
+o@
+00:40
+```
+
+## frame_00086.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+1
+ob:oo
+oo.•ao
+```
+
+## frame_00087.jpg
+
+```
+epiplexity_swapped_optimized2.mp4 v
+00:00 |
+00:40
+```
+
+## frame_00088.jpg
+
+```
+epiplexity_swapped_optimized2.mp4 v
+oo:ca •I
+1
+00:40
+```
+
+## frame_00089.jpg
+
+```
+epiplexity_swapped_optimized2.mp4 v
+00:40
+```
+
+## frame_00090.jpg
+
+```
+epiplexity_swapped_optimized2.mp4 v
+00:01
+00:40
+```
+
+## frame_00091.jpg
+
+```
+epiplexity_swapped_optimized2.mp4 v
+00:01
+00:40
+```
+
+## frame_00092.jpg
+
+```
+epiplexity_swapped_optimized2.mp4 v
+00:01
+00:40
+```
+
+## frame_00093.jpg
+
+```
+epiplexity_swapped_optimized2.mp4 v
+00:02
+00:40
+```
+
+## frame_00094.jpg
+
+```
+epiplexity_swapped_optimized2.mp4 v
+Lui •
+00:02
+00:40
+```
+
+## frame_00095.jpg
+
+```
+epiplexity_swapped_optimized2.mp4 v
+00:02
+00:40
+```
+
+## frame_00096.jpg
+
+```
+epiplexity_swapped_optimized2.mp4 v
+00:02
+00:40
+```
+
+## frame_00097.jpg
+
+```
+00:03
+epiplexity_swapped_optimized2.mp4 v
+00:40
+```
+
+## frame_00098.jpg
+
+```
+epiplexity_swapped_optimized2.mp4 v
+00:03
+00:40
+```
+
+## frame_00099.jpg
+
+```
+epiplexity_swapped_optimized2.mp4 v
+00:03
+00:40
+```
+
+## frame_00100.jpg
+
+```
+epiplexity_swapped_optimized2.mp4 v
+00:03
+00:40
+```
+
+## frame_00101.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:40
+```
+
+## frame_00102.jpg
+
+```
+1
+epiplexity_swapped_optimized2.mp4
+00:04
+00:40
+```
+
+## frame_00103.jpg
+
+```
+00:04
+epiplexity_swapped_optimized2.mp4
+00:40
+```
+
+## frame_00104.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:40
+```
+
+## frame_00105.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:04
+00:40
+```
+
+## frame_00106.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:05
+00:40
+```
+
+## frame_00107.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:05
+00:40
+```
+
+## frame_00108.jpg
+
+```
+00:05
+epiplexity_swapped_optimized2.mp4
+00:40
+```
+
+## frame_00109.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:40
+```
+
+## frame_00110.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00•.06
+00:40
+```
+
+## frame_00111.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:06
+00:40
+```
+
+## frame_00112.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:06
+00:40
+```
+
+## frame_00113.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:06
+00:40
+```
+
+## frame_00115.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:07
+00:40
+```
+
+## frame_00116.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:07
+00:40
+```
+
+## frame_00117.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:07
+00:40
+```
+
+## frame_00119.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:40
+```
+
+## frame_00122.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+oo:oa
+00:40
+```
+
+## frame_00123.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:40
+```
+
+## frame_00126.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00128.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00129.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00130.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00131.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00133.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00134.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00137.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00141.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00143.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00145.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00146.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00147.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00148.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00149.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00150.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00152.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00153.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00154.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00160.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00162.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00163.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00165.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00167.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00168.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00169.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00170.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00171.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00173.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00174.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00175.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00176.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00179.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00180.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00181.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00182.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00184.jpg
+
+```
+Ar+l
+```
+
+## frame_00185.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00186.jpg
+
+```
+epiplexity_swapped_optimized2.mp4
+00:21
+00:40
+1
+```
+
+## frame_00187.jpg
+
+```
+epiplexity_swapped_optimized2.mp4 v
+00:21
+00:40
+```
+
+## frame_00188.jpg
+
+```
+epiplexity_swapped_optimized2.mp4 v
+00:21
+11
+00:40
+```
+
+## frame_00189.jpg
+
+```
+epiplexity_swapped_optimized2.mp4 v
+```
+
+## frame_00190.jpg
+
+```
+(no text extracted)
+```
+
+## frame_00193.jpg
+
+```
+andr
+Page
+(Ct'ZA i
+Noise or
+Show Tab Bar
+Hide Sidebar
+Thumbnails
+Table of Contents
+Highlights and Notes
+Bookmarks
+Contact Sheet
+Continuous Scroll
+Single Page
+Two Pages
+Soft Proof with Profile
+C.V Document
+Actual Size
+Zoom In
+Zoom Out
+Show Markup Toolbar
+Hide Toolbar
+Customize Toolbar...
+Slideshow
+Enter Full Screen
+Q
+Q
+6/18
+says that these have same amount of
+Initial Seed
+Evolution Rules
+1
+```
+
+## frame_00195.jpg
+
+```
+Page 8 of 18
+Randomness versus Structure
+Random vs structural information
+Low random info, Iow structural info
+High random info, Iow structural info
+def is
+if n
+eLif
+elif
+elif
+elif
+elif
+return True
+Epiplexity
+— — Entropy
+2:
+return False
+return True
+return False
+return True
+return False
+Moderate random info, high structural info
+def dijkstra(o s)
+while q:
+d, u pop(q)
+if d D(u]:
+for v, in g.get(u,
+if (nd
+D(V) = nd; push(q. (nd, v))
+return D
+API KEY -sk_7aF2jK1ycP9LmvYzz34"
+USER ID -usr 4f8a2c1e9b7d3ess-
+BUCKET -s3://data-8a3f1b-west-prod"
+SAVE DIR - -
+SAVE CKPT - True
+DEBUC False
+SEED 928471S
+o
+o
+Step
+Step
+Step
+8/18
+```
+
+## frame_00196.jpg
+
+```
+OOD Generalization
+Why is language data so transferable?
+Time Series
+•and
+Te jurnvvd up on the
+"and bit my
+Inorganic Materials
+us use.»
+•631.056.650. 487.48S 4S'-
+Neural Cellular Automata
+data useful for text, code
+and math!
+'479,
+•492. 499.
+Pre-Trüü•o
+9/18
+```
+
+## frame_00197.jpg
+
+```
+Page 10 of 18
+What is information?
+There are many different measures and theories...
+In classical (Shannon) information theory, information is the surprisal in seeing
+the value of a random variable.
+Algorithmic information theory also applies to non-random variables, and
+measures incompressibility of data.
+Intuitively, useful information can reduce uncertainty in predictions.
+WE WULMAÄE
+THE LIES LEARN
+10/18
+```
+
+## frame_00198.jpg
+
+```
+Page 11 of 18
+Shannon Information
+Given a random variable X, with distribution P(x):
+The Shannon information of outcome x is h(x) log2 FOY ,
+measured in bits.
+It measures the surprisal in observing x.
+The Shannon entropy measures the average information content in X:
+H(x) P(x) log
+Mutual information
+I(x; Y) = H(x) — H(xlY) H(Y) - H(Ylx) H(x) + H(Y) - H(x, Y).
+Key properties:
+Symmetry ofinformation: H(xlY) + H(Y) H(x, Y) H(Ylx) + H(x). The
+information in predicting x is equal to the information in predicting y then x.
+Deterministic transformations add no information: for a deterministic
+transformation, Y H(Ylx) O. Corollary: H(f(X)) H(x).
+Data Processing Inequality: If Y is obtained from X through some processing,
+and similarly Z through Y, then I(X; Z) I(X; Y).
+Objects which are not random must contain no information.
+11/18
+```
+
+## frame_00199.jpg
+
+```
+Page 12 of 18
+Algorithmic Information Theory
+Studies the information content of any object x, which does not need to be a random
+variable.
+The (prefix) Kolmogorov complexity of x is defined as:
+K(x) min{lpl : u(p) = x}
+where the valid programs form a prefix free set.
+(1)
+The shortest self-delimiting program (a program that encodes its own length)
+that outputs x and then halts (no valid codeword is a prefix for another).
+Symmetry of information: K(ylx) + K(x) K(xly) + K(y) + 0(1).
+Information non-increase: K(f(x)) K(x) + K(f) + 0(1).
+Like Shannon information, is an absolute measure of information, and doesn't
+separate useful from unpredictable structure.
+Incomputable (but can be upper bounded).
+12/18
+```
+
+## frame_00200.jpg
+
+```
+Page 13 of 18
+Sophistication
+Sophistication is the smallest Kolmogorov complexity of a set S such that x is a
+random element from that set:
+nsophc(x) min : {K(S) : K (x I S) > log ISI u— c}
+(2)
+Difficult to find high sophistication objects due to Chaitin's incompleteness
+theorem (can't prove K (x) > L).
+Owing to unbounded computation, complex objects appear to lose their
+complexity as measured by sophistication.
+Cannot simply make sophistication time-bounded: we show it becomes
+essentially constant for all strings (a time-bound makes it possible to choose a
+tiny universal interpreter for Sreusable structure that halts, and put everything
+into a leftover data string).
+Understanding the role of computation is central to phenomena such as
+induction, emergence, chaos, and cryptography.
+13/18
+```
+
+## frame_00201.jpg
+
+```
+Page 14 of 18
+Levin Complexity
+Levin complexity is a compute-limited Kolmogorov complexity.
+It is concerned with how compactly you can generate one specific output, rather
+than what can be extracted from a distribution.
+Pseudorandom numbers are treated by Levin complexity as simple: suppose
+x = G(s) where G is a PRNG. Then there is a short program: "run G on seed s".
+However, there's almost no learnable structure for polynomial-time models.
+Doesn't distinguish between unpredictable and predictable structure.
+14/18
+```
+
+## frame_00202.jpg
+
+```
+Page 15 of 18
+What is Random?
+A random variable defines a map from a given measurable probability space to
+different outcomes, with probabilities corresponding to the measure of the
+space that lead to a certain outcome.
+In the mid 1900s, mathematicians were interested in formalizing precisely what
+it means for a given sample to be a random draw from a given distribution.
+Consider a uniformly sampled binary sequence from which other
+distributions can be constructed.
+Are all sequences equally random, since they are equally likely? What about
+But what about statistics? LLN says lim,v-+oo
+= 0.5.
+Martin Lof randomness:Ä sequence must pass all computable randomness tests
+Cryptographic randomness: sequence must pass all polynomial time
+randomness tests
+15/18
+```
+
+## frame_00203.jpg
+
+```
+Page 16 of 18
+Pseudorandom Numbers
+Cryptographically secure pseudorandom number generators CSPRNG[k] contain
+polynomial time functions Gn : {0, —+ {0, 1 Y that stretch k input bits into
+n poly(k) > k output bits. For any non-uniform PPT distinguisher D and c 2 1:
+1
+(3)
+Pseudorandom numbers are indistinguishable from true random numbers with
+polynomial-time computation
+A closely related concept is a one-way function, f : {0, —+ {0, l}m, which is
+computable in poly(n) time but computationally expensive to invert on average. For
+any non-uniform PPT inverter A:
+1
+(4)
+16/18
+```
+
+## frame_00204.jpg
+
+```
+Pseudorandom numbers don't add information?
+G: PRNG
+Transformation
+function
+Initialization
+function
+Output
+function
+G(Uk)
+Random bits
+State
+pRNG
+Shannon Information
+Suppose the seed is drawn from Ük,
+then
+H(x) H(Uk) k
+by DPI.
+Algorithmic Information
+K(Uk) +K(G)
+K(Uk) + 0(1), since G has constant
+description length.
+Pseudorandom numbers are practically indistinguishable from actual random
+numbers but add no information?
+17/18
+```
+
+## frame_00205.jpg
+
+```
+Page 18 of 18
+Conway's Game of Life and Cellular Automata
+Elementary cellular automata (ECA) provide a natural mechanism for reasoning
+about emergent structure, deterministic transformations, and the role of computation.
+ID array of binary cells xft) e {0, 1}.
+Each cell's next value only depends on itself and its two neighbours:
+Because each local neighbourhood has 3 bits, there are 23
+8 local
+neighbourhoods: 111, 110, 101, 100, 011, 010, 001, 000.
+A rule assigns an output to each of these 8 cases. There are 28
+256 ECA
+rules. Different rules give rise to different complexities and structures.
+ECA are represented visually with time evolution from top to bottom.
+nun
+No interesting
+structures
+Rule 15
+Interesting but
+predictable structures
+Rule 54
+Effectively random
+Rule 30
+18/18
+```
+
+## frame_00207.jpg
+
+```
+levin_presentation_revised.pptx Microsoft PowerPoint (Product Activation Failed)
+x
+Home
+Cut
+Copy v
+Paste
+Insert Design
+Transitions
+Layout •
+Reset
+New
+Animations
+Font
+Slide Show
+Review
+Clipboard
+Slides Outline
+View
+4
+Acrobat
+Text Direction
+Align Text
+- Convert to SmartArt -
+OCAUU
+1
+j Shape Fill
+Shape Outline
+Arrange Quick
+Shape Effects •
+Styles
+Drawing
+0
+Find
+•ac Replace
+Select v
+Editing
+1
+arxiv.org/pdf/2601.03220
+aculty apps Bookmarks Physics and Math
+Finish update
+All Bookmarks
+Format Painter Slide
+Section
+Slides
+Paragraph
+3
+2
+Snap Snap to
+to Grid Shape
+stuff
+2
+3
+4
+Entropy to Epiplexity: Rethin...
+Bookmarks
+119%
+Noise Or Structure?
+Noise Or Structure?
+Epiplexity definition
+Epiplexity definition
+:= set of programs implementing normalized
+probability distributions on that can both
+compute probabilities and sample in time T (n)
+Definition 8 (Epiplexity and Time-Bounded Entropy) Consider a random variable X
+13 / 65
+log 1/PHZi)
+log
+IP preql
+I preql
+wholesome
+12
+nAudia
+5.0
+2.5
+0.0
+ä
+6
+5
+ECA
+Ask Gemini
+School
+Induct Easy
+6
+5
+4
+3
+log 1/Pb(Z0, ...ZD- 1)
+# Train Tokens
+(a) Estimate information in model
+Hr(X) = E log 1/"' (X)
+Compute (T
+= 6ND + 2ND)
+(b) Compute-optimal 2-part code
+0.0
+0.5 1.0 0.1
+0.5 0.9
+Induct Hard
+Natural
+90
+0
+50
+10
+0.50 0.75 1.00
+10
+30
+50
+sreq (MB)
+• programs implementing normalized
+probability distributions on (O,IY that can both
+compute probabilities and sample in time T (n)
+4
+Epiplexity= Size of Optimal Model
+Small model size
+Lcnv SAX), Iow HT(X)
+-> Small model size
+Low SAX), high HT(X)
+Large model size
+high SAX), mid HT(X)
+5
+Estimating Epiplexity
+Code for neural network
+training)
+• Train neural networkswithdifferent parameter-sand compute
+Compute total code length for data at given compute
+I uatecom presæd mod elsizefa best compresorofdata
+Epiplexity: Two Key Ideas
+I. Weshculd tp,' to separate
+rsndcmcontent from
+structured acntent S H
+(c) Requential vs Prequential
+on {0, l}n. Let
+P* arg min {IPl+E[log I/P(X)]}
+(3)
+be the program that minimizes the time bounded MDL with ties broken by the smallest program,
+and eapectations taken over X. IPl denotes the length of the program P in bits, and logarithms
+are in base 2. We define the T-bounded epiplexity ST and entropy HT of the random variable
+ST(X) IP*I,
+and HT(X)
+Click to add notes
+(4)
+125% —j
+Figure 2: How to estimate epiplexity. (a) We consider two approaches for efficiently coding trained
+neural networks. Prequential estimation estimates information content as the area under the loss curve of
+a model above its final loss, with the training set matching the test data drstribution. Requential coding,
+which provides an explicit code for PS with expected length as the cumulative KL between a student model
+PS and the teacher Pt that generates its synthetic training data, visualized approximately by their loss gap.
+We typically choose Pt to be a model trained on the real training set, as in prequential coding. (b) Using
+either approach, we optimize hyperparameters (model size N, training tokens D, etc.) to find the shortest
+two-part code for each compute budget, which decomposes into the estimated epiplexity and time-bounded
+entropy. (c) Comparing prequential and requential coding on four groups of datsets used in this work. The
+prequential estimate is typically larger, but the two correlate well, particularly within each group.
+modalities (MacKay, 2003; Goldblum et al., 2023; Delétang et al., 2023; Ballé et al., 2018) and
+capture the most relevant ML phenomenology. While a naive approach is to let P be a program that
+directly stores the architecture and weights of a neural network and evaluates it on the given data,
+this approach can significantly overestimate the information content in the weights, particularly for
+large models trained on relatively little data. Instead, we will use a more efficient approach that
+encodes the training process that produces the weights. We will discuss two approaches for encoding
+neural network training processes, based on prequential coding (Dawid, 1984) and requential coding
+(Finzi et al., 2026), respectively. The former is more straightforward to understand and evaluate, but
+relies on a heuristic argument to separate structure bits from noise bits, while the latter is rigorous
+at the cost of being more difficult to evaluate. Fortunately, both approaches often yield comparable
+rankings of epiplexity across datasets (Section 4.3).
+Moving forward, we will measure time by the number of floating-point operations (FLOPs) and
+dataset size by number of tokens, so that training a model with N pararneters on D tokens takes time
+approximately 6ND (Kaplan et al., 2020), while evaluating it on X takes time 2ND with D IXI
+the number of tokens in X. To distinguish X from the training dataset, which we are free to choose,
+we will refer to X as the test dataset, as it is the data we need to perform inference on.
+4.1 Approximating Model Description Length with Prequential Coding
+Prequential coding provides a classic approach for compressing the training process of a neural
+network. We assume a batch size of one for simplicity, but generalizing to batch sizes larger than one
+is straightforward. Starting with a randomly initialized network Po (where
+using log 1/Pi(Zi) bits, then train the model on this token to produce Pi+l.
+i.i.d. from the same distribution as X. On the side of the decoder, a synchronized model is maintained;
+the model decodes Zi using Pi and then trains on it to produce the identical Pi+l. Omitting small
+Slide 3 of 25 "Office Theme"
+English (U.S.)
+8:28 AM
+ENG
+4/7/2026
+```
+
+## frame_00208.jpg
+
+```
+Epiplexity definition
+' PT'.= set of programs implementing normalized
+probability distributions on that can both
+compute probabilities and sample in time T (n)
+Definition 8 (Epiplexity and Time-Bounded Entropy) Consider a random variable X
+on {0, l}n. Let
+P* arg min {IPI+E[10g I/P(X)]}
+PEPT
+(3)
+be the program that minimizes the time bounded MDL with ties broken by the smallest program,
+and expectations taken over X. IPl denotes the length of the program P in bits, and logarithms
+are in base 2. We define the T -bounded epiplexity ST and entropy HT of the random variable
+and HT(x)
+ST(x) IP*I,
+(4)
+ivate Windows
+o Settings to activate Windows.
+```
+
+## frame_00209.jpg
+
+```
+Epiplexity = Size of Optimal Model
+def is
+_ even (n)
+if n
+elif
+elif
+elif
+elif
+elif
+API KEY =
+USER ID =
+BUCKET =
+SAVE DIR -
+SAVE CKPT -
+0: return True
+Low random info, Iow structural info
+o
+return False
+return True
+return False
+return True
+return False
+High random info, Iow structural info
+Epiplexity
+— Entropy
+Step
+"sk_7aF2jK1ycP9LmvYzz34"
+"usr 4f8a2c1e9b7d3065"
+"s3 ://data-8a3f1b-west-prod "
+" /mnt/marc/exp_7f2a/ckpts "
+- True
+DEBUG = False
+SEED = 9284715
+o
+Step
+Moderate random info, high structural info
+def dijkstra(g, s):
+D = 'inf' ) )
+while q:
+pop(q)
+if d =
+for v, w in g.get(u,
+if (nd
+= nd; push(q, (nd,
+return D
+o
+-> Small model size
+Low S (X), Iow H (X)
+-> Small model size
+Low S (X), high H (X)
+-> Large model size
+high S (X), midH (X)
+Step
+ivate Windows
+o Settings to activate Windows.
+```
+
+## frame_00210.jpg
+
+```
+Estimating Epiplexity
+Code for neural network
+Requential coding (code length = summed kl between a teacher and
+student model over training)
+Train neural networks with different parameters and compute
+Compute total code length for data at given compute
+Evaluate compressed model size for best compressor of data
+log 1/Pit(Zi)
+log 1/PiS(Zi)
+z
+preq
+preql
+log 1/Pb(Z0, ... , 0-1)
+# Train Tokens
+o
+HT(X) = E log I/P* (X)
+ST(X) = I
+Compute (T =
+6ND + 2ND)
+ivate Windows
+o Settings to activate Windows.
+(a) Estimate information in model
+(b) Compute-optimal 2-part code
+```
+
+## frame_00211.jpg
+
+```
+Three Paradoxes of Information
+Paradox 1: Information cannot be increased by deterministic processes
+-> Time bounded entropy and epiplexity can be created through computation
+PRG
+SEED
+(PSEUDORANDOM
+GENEUIOR)
+PSEUDORANDOM
+Rule 15
+Rule 30
+Rule 54
+Paradox 2: Information is independent of factorization order.
+Paradox 3: Likelihood modelling is merely distribution matching.
+ivate Windows
+o Settings to activate Windows.
+```
+
+## frame_00212.jpg
+
+```
+Paradox 1 (Information non increase)
+Case Study: Pseudorandom Number Generation
+PRG (pseudorandom generator):
+No polynomial sized circuit D can
+distinguish the output sequence
+from random substantially better
+than random chance
+SEED VALUE
+PRG
+(PSEUDORANDOM
+GENERATOR)
+DETERMINISTIC PROCESS
+1
+1] - Pr [Dn(u) = 1]
+PRGs have high time bounded entropy and Iow epiplexity
+Theorem 9 For any T e Poly(n) and G e CSPRNG that stretches the input to n poly(k)
+bits and allowing for an advantage of at most E(k), the time bounded entropy is nearly maximal:
+n -2 - ne(k) < c,
+and the epiplexity is nearly constant
+G(Uk)
+01001101001110
+010001011
+PSEUDORANDOM
+OUTPUT STREAM
+ivate Windows
+o Settings to activate Windows.
+```
+
+## frame_00213.jpg
+
+```
+Case Study: Elementary Cellular Automata
+Elementary cellular
+automata
+— Random ICs
+Predict Y=f(X) given X
+Rule 15
+Rule 30
+Rule 54
+ivate Windows
+o Settings to activate Windows.
+```
diff --git a/conductor/tracks/video_analysis_entropy_epiplexity_20260621/artifacts/transcript.json b/conductor/tracks/video_analysis_entropy_epiplexity_20260621/artifacts/transcript.json
new file mode 100644
index 00000000..8d732bd1
--- /dev/null
+++ b/conductor/tracks/video_analysis_entropy_epiplexity_20260621/artifacts/transcript.json
@@ -0,0 +1,18958 @@
+{
+ "video_id": "_U8AwUq_aJQ",
+ "segments": [
+ {
+ "start": 1.44,
+ "duration": 0.0,
+ "text": "So,<00:00:01.560> I'm<00:00:01.720> Andrew<00:00:02.160> Wilson<00:00:02.680> and<00:00:03.080> I'm<00:00:03.200> going<00:00:03.320> to"
+ },
+ {
+ "start": 3.35,
+ "duration": 0.0,
+ "text": "So, I'm Andrew Wilson and I'm going to"
+ },
+ {
+ "start": 3.36,
+ "duration": 0.0,
+ "text": "So, I'm Andrew Wilson and I'm going to be<00:00:03.560> presenting<00:00:04.200> this<00:00:04.440> work<00:00:04.720> with<00:00:05.080> Mark<00:00:05.360> Finzi,"
+ },
+ {
+ "start": 5.87,
+ "duration": 0.0,
+ "text": "be presenting this work with Mark Finzi,"
+ },
+ {
+ "start": 5.88,
+ "duration": 0.0,
+ "text": "be presenting this work with Mark Finzi, who<00:00:06.280> led<00:00:06.520> the<00:00:06.640> work<00:00:06.960> along<00:00:07.280> with<00:00:07.520> Shikai<00:00:08.120> and"
+ },
+ {
+ "start": 8.51,
+ "duration": 0.0,
+ "text": "who led the work along with Shikai and"
+ },
+ {
+ "start": 8.52,
+ "duration": 0.0,
+ "text": "who led the work along with Shikai and Yiding,<00:00:09.120> and<00:00:09.400> we<00:00:09.520> also<00:00:09.920> collaborated<00:00:10.480> with"
+ },
+ {
+ "start": 10.63,
+ "duration": 0.0,
+ "text": "Yiding, and we also collaborated with"
+ },
+ {
+ "start": 10.64,
+ "duration": 0.0,
+ "text": "Yiding, and we also collaborated with Pavel<00:00:11.120> and<00:00:11.360> Zico."
+ },
+ {
+ "start": 12.59,
+ "duration": 0.0,
+ "text": "Pavel and Zico."
+ },
+ {
+ "start": 12.6,
+ "duration": 0.0,
+ "text": "Pavel and Zico. Uh<00:00:12.800> so,<00:00:13.200> let's<00:00:13.720> start<00:00:14.080> with<00:00:14.240> a<00:00:14.280> question."
+ },
+ {
+ "start": 15.67,
+ "duration": 0.0,
+ "text": "Uh so, let's start with a question."
+ },
+ {
+ "start": 15.68,
+ "duration": 0.0,
+ "text": "Uh so, let's start with a question. Does<00:00:15.960> this<00:00:16.280> image<00:00:16.960> to<00:00:17.080> you<00:00:17.320> look<00:00:17.600> like<00:00:17.920> noise"
+ },
+ {
+ "start": 18.47,
+ "duration": 0.0,
+ "text": "Does this image to you look like noise"
+ },
+ {
+ "start": 18.48,
+ "duration": 0.0,
+ "text": "Does this image to you look like noise or<00:00:19.000> signal?<00:00:19.920> I<00:00:20.040> imagine<00:00:20.760> it<00:00:21.000> looks<00:00:21.240> a<00:00:21.320> lot<00:00:21.560> like"
+ },
+ {
+ "start": 21.83,
+ "duration": 0.0,
+ "text": "or signal? I imagine it looks a lot like"
+ },
+ {
+ "start": 21.84,
+ "duration": 0.0,
+ "text": "or signal? I imagine it looks a lot like noise.<00:00:22.320> Perhaps<00:00:22.760> you<00:00:22.880> could<00:00:23.040> stare<00:00:23.280> at<00:00:23.440> it<00:00:23.560> for"
+ },
+ {
+ "start": 23.67,
+ "duration": 0.0,
+ "text": "noise. Perhaps you could stare at it for"
+ },
+ {
+ "start": 23.68,
+ "duration": 0.0,
+ "text": "noise. Perhaps you could stare at it for a<00:00:23.720> very<00:00:23.920> long<00:00:24.160> time<00:00:24.400> and<00:00:24.520> it<00:00:24.600> might<00:00:24.800> be<00:00:24.920> like<00:00:25.200> a"
+ },
+ {
+ "start": 25.27,
+ "duration": 0.0,
+ "text": "a very long time and it might be like a"
+ },
+ {
+ "start": 25.28,
+ "duration": 0.0,
+ "text": "a very long time and it might be like a modern<00:00:25.640> piece<00:00:25.920> of<00:00:26.160> artwork<00:00:26.640> where<00:00:26.760> a<00:00:26.840> face<00:00:27.160> or"
+ },
+ {
+ "start": 27.27,
+ "duration": 0.0,
+ "text": "modern piece of artwork where a face or"
+ },
+ {
+ "start": 27.28,
+ "duration": 0.0,
+ "text": "modern piece of artwork where a face or something<00:00:28.120> jumps<00:00:28.520> out<00:00:28.720> at<00:00:28.840> you.<00:00:29.200> In<00:00:29.440> fact,"
+ },
+ {
+ "start": 29.87,
+ "duration": 0.0,
+ "text": "something jumps out at you. In fact,"
+ },
+ {
+ "start": 29.88,
+ "duration": 0.0,
+ "text": "something jumps out at you. In fact, actually<00:00:30.160> there<00:00:30.400> is<00:00:30.640> structure.<00:00:31.920> Um<00:00:32.320> so,<00:00:32.960> uh"
+ },
+ {
+ "start": 33.07,
+ "duration": 0.0,
+ "text": "actually there is structure. Um so, uh"
+ },
+ {
+ "start": 33.08,
+ "duration": 0.0,
+ "text": "actually there is structure. Um so, uh you<00:00:33.280> might<00:00:33.480> have<00:00:33.640> to<00:00:33.760> stare<00:00:34.040> for<00:00:34.160> a<00:00:34.200> very,<00:00:34.440> very"
+ },
+ {
+ "start": 34.67,
+ "duration": 0.0,
+ "text": "you might have to stare for a very, very"
+ },
+ {
+ "start": 34.68,
+ "duration": 0.0,
+ "text": "you might have to stare for a very, very long<00:00:34.920> time,<00:00:35.440> but<00:00:36.040> if<00:00:36.400> you<00:00:36.600> have<00:00:36.800> good<00:00:36.960> vision,"
+ },
+ {
+ "start": 37.83,
+ "duration": 0.0,
+ "text": "long time, but if you have good vision,"
+ },
+ {
+ "start": 37.84,
+ "duration": 0.0,
+ "text": "long time, but if you have good vision, you'll<00:00:38.080> see<00:00:38.280> that<00:00:38.560> the<00:00:38.640> word<00:00:38.920> epiplexity<00:00:39.720> is"
+ },
+ {
+ "start": 39.87,
+ "duration": 0.0,
+ "text": "you'll see that the word epiplexity is"
+ },
+ {
+ "start": 39.88,
+ "duration": 0.0,
+ "text": "you'll see that the word epiplexity is sort<00:00:40.080> of<00:00:40.160> buried<00:00:40.560> amongst<00:00:41.040> the<00:00:41.360> the<00:00:41.480> white"
+ },
+ {
+ "start": 41.71,
+ "duration": 0.0,
+ "text": "sort of buried amongst the the white"
+ },
+ {
+ "start": 41.72,
+ "duration": 0.0,
+ "text": "sort of buried amongst the the white noise.<00:00:42.560> And<00:00:43.120> the<00:00:43.280> point<00:00:43.640> that<00:00:43.960> I'm<00:00:44.280> making"
+ },
+ {
+ "start": 44.75,
+ "duration": 0.0,
+ "text": "noise. And the point that I'm making"
+ },
+ {
+ "start": 44.76,
+ "duration": 0.0,
+ "text": "noise. And the point that I'm making with<00:00:44.920> this<00:00:45.080> example<00:00:45.640> is<00:00:45.800> that<00:00:45.960> whether<00:00:46.240> or<00:00:46.320> not"
+ },
+ {
+ "start": 46.59,
+ "duration": 0.0,
+ "text": "with this example is that whether or not"
+ },
+ {
+ "start": 46.6,
+ "duration": 0.0,
+ "text": "with this example is that whether or not something<00:00:47.080> appears<00:00:47.480> random<00:00:48.240> depends<00:00:48.640> on<00:00:48.920> on"
+ },
+ {
+ "start": 49.19,
+ "duration": 0.0,
+ "text": "something appears random depends on on"
+ },
+ {
+ "start": 49.2,
+ "duration": 0.0,
+ "text": "something appears random depends on on on<00:00:49.360> the<00:00:49.640> computation<00:00:50.240> available<00:00:50.680> to<00:00:50.840> us.<00:00:51.120> So,"
+ },
+ {
+ "start": 51.35,
+ "duration": 0.0,
+ "text": "on the computation available to us. So,"
+ },
+ {
+ "start": 51.36,
+ "duration": 0.0,
+ "text": "on the computation available to us. So, pseudorandom<00:00:51.920> numbers,<00:00:52.240> for<00:00:52.360> example,<00:00:52.960> are"
+ },
+ {
+ "start": 53.19,
+ "duration": 0.0,
+ "text": "pseudorandom numbers, for example, are"
+ },
+ {
+ "start": 53.2,
+ "duration": 0.0,
+ "text": "pseudorandom numbers, for example, are indistinguishable<00:00:54.040> from<00:00:54.400> actual<00:00:54.760> random"
+ },
+ {
+ "start": 55.03,
+ "duration": 0.0,
+ "text": "indistinguishable from actual random"
+ },
+ {
+ "start": 55.04,
+ "duration": 0.0,
+ "text": "indistinguishable from actual random numbers<00:00:55.440> if<00:00:55.600> we<00:00:55.760> have<00:00:56.400> only<00:00:56.640> polynomial<00:00:57.200> time"
+ },
+ {
+ "start": 57.51,
+ "duration": 0.0,
+ "text": "numbers if we have only polynomial time"
+ },
+ {
+ "start": 57.52,
+ "duration": 0.0,
+ "text": "numbers if we have only polynomial time computation<00:00:58.320> and<00:00:59.200> in<00:00:59.360> many<00:00:59.600> respects,<00:01:00.080> that's"
+ },
+ {
+ "start": 60.31,
+ "duration": 0.0,
+ "text": "computation and in many respects, that's"
+ },
+ {
+ "start": 60.32,
+ "duration": 0.0,
+ "text": "computation and in many respects, that's why<00:01:00.480> pseudorandom<00:01:01.360> numbers<00:01:01.480> are<00:01:01.800> ubiquitous"
+ },
+ {
+ "start": 62.59,
+ "duration": 0.0,
+ "text": "why pseudorandom numbers are ubiquitous"
+ },
+ {
+ "start": 62.6,
+ "duration": 0.0,
+ "text": "why pseudorandom numbers are ubiquitous and<00:01:03.040> useful<00:01:03.480> in<00:01:03.640> so<00:01:03.800> many<00:01:04.120> different"
+ },
+ {
+ "start": 64.67,
+ "duration": 0.0,
+ "text": "and useful in so many different"
+ },
+ {
+ "start": 64.68,
+ "duration": 0.0,
+ "text": "and useful in so many different settings.<00:01:05.720> And<00:01:05.960> so,"
+ },
+ {
+ "start": 67.47,
+ "duration": 0.0,
+ "text": "settings. And so,"
+ },
+ {
+ "start": 67.48,
+ "duration": 0.0,
+ "text": "settings. And so, accounting<00:01:07.880> for<00:01:08.000> computation<00:01:08.840> was<00:01:09.080> a<00:01:09.160> key"
+ },
+ {
+ "start": 69.39,
+ "duration": 0.0,
+ "text": "accounting for computation was a key"
+ },
+ {
+ "start": 69.4,
+ "duration": 0.0,
+ "text": "accounting for computation was a key consideration<00:01:10.360> in<00:01:10.560> reasoning<00:01:11.120> about<00:01:11.800> what"
+ },
+ {
+ "start": 71.95,
+ "duration": 0.0,
+ "text": "consideration in reasoning about what"
+ },
+ {
+ "start": 71.96,
+ "duration": 0.0,
+ "text": "consideration in reasoning about what Mark<00:01:12.240> is<00:01:12.360> going<00:01:12.560> to<00:01:12.680> introduce<00:01:13.120> in<00:01:13.200> a<00:01:13.280> moment,"
+ },
+ {
+ "start": 73.79,
+ "duration": 0.0,
+ "text": "Mark is going to introduce in a moment,"
+ },
+ {
+ "start": 73.8,
+ "duration": 0.0,
+ "text": "Mark is going to introduce in a moment, epiplexity,<00:01:14.560> this<00:01:14.760> new<00:01:14.920> measure<00:01:15.240> of"
+ },
+ {
+ "start": 75.35,
+ "duration": 0.0,
+ "text": "epiplexity, this new measure of"
+ },
+ {
+ "start": 75.36,
+ "duration": 0.0,
+ "text": "epiplexity, this new measure of information,<00:01:16.560> as<00:01:16.760> well<00:01:16.960> as<00:01:17.120> several"
+ },
+ {
+ "start": 77.63,
+ "duration": 0.0,
+ "text": "information, as well as several"
+ },
+ {
+ "start": 77.64,
+ "duration": 0.0,
+ "text": "information, as well as several paradoxes<00:01:18.520> which<00:01:19.000> um<00:01:19.560> can<00:01:19.760> partly<00:01:20.200> be"
+ },
+ {
+ "start": 80.55,
+ "duration": 0.0,
+ "text": "paradoxes which um can partly be"
+ },
+ {
+ "start": 80.56,
+ "duration": 0.0,
+ "text": "paradoxes which um can partly be explained<00:01:21.240> by<00:01:21.520> not<00:01:21.880> accounting<00:01:22.320> for"
+ },
+ {
+ "start": 82.43,
+ "duration": 0.0,
+ "text": "explained by not accounting for"
+ },
+ {
+ "start": 82.44,
+ "duration": 0.0,
+ "text": "explained by not accounting for computation.<00:01:23.560> So,"
+ },
+ {
+ "start": 84.55,
+ "duration": 0.0,
+ "text": "computation. So,"
+ },
+ {
+ "start": 84.56,
+ "duration": 0.0,
+ "text": "computation. So, uh<00:01:24.680> in<00:01:24.880> the<00:01:25.000> paper,<00:01:25.400> we<00:01:25.600> present<00:01:26.120> what<00:01:26.240> we<00:01:26.360> call"
+ },
+ {
+ "start": 86.55,
+ "duration": 0.0,
+ "text": "uh in the paper, we present what we call"
+ },
+ {
+ "start": 86.56,
+ "duration": 0.0,
+ "text": "uh in the paper, we present what we call three<00:01:26.760> apparent<00:01:27.160> paradoxes.<00:01:28.120> Uh<00:01:28.240> paradox<00:01:28.840> one"
+ },
+ {
+ "start": 89.23,
+ "duration": 0.0,
+ "text": "three apparent paradoxes. Uh paradox one"
+ },
+ {
+ "start": 89.24,
+ "duration": 0.0,
+ "text": "three apparent paradoxes. Uh paradox one is<00:01:29.440> that<00:01:29.600> information<00:01:30.240> can't<00:01:30.520> be<00:01:30.640> increased"
+ },
+ {
+ "start": 91.07,
+ "duration": 0.0,
+ "text": "is that information can't be increased"
+ },
+ {
+ "start": 91.08,
+ "duration": 0.0,
+ "text": "is that information can't be increased by<00:01:31.240> deterministic<00:01:32.360> processes.<00:01:33.560> Uh<00:01:33.800> yet,<00:01:34.280> as"
+ },
+ {
+ "start": 94.51,
+ "duration": 0.0,
+ "text": "by deterministic processes. Uh yet, as"
+ },
+ {
+ "start": 94.52,
+ "duration": 0.0,
+ "text": "by deterministic processes. Uh yet, as we<00:01:34.640> said,<00:01:34.960> pseudorandom<00:01:35.920> numbers<00:01:36.520> are"
+ },
+ {
+ "start": 96.79,
+ "duration": 0.0,
+ "text": "we said, pseudorandom numbers are"
+ },
+ {
+ "start": 96.8,
+ "duration": 0.0,
+ "text": "we said, pseudorandom numbers are everywhere<00:01:37.440> and<00:01:37.760> synthetic<00:01:38.200> data<00:01:38.560> is"
+ },
+ {
+ "start": 98.71,
+ "duration": 0.0,
+ "text": "everywhere and synthetic data is"
+ },
+ {
+ "start": 98.72,
+ "duration": 0.0,
+ "text": "everywhere and synthetic data is incredibly<00:01:39.200> useful<00:01:39.680> in<00:01:39.840> systems<00:01:40.240> like"
+ },
+ {
+ "start": 100.47,
+ "duration": 0.0,
+ "text": "incredibly useful in systems like"
+ },
+ {
+ "start": 100.48,
+ "duration": 0.0,
+ "text": "incredibly useful in systems like AlphaZero,<00:01:41.640> which<00:01:42.000> involve<00:01:42.400> a<00:01:42.440> bunch<00:01:42.680> of"
+ },
+ {
+ "start": 102.71,
+ "duration": 0.0,
+ "text": "AlphaZero, which involve a bunch of"
+ },
+ {
+ "start": 102.72,
+ "duration": 0.0,
+ "text": "AlphaZero, which involve a bunch of deterministic<00:01:43.360> processes,<00:01:44.040> learn"
+ },
+ {
+ "start": 104.27,
+ "duration": 0.0,
+ "text": "deterministic processes, learn"
+ },
+ {
+ "start": 104.28,
+ "duration": 0.0,
+ "text": "deterministic processes, learn sophisticated<00:01:45.000> strategies<00:01:45.640> from<00:01:46.240> games.<00:01:47.240> Uh"
+ },
+ {
+ "start": 107.59,
+ "duration": 0.0,
+ "text": "sophisticated strategies from games. Uh"
+ },
+ {
+ "start": 107.6,
+ "duration": 0.0,
+ "text": "sophisticated strategies from games. Uh paradox<00:01:48.040> two,<00:01:48.360> information<00:01:48.960> is<00:01:49.160> independent"
+ },
+ {
+ "start": 109.91,
+ "duration": 0.0,
+ "text": "paradox two, information is independent"
+ },
+ {
+ "start": 109.92,
+ "duration": 0.0,
+ "text": "paradox two, information is independent of<00:01:50.080> factorization<00:01:51.080> order.<00:01:51.440> So,<00:01:51.600> this<00:01:51.800> is"
+ },
+ {
+ "start": 111.95,
+ "duration": 0.0,
+ "text": "of factorization order. So, this is"
+ },
+ {
+ "start": 111.96,
+ "duration": 0.0,
+ "text": "of factorization order. So, this is given<00:01:52.240> by<00:01:52.800> Shannon<00:01:53.200> symmetry<00:01:53.680> of<00:01:53.800> information"
+ },
+ {
+ "start": 114.51,
+ "duration": 0.0,
+ "text": "given by Shannon symmetry of information"
+ },
+ {
+ "start": 114.52,
+ "duration": 0.0,
+ "text": "given by Shannon symmetry of information as<00:01:54.680> well<00:01:54.840> as<00:01:54.920> something<00:01:55.200> similar<00:01:55.600> for"
+ },
+ {
+ "start": 115.87,
+ "duration": 0.0,
+ "text": "as well as something similar for"
+ },
+ {
+ "start": 115.88,
+ "duration": 0.0,
+ "text": "as well as something similar for Kolmogorov<00:01:56.400> complexity<00:01:57.120> and<00:01:57.320> algorithmic"
+ },
+ {
+ "start": 118.19,
+ "duration": 0.0,
+ "text": "Kolmogorov complexity and algorithmic"
+ },
+ {
+ "start": 118.2,
+ "duration": 0.0,
+ "text": "Kolmogorov complexity and algorithmic information<00:01:58.840> theory.<00:01:59.560> Yet,<00:02:00.600> LLMs<00:02:01.080> are<00:02:01.160> going"
+ },
+ {
+ "start": 121.27,
+ "duration": 0.0,
+ "text": "information theory. Yet, LLMs are going"
+ },
+ {
+ "start": 121.28,
+ "duration": 0.0,
+ "text": "information theory. Yet, LLMs are going to<00:02:01.360> learn<00:02:01.680> a<00:02:01.760> lot<00:02:02.040> more<00:02:02.320> from<00:02:03.280> English<00:02:03.640> text"
+ },
+ {
+ "start": 124.03,
+ "duration": 0.0,
+ "text": "to learn a lot more from English text"
+ },
+ {
+ "start": 124.04,
+ "duration": 0.0,
+ "text": "to learn a lot more from English text ordered<00:02:04.360> from<00:02:04.760> left<00:02:04.960> to<00:02:05.080> right,<00:02:05.720> uh<00:02:05.920> picking"
+ },
+ {
+ "start": 126.19,
+ "duration": 0.0,
+ "text": "ordered from left to right, uh picking"
+ },
+ {
+ "start": 126.2,
+ "duration": 0.0,
+ "text": "ordered from left to right, uh picking out<00:02:06.360> an<00:02:06.520> arrow<00:02:06.800> of<00:02:06.920> time,<00:02:07.240> and<00:02:07.320> this<00:02:07.480> is<00:02:07.600> true"
+ },
+ {
+ "start": 127.87,
+ "duration": 0.0,
+ "text": "out an arrow of time, and this is true"
+ },
+ {
+ "start": 127.88,
+ "duration": 0.0,
+ "text": "out an arrow of time, and this is true of<00:02:08.080> all<00:02:08.240> sorts<00:02:08.520> of<00:02:08.640> different<00:02:09.360> problem"
+ },
+ {
+ "start": 129.71,
+ "duration": 0.0,
+ "text": "of all sorts of different problem"
+ },
+ {
+ "start": 129.72,
+ "duration": 0.0,
+ "text": "of all sorts of different problem settings.<00:02:10.600> And<00:02:10.880> paradox<00:02:11.280> three,<00:02:11.960> likelihood"
+ },
+ {
+ "start": 132.51,
+ "duration": 0.0,
+ "text": "settings. And paradox three, likelihood"
+ },
+ {
+ "start": 132.52,
+ "duration": 0.0,
+ "text": "settings. And paradox three, likelihood modeling<00:02:12.960> is<00:02:13.240> just<00:02:13.560> distribution<00:02:14.200> matching."
+ },
+ {
+ "start": 134.67,
+ "duration": 0.0,
+ "text": "modeling is just distribution matching."
+ },
+ {
+ "start": 134.68,
+ "duration": 0.0,
+ "text": "modeling is just distribution matching. So,<00:02:14.840> we<00:02:15.000> can't<00:02:15.280> hope<00:02:15.480> to<00:02:15.600> go<00:02:15.760> beyond<00:02:16.200> the"
+ },
+ {
+ "start": 136.31,
+ "duration": 0.0,
+ "text": "So, we can't hope to go beyond the"
+ },
+ {
+ "start": 136.32,
+ "duration": 0.0,
+ "text": "So, we can't hope to go beyond the generative<00:02:16.800> processes<00:02:17.640> that<00:02:18.160> created<00:02:18.520> the"
+ },
+ {
+ "start": 138.59,
+ "duration": 0.0,
+ "text": "generative processes that created the"
+ },
+ {
+ "start": 138.6,
+ "duration": 0.0,
+ "text": "generative processes that created the data<00:02:18.880> that<00:02:19.040> we're<00:02:19.160> training<00:02:19.520> on.<00:02:19.840> Yet,<00:02:20.040> we<00:02:20.200> see"
+ },
+ {
+ "start": 140.47,
+ "duration": 0.0,
+ "text": "data that we're training on. Yet, we see"
+ },
+ {
+ "start": 140.48,
+ "duration": 0.0,
+ "text": "data that we're training on. Yet, we see models<00:02:20.920> doing<00:02:21.240> precisely<00:02:21.800> that<00:02:22.160> in<00:02:22.320> all<00:02:22.480> sorts"
+ },
+ {
+ "start": 142.75,
+ "duration": 0.0,
+ "text": "models doing precisely that in all sorts"
+ },
+ {
+ "start": 142.76,
+ "duration": 0.0,
+ "text": "models doing precisely that in all sorts of<00:02:22.880> different<00:02:23.600> settings.<00:02:24.480> And<00:02:24.720> so,"
+ },
+ {
+ "start": 145.67,
+ "duration": 0.0,
+ "text": "of different settings. And so,"
+ },
+ {
+ "start": 145.68,
+ "duration": 0.0,
+ "text": "of different settings. And so, these<00:02:26.040> are<00:02:26.640> statements<00:02:27.280> which<00:02:27.520> can<00:02:27.720> be"
+ },
+ {
+ "start": 148.07,
+ "duration": 0.0,
+ "text": "these are statements which can be"
+ },
+ {
+ "start": 148.08,
+ "duration": 0.0,
+ "text": "these are statements which can be mathematically<00:02:28.920> justified<00:02:30.040> by<00:02:30.360> information"
+ },
+ {
+ "start": 150.95,
+ "duration": 0.0,
+ "text": "mathematically justified by information"
+ },
+ {
+ "start": 150.96,
+ "duration": 0.0,
+ "text": "mathematically justified by information theory,<00:02:31.320> but<00:02:32.080> um<00:02:32.320> really<00:02:32.600> don't<00:02:32.960> align<00:02:33.520> with"
+ },
+ {
+ "start": 153.87,
+ "duration": 0.0,
+ "text": "theory, but um really don't align with"
+ },
+ {
+ "start": 153.88,
+ "duration": 0.0,
+ "text": "theory, but um really don't align with our<00:02:34.120> intuitions<00:02:34.840> or<00:02:35.240> increasingly<00:02:36.000> what"
+ },
+ {
+ "start": 156.19,
+ "duration": 0.0,
+ "text": "our intuitions or increasingly what"
+ },
+ {
+ "start": 156.2,
+ "duration": 0.0,
+ "text": "our intuitions or increasingly what we're<00:02:36.360> seeing<00:02:36.840> in<00:02:37.240> practice.<00:02:38.000> And<00:02:38.520> it's<00:02:38.800> our"
+ },
+ {
+ "start": 158.99,
+ "duration": 0.0,
+ "text": "we're seeing in practice. And it's our"
+ },
+ {
+ "start": 159.0,
+ "duration": 0.0,
+ "text": "we're seeing in practice. And it's our contention<00:02:39.640> this<00:02:39.840> is<00:02:40.000> because"
+ },
+ {
+ "start": 161.39,
+ "duration": 0.0,
+ "text": "contention this is because"
+ },
+ {
+ "start": 161.4,
+ "duration": 0.0,
+ "text": "contention this is because quite<00:02:41.680> often<00:02:42.040> we're<00:02:42.360> assuming<00:02:43.000> unlimited"
+ },
+ {
+ "start": 163.59,
+ "duration": 0.0,
+ "text": "quite often we're assuming unlimited"
+ },
+ {
+ "start": 163.6,
+ "duration": 0.0,
+ "text": "quite often we're assuming unlimited computation<00:02:44.840> and<00:02:45.000> we're<00:02:45.120> not<00:02:45.400> targeting"
+ },
+ {
+ "start": 166.11,
+ "duration": 0.0,
+ "text": "computation and we're not targeting"
+ },
+ {
+ "start": 166.12,
+ "duration": 0.0,
+ "text": "computation and we're not targeting useful<00:02:46.520> information<00:02:47.080> content."
+ },
+ {
+ "start": 169.27,
+ "duration": 0.0,
+ "text": "useful information content."
+ },
+ {
+ "start": 169.28,
+ "duration": 0.0,
+ "text": "useful information content. So,<00:02:49.440> just<00:02:49.680> to<00:02:49.800> get<00:02:50.240> another<00:02:50.880> sort<00:02:51.080> of<00:02:51.600> sense<00:02:51.960> of"
+ },
+ {
+ "start": 172.19,
+ "duration": 0.0,
+ "text": "So, just to get another sort of sense of"
+ },
+ {
+ "start": 172.2,
+ "duration": 0.0,
+ "text": "So, just to get another sort of sense of some<00:02:52.400> of<00:02:52.480> these<00:02:52.720> points,<00:02:53.120> we<00:02:53.240> can<00:02:53.360> imagine<00:02:53.960> a"
+ },
+ {
+ "start": 174.03,
+ "duration": 0.0,
+ "text": "some of these points, we can imagine a"
+ },
+ {
+ "start": 174.04,
+ "duration": 0.0,
+ "text": "some of these points, we can imagine a system<00:02:54.600> like<00:02:55.400> AlphaZero<00:02:56.520> where<00:02:57.240> the"
+ },
+ {
+ "start": 177.39,
+ "duration": 0.0,
+ "text": "system like AlphaZero where the"
+ },
+ {
+ "start": 177.4,
+ "duration": 0.0,
+ "text": "system like AlphaZero where the description<00:02:57.960> length<00:02:58.200> of<00:02:58.320> the<00:02:58.400> whole<00:02:58.600> system"
+ },
+ {
+ "start": 179.03,
+ "duration": 0.0,
+ "text": "description length of the whole system"
+ },
+ {
+ "start": 179.04,
+ "duration": 0.0,
+ "text": "description length of the whole system is<00:02:59.200> actually<00:02:59.560> quite<00:02:59.960> small.<00:03:00.400> We<00:03:00.520> can<00:03:00.720> store"
+ },
+ {
+ "start": 180.95,
+ "duration": 0.0,
+ "text": "is actually quite small. We can store"
+ },
+ {
+ "start": 180.96,
+ "duration": 0.0,
+ "text": "is actually quite small. We can store the<00:03:01.040> rules<00:03:01.400> of<00:03:01.840> chess<00:03:02.200> using<00:03:02.520> a<00:03:02.560> small<00:03:02.800> number"
+ },
+ {
+ "start": 183.11,
+ "duration": 0.0,
+ "text": "the rules of chess using a small number"
+ },
+ {
+ "start": 183.12,
+ "duration": 0.0,
+ "text": "the rules of chess using a small number of<00:03:03.240> bytes.<00:03:03.600> The<00:03:03.680> training<00:03:04.080> algorithm"
+ },
+ {
+ "start": 185.11,
+ "duration": 0.0,
+ "text": "of bytes. The training algorithm"
+ },
+ {
+ "start": 185.12,
+ "duration": 0.0,
+ "text": "of bytes. The training algorithm shouldn't<00:03:05.480> take<00:03:05.720> much<00:03:05.960> more<00:03:06.120> than<00:03:06.240> about<00:03:06.520> 10"
+ },
+ {
+ "start": 186.71,
+ "duration": 0.0,
+ "text": "shouldn't take much more than about 10"
+ },
+ {
+ "start": 186.72,
+ "duration": 0.0,
+ "text": "shouldn't take much more than about 10 kilobytes.<00:03:07.720> Uh<00:03:07.800> random<00:03:08.160> seed,<00:03:08.680> also<00:03:08.960> very"
+ },
+ {
+ "start": 189.19,
+ "duration": 0.0,
+ "text": "kilobytes. Uh random seed, also very"
+ },
+ {
+ "start": 189.2,
+ "duration": 0.0,
+ "text": "kilobytes. Uh random seed, also very small.<00:03:10.080> Um<00:03:10.600> yet,<00:03:11.360> it<00:03:11.560> seems<00:03:11.960> like<00:03:12.280> we're"
+ },
+ {
+ "start": 192.39,
+ "duration": 0.0,
+ "text": "small. Um yet, it seems like we're"
+ },
+ {
+ "start": 192.4,
+ "duration": 0.0,
+ "text": "small. Um yet, it seems like we're learning<00:03:12.760> something<00:03:13.400> very<00:03:14.160> useful.<00:03:15.200> Um<00:03:15.520> and"
+ },
+ {
+ "start": 195.75,
+ "duration": 0.0,
+ "text": "learning something very useful. Um and"
+ },
+ {
+ "start": 195.76,
+ "duration": 0.0,
+ "text": "learning something very useful. Um and so,<00:03:16.520> since<00:03:16.960> information<00:03:17.640> can't<00:03:17.960> be<00:03:18.200> created,"
+ },
+ {
+ "start": 199.51,
+ "duration": 0.0,
+ "text": "so, since information can't be created,"
+ },
+ {
+ "start": 199.52,
+ "duration": 0.0,
+ "text": "so, since information can't be created, what<00:03:19.960> is<00:03:20.320> AlphaGo<00:03:21.040> actually<00:03:21.680> learning?<00:03:22.160> And"
+ },
+ {
+ "start": 202.75,
+ "duration": 0.0,
+ "text": "what is AlphaGo actually learning? And"
+ },
+ {
+ "start": 202.76,
+ "duration": 0.0,
+ "text": "what is AlphaGo actually learning? And this<00:03:22.960> is<00:03:23.200> exactly<00:03:23.760> the<00:03:23.880> kind<00:03:24.120> of<00:03:24.240> question"
+ },
+ {
+ "start": 204.63,
+ "duration": 0.0,
+ "text": "this is exactly the kind of question"
+ },
+ {
+ "start": 204.64,
+ "duration": 0.0,
+ "text": "this is exactly the kind of question that<00:03:24.800> motivated<00:03:25.560> our<00:03:25.720> work<00:03:26.040> on<00:03:26.440> epiplexity."
+ },
+ {
+ "start": 208.79,
+ "duration": 0.0,
+ "text": "that motivated our work on epiplexity."
+ },
+ {
+ "start": 208.8,
+ "duration": 0.0,
+ "text": "that motivated our work on epiplexity. Uh<00:03:29.000> we<00:03:29.160> have<00:03:29.480> one<00:03:29.680> more<00:03:29.840> example<00:03:30.280> here,<00:03:30.440> so<00:03:30.560> I'm"
+ },
+ {
+ "start": 210.63,
+ "duration": 0.0,
+ "text": "Uh we have one more example here, so I'm"
+ },
+ {
+ "start": 210.64,
+ "duration": 0.0,
+ "text": "Uh we have one more example here, so I'm just<00:03:30.760> going<00:03:30.880> to<00:03:30.960> play<00:03:31.120> a<00:03:31.160> bit<00:03:31.320> of<00:03:31.440> a<00:03:31.480> video<00:03:32.040> and"
+ },
+ {
+ "start": 212.63,
+ "duration": 0.0,
+ "text": "just going to play a bit of a video and"
+ },
+ {
+ "start": 212.64,
+ "duration": 0.0,
+ "text": "just going to play a bit of a video and uh<00:03:32.720> Mark<00:03:33.040> will<00:03:33.200> just<00:03:33.640> narrate<00:03:34.040> through<00:03:34.240> this"
+ },
+ {
+ "start": 214.43,
+ "duration": 0.0,
+ "text": "uh Mark will just narrate through this"
+ },
+ {
+ "start": 214.44,
+ "duration": 0.0,
+ "text": "uh Mark will just narrate through this example."
+ },
+ {
+ "start": 216.99,
+ "duration": 0.0,
+ "text": "example."
+ },
+ {
+ "start": 217.0,
+ "duration": 0.0,
+ "text": "example. Okay.<00:03:37.800> All<00:03:37.880> right.<00:03:38.200> So,<00:03:38.360> let's<00:03:38.560> see<00:03:38.640> if<00:03:38.760> we<00:03:38.840> can"
+ },
+ {
+ "start": 218.95,
+ "duration": 0.0,
+ "text": "Okay. All right. So, let's see if we can"
+ },
+ {
+ "start": 218.96,
+ "duration": 0.0,
+ "text": "Okay. All right. So, let's see if we can get<00:03:39.120> that<00:03:39.320> video.<00:03:40.120> Oh,<00:03:40.280> you<00:03:40.400> can<00:03:40.520> you<00:03:40.600> see<00:03:40.720> the"
+ },
+ {
+ "start": 220.75,
+ "duration": 0.0,
+ "text": "get that video. Oh, you can you see the"
+ },
+ {
+ "start": 220.76,
+ "duration": 0.0,
+ "text": "get that video. Oh, you can you see the video?"
+ },
+ {
+ "start": 222.11,
+ "duration": 0.0,
+ "text": "video?"
+ },
+ {
+ "start": 222.12,
+ "duration": 0.0,
+ "text": "video? Uh<00:03:42.760> it's<00:03:42.960> just<00:03:43.160> showing<00:03:43.320> the<00:03:43.400> presentation"
+ },
+ {
+ "start": 223.91,
+ "duration": 0.0,
+ "text": "Uh it's just showing the presentation"
+ },
+ {
+ "start": 223.92,
+ "duration": 0.0,
+ "text": "Uh it's just showing the presentation right<00:03:44.040> now.<00:03:44.440> Okay.<00:03:44.760> So,<00:03:44.840> I'll<00:03:44.920> just<00:03:45.120> change"
+ },
+ {
+ "start": 225.43,
+ "duration": 0.0,
+ "text": "right now. Okay. So, I'll just change"
+ },
+ {
+ "start": 225.44,
+ "duration": 0.0,
+ "text": "right now. Okay. So, I'll just change the<00:03:45.640> screen<00:03:46.000> sharing."
+ },
+ {
+ "start": 227.67,
+ "duration": 0.0,
+ "text": "the screen sharing."
+ },
+ {
+ "start": 227.68,
+ "duration": 0.0,
+ "text": "the screen sharing. Okay."
+ },
+ {
+ "start": 229.31,
+ "duration": 0.0,
+ "text": "Okay."
+ },
+ {
+ "start": 229.32,
+ "duration": 0.0,
+ "text": "Okay. All<00:03:49.440> right,<00:03:49.640> you<00:03:49.720> should<00:03:49.880> see<00:03:49.960> it<00:03:50.040> now."
+ },
+ {
+ "start": 231.47,
+ "duration": 0.0,
+ "text": "All right, you should see it now."
+ },
+ {
+ "start": 231.48,
+ "duration": 0.0,
+ "text": "All right, you should see it now. So,"
+ },
+ {
+ "start": 232.63,
+ "duration": 0.0,
+ "text": "So,"
+ },
+ {
+ "start": 232.64,
+ "duration": 0.0,
+ "text": "So, right."
+ },
+ {
+ "start": 233.67,
+ "duration": 0.0,
+ "text": "right."
+ },
+ {
+ "start": 233.68,
+ "duration": 0.0,
+ "text": "right. So,<00:03:53.800> we're<00:03:53.880> watching<00:03:54.120> this<00:03:54.240> video.<00:03:54.800> And"
+ },
+ {
+ "start": 234.91,
+ "duration": 0.0,
+ "text": "So, we're watching this video. And"
+ },
+ {
+ "start": 234.92,
+ "duration": 0.0,
+ "text": "So, we're watching this video. And again,<00:03:55.800> um"
+ },
+ {
+ "start": 237.07,
+ "duration": 0.0,
+ "text": "again, um"
+ },
+ {
+ "start": 237.08,
+ "duration": 0.0,
+ "text": "again, um is<00:03:57.320> this<00:03:57.720> structure<00:03:58.760> or<00:03:58.960> noise?"
+ },
+ {
+ "start": 241.03,
+ "duration": 0.0,
+ "text": "is this structure or noise?"
+ },
+ {
+ "start": 241.04,
+ "duration": 0.0,
+ "text": "is this structure or noise? I<00:04:01.120> think<00:04:01.360> I'll<00:04:01.480> play<00:04:01.560> it.<00:04:02.000> Mhm."
+ },
+ {
+ "start": 243.75,
+ "duration": 0.0,
+ "text": "I think I'll play it. Mhm."
+ },
+ {
+ "start": 243.76,
+ "duration": 0.0,
+ "text": "I think I'll play it. Mhm. So,<00:04:03.880> I<00:04:03.920> think<00:04:04.240> I<00:04:04.280> think<00:04:04.480> most<00:04:04.680> people<00:04:05.000> would"
+ },
+ {
+ "start": 245.47,
+ "duration": 0.0,
+ "text": "So, I think I think most people would"
+ },
+ {
+ "start": 245.48,
+ "duration": 0.0,
+ "text": "So, I think I think most people would agree<00:04:05.960> that<00:04:06.160> this<00:04:06.680> is<00:04:06.840> noise."
+ },
+ {
+ "start": 248.71,
+ "duration": 0.0,
+ "text": "agree that this is noise."
+ },
+ {
+ "start": 248.72,
+ "duration": 0.0,
+ "text": "agree that this is noise. But,<00:04:09.680> if<00:04:09.760> we<00:04:10.240> get<00:04:10.320> the<00:04:10.400> next<00:04:10.640> video,"
+ },
+ {
+ "start": 251.59,
+ "duration": 0.0,
+ "text": "But, if we get the next video,"
+ },
+ {
+ "start": 251.6,
+ "duration": 0.0,
+ "text": "But, if we get the next video, Mhm."
+ },
+ {
+ "start": 253.19,
+ "duration": 0.0,
+ "text": "Mhm."
+ },
+ {
+ "start": 253.2,
+ "duration": 0.0,
+ "text": "Mhm. One<00:04:13.400> moment."
+ },
+ {
+ "start": 255.55,
+ "duration": 0.0,
+ "text": "One moment."
+ },
+ {
+ "start": 255.56,
+ "duration": 0.0,
+ "text": "One moment. All<00:04:15.800> right."
+ },
+ {
+ "start": 263.36,
+ "duration": 0.0,
+ "text": "Okay."
+ },
+ {
+ "start": 265.11,
+ "duration": 0.0,
+ "text": "Okay."
+ },
+ {
+ "start": 265.12,
+ "duration": 0.0,
+ "text": "Okay. Most<00:04:25.400> people<00:04:25.520> would<00:04:25.640> agree<00:04:25.800> that<00:04:25.920> this<00:04:26.120> is"
+ },
+ {
+ "start": 266.67,
+ "duration": 0.0,
+ "text": "Most people would agree that this is"
+ },
+ {
+ "start": 266.68,
+ "duration": 0.0,
+ "text": "Most people would agree that this is noise.<00:04:27.720> But,<00:04:28.080> the<00:04:28.200> way<00:04:28.480> that<00:04:29.040> I<00:04:29.160> generated"
+ },
+ {
+ "start": 269.63,
+ "duration": 0.0,
+ "text": "noise. But, the way that I generated"
+ },
+ {
+ "start": 269.64,
+ "duration": 0.0,
+ "text": "noise. But, the way that I generated this<00:04:30.120> is<00:04:30.880> through<00:04:31.080> the<00:04:31.400> Wait,<00:04:31.640> wait.<00:04:32.520> Yes.<00:04:32.840> We"
+ },
+ {
+ "start": 272.95,
+ "duration": 0.0,
+ "text": "this is through the Wait, wait. Yes. We"
+ },
+ {
+ "start": 272.96,
+ "duration": 0.0,
+ "text": "this is through the Wait, wait. Yes. We don't<00:04:33.280> see<00:04:33.480> a<00:04:33.560> thing."
+ },
+ {
+ "start": 275.51,
+ "duration": 0.0,
+ "text": "don't see a thing."
+ },
+ {
+ "start": 275.52,
+ "duration": 0.0,
+ "text": "don't see a thing. At<00:04:35.800> least<00:04:36.040> I<00:04:36.120> don't."
+ },
+ {
+ "start": 276.63,
+ "duration": 0.0,
+ "text": "At least I don't."
+ },
+ {
+ "start": 276.64,
+ "duration": 0.0,
+ "text": "At least I don't. >> we<00:04:36.840> can<00:04:37.080> see<00:04:37.440> it."
+ },
+ {
+ "start": 279.67,
+ "duration": 0.0,
+ "text": ">> we can see it."
+ },
+ {
+ "start": 279.68,
+ "duration": 0.0,
+ "text": ">> we can see it. Let<00:04:39.960> me<00:04:40.040> know<00:04:40.240> if<00:04:40.360> you<00:04:40.480> see<00:04:40.600> it."
+ },
+ {
+ "start": 280.75,
+ "duration": 0.0,
+ "text": "Let me know if you see it."
+ },
+ {
+ "start": 280.76,
+ "duration": 0.0,
+ "text": "Let me know if you see it. >> able<00:04:40.920> to<00:04:41.000> see<00:04:41.280> it.<00:04:41.600> Uh"
+ },
+ {
+ "start": 282.51,
+ "duration": 0.0,
+ "text": ">> able to see it. Uh"
+ },
+ {
+ "start": 282.52,
+ "duration": 0.0,
+ "text": ">> able to see it. Uh Yeah,<00:04:42.760> I<00:04:42.800> see"
+ },
+ {
+ "start": 284.27,
+ "duration": 0.0,
+ "text": "Yeah, I see"
+ },
+ {
+ "start": 284.28,
+ "duration": 0.0,
+ "text": "Yeah, I see Yeah,<00:04:44.480> I<00:04:44.560> can<00:04:44.760> see<00:04:44.920> it<00:04:45.080> fine.<00:04:45.920> Yeah.<00:04:46.520> Me,<00:04:46.680> too."
+ },
+ {
+ "start": 286.95,
+ "duration": 0.0,
+ "text": "Yeah, I can see it fine. Yeah. Me, too."
+ },
+ {
+ "start": 286.96,
+ "duration": 0.0,
+ "text": "Yeah, I can see it fine. Yeah. Me, too. >> It's<00:04:47.120> only<00:04:47.320> my<00:04:47.520> problem,<00:04:47.960> probably.<00:04:48.520> Okay."
+ },
+ {
+ "start": 289.43,
+ "duration": 0.0,
+ "text": ">> It's only my problem, probably. Okay."
+ },
+ {
+ "start": 289.44,
+ "duration": 0.0,
+ "text": ">> It's only my problem, probably. Okay. Right.<00:04:49.760> So,<00:04:50.520> um<00:04:51.160> the<00:04:51.440> way<00:04:51.640> that<00:04:51.920> this<00:04:52.360> noise"
+ },
+ {
+ "start": 292.95,
+ "duration": 0.0,
+ "text": "Right. So, um the way that this noise"
+ },
+ {
+ "start": 292.96,
+ "duration": 0.0,
+ "text": "Right. So, um the way that this noise was<00:04:53.120> actually<00:04:53.440> generated<00:04:54.000> was<00:04:54.800> through<00:04:55.440> this"
+ },
+ {
+ "start": 296.11,
+ "duration": 0.0,
+ "text": "was actually generated was through this"
+ },
+ {
+ "start": 296.12,
+ "duration": 0.0,
+ "text": "was actually generated was through this game<00:04:56.320> of<00:04:56.440> life<00:04:56.680> cellular<00:04:56.960> automaton<00:04:57.880> and<00:04:58.120> a"
+ },
+ {
+ "start": 298.15,
+ "duration": 0.0,
+ "text": "game of life cellular automaton and a"
+ },
+ {
+ "start": 298.16,
+ "duration": 0.0,
+ "text": "game of life cellular automaton and a set<00:04:58.400> of<00:04:58.920> initial<00:04:59.240> conditions<00:04:59.840> which<00:05:00.040> I<00:05:00.120> then"
+ },
+ {
+ "start": 300.83,
+ "duration": 0.0,
+ "text": "set of initial conditions which I then"
+ },
+ {
+ "start": 300.84,
+ "duration": 0.0,
+ "text": "set of initial conditions which I then encrypted."
+ },
+ {
+ "start": 302.27,
+ "duration": 0.0,
+ "text": "encrypted."
+ },
+ {
+ "start": 302.28,
+ "duration": 0.0,
+ "text": "encrypted. So,"
+ },
+ {
+ "start": 304.39,
+ "duration": 0.0,
+ "text": "So,"
+ },
+ {
+ "start": 304.4,
+ "duration": 0.0,
+ "text": "So, uh"
+ },
+ {
+ "start": 306.31,
+ "duration": 0.0,
+ "text": "uh"
+ },
+ {
+ "start": 306.32,
+ "duration": 0.0,
+ "text": "uh somehow,<00:05:07.040> if"
+ },
+ {
+ "start": 308.27,
+ "duration": 0.0,
+ "text": "somehow, if"
+ },
+ {
+ "start": 308.28,
+ "duration": 0.0,
+ "text": "somehow, if for<00:05:08.640> somebody<00:05:09.000> with<00:05:09.440> infinite<00:05:09.800> compute,"
+ },
+ {
+ "start": 311.27,
+ "duration": 0.0,
+ "text": "for somebody with infinite compute,"
+ },
+ {
+ "start": 311.28,
+ "duration": 0.0,
+ "text": "for somebody with infinite compute, they<00:05:11.480> would<00:05:11.640> see<00:05:11.880> that<00:05:12.080> those<00:05:12.360> two<00:05:12.520> objects"
+ },
+ {
+ "start": 312.95,
+ "duration": 0.0,
+ "text": "they would see that those two objects"
+ },
+ {
+ "start": 312.96,
+ "duration": 0.0,
+ "text": "they would see that those two objects are<00:05:13.080> essentially<00:05:13.440> the<00:05:13.520> same."
+ },
+ {
+ "start": 314.55,
+ "duration": 0.0,
+ "text": "are essentially the same."
+ },
+ {
+ "start": 314.56,
+ "duration": 0.0,
+ "text": "are essentially the same. But,<00:05:15.080> it<00:05:15.880> is<00:05:16.080> kind<00:05:16.360> of<00:05:17.200> incredible<00:05:18.080> to<00:05:19.160> assert"
+ },
+ {
+ "start": 319.59,
+ "duration": 0.0,
+ "text": "But, it is kind of incredible to assert"
+ },
+ {
+ "start": 319.6,
+ "duration": 0.0,
+ "text": "But, it is kind of incredible to assert that<00:05:19.760> they<00:05:19.880> are<00:05:20.000> the<00:05:20.120> same<00:05:21.120> for<00:05:21.280> people<00:05:21.560> like"
+ },
+ {
+ "start": 321.75,
+ "duration": 0.0,
+ "text": "that they are the same for people like"
+ },
+ {
+ "start": 321.76,
+ "duration": 0.0,
+ "text": "that they are the same for people like us<00:05:22.240> with<00:05:22.360> limited<00:05:22.680> compute.<00:05:23.680> We<00:05:23.800> don't<00:05:23.960> have"
+ },
+ {
+ "start": 324.07,
+ "duration": 0.0,
+ "text": "us with limited compute. We don't have"
+ },
+ {
+ "start": 324.08,
+ "duration": 0.0,
+ "text": "us with limited compute. We don't have that<00:05:24.280> decryption<00:05:24.720> key.<00:05:25.240> We<00:05:25.360> can't<00:05:25.600> see<00:05:25.720> that"
+ },
+ {
+ "start": 325.91,
+ "duration": 0.0,
+ "text": "that decryption key. We can't see that"
+ },
+ {
+ "start": 325.92,
+ "duration": 0.0,
+ "text": "that decryption key. We can't see that structure.<00:05:26.680> If<00:05:26.760> we're<00:05:26.880> trying<00:05:27.080> to<00:05:27.120> train<00:05:27.360> on"
+ },
+ {
+ "start": 327.47,
+ "duration": 0.0,
+ "text": "structure. If we're trying to train on"
+ },
+ {
+ "start": 327.48,
+ "duration": 0.0,
+ "text": "structure. If we're trying to train on that<00:05:27.640> data,"
+ },
+ {
+ "start": 329.07,
+ "duration": 0.0,
+ "text": "that data,"
+ },
+ {
+ "start": 329.08,
+ "duration": 0.0,
+ "text": "that data, yeah,<00:05:29.320> and<00:05:29.680> we<00:05:29.800> don't<00:05:29.920> have<00:05:30.040> the<00:05:30.120> compute<00:05:30.520> to"
+ },
+ {
+ "start": 330.59,
+ "duration": 0.0,
+ "text": "yeah, and we don't have the compute to"
+ },
+ {
+ "start": 330.6,
+ "duration": 0.0,
+ "text": "yeah, and we don't have the compute to be<00:05:30.680> able<00:05:30.800> to<00:05:30.880> decrypt,<00:05:31.880> um<00:05:32.360> and<00:05:32.480> it's<00:05:32.600> just"
+ },
+ {
+ "start": 332.75,
+ "duration": 0.0,
+ "text": "be able to decrypt, um and it's just"
+ },
+ {
+ "start": 332.76,
+ "duration": 0.0,
+ "text": "be able to decrypt, um and it's just going<00:05:32.880> to<00:05:32.960> look<00:05:33.080> like<00:05:33.280> noise<00:05:33.560> to<00:05:33.680> us."
+ },
+ {
+ "start": 334.71,
+ "duration": 0.0,
+ "text": "going to look like noise to us."
+ },
+ {
+ "start": 334.72,
+ "duration": 0.0,
+ "text": "going to look like noise to us. And<00:05:34.960> again,<00:05:35.240> you<00:05:35.360> can<00:05:35.480> go<00:05:35.640> a<00:05:35.840> level<00:05:36.120> further."
+ },
+ {
+ "start": 337.31,
+ "duration": 0.0,
+ "text": "And again, you can go a level further."
+ },
+ {
+ "start": 337.32,
+ "duration": 0.0,
+ "text": "And again, you can go a level further. Um<00:05:38.040> so,<00:05:38.320> we<00:05:38.440> have<00:05:38.600> a<00:05:38.760> a<00:05:38.840> level<00:05:39.080> of<00:05:39.160> structure"
+ },
+ {
+ "start": 339.51,
+ "duration": 0.0,
+ "text": "Um so, we have a a level of structure"
+ },
+ {
+ "start": 339.52,
+ "duration": 0.0,
+ "text": "Um so, we have a a level of structure noise<00:05:39.840> that<00:05:39.920> we<00:05:40.000> see<00:05:40.480> on<00:05:40.600> the<00:05:40.680> left,<00:05:41.560> on<00:05:41.680> the"
+ },
+ {
+ "start": 341.75,
+ "duration": 0.0,
+ "text": "noise that we see on the left, on the"
+ },
+ {
+ "start": 341.76,
+ "duration": 0.0,
+ "text": "noise that we see on the left, on the middle,"
+ },
+ {
+ "start": 342.71,
+ "duration": 0.0,
+ "text": "middle,"
+ },
+ {
+ "start": 342.72,
+ "duration": 0.0,
+ "text": "middle, and<00:05:42.840> then<00:05:42.960> also<00:05:43.680> in<00:05:44.040> the<00:05:44.120> generating<00:05:44.520> process."
+ },
+ {
+ "start": 345.59,
+ "duration": 0.0,
+ "text": "and then also in the generating process."
+ },
+ {
+ "start": 345.6,
+ "duration": 0.0,
+ "text": "and then also in the generating process. And<00:05:46.120> my<00:05:46.840> right,<00:05:47.120> the<00:05:47.240> our<00:05:47.400> assertion<00:05:47.920> is<00:05:48.120> that"
+ },
+ {
+ "start": 349.07,
+ "duration": 0.0,
+ "text": "And my right, the our assertion is that"
+ },
+ {
+ "start": 349.08,
+ "duration": 0.0,
+ "text": "And my right, the our assertion is that um"
+ },
+ {
+ "start": 350.23,
+ "duration": 0.0,
+ "text": "um"
+ },
+ {
+ "start": 350.24,
+ "duration": 0.0,
+ "text": "um that<00:05:50.440> these<00:05:50.600> can<00:05:50.760> be<00:05:50.880> different"
+ },
+ {
+ "start": 352.03,
+ "duration": 0.0,
+ "text": "that these can be different"
+ },
+ {
+ "start": 352.04,
+ "duration": 0.0,
+ "text": "that these can be different um<00:05:52.840> because<00:05:53.400> of<00:05:53.520> the<00:05:53.600> compute<00:05:54.280> that<00:05:54.440> went<00:05:54.680> into"
+ },
+ {
+ "start": 355.15,
+ "duration": 0.0,
+ "text": "um because of the compute that went into"
+ },
+ {
+ "start": 355.16,
+ "duration": 0.0,
+ "text": "um because of the compute that went into the<00:05:55.240> computation<00:05:56.040> and<00:05:56.280> how<00:05:56.400> much<00:05:57.000> is<00:05:57.200> required"
+ },
+ {
+ "start": 357.67,
+ "duration": 0.0,
+ "text": "the computation and how much is required"
+ },
+ {
+ "start": 357.68,
+ "duration": 0.0,
+ "text": "the computation and how much is required to<00:05:57.720> actually<00:05:57.960> unravel<00:05:58.320> it.<00:05:58.840> Okay.<00:05:59.400> Yeah,<00:05:59.560> so"
+ },
+ {
+ "start": 359.67,
+ "duration": 0.0,
+ "text": "to actually unravel it. Okay. Yeah, so"
+ },
+ {
+ "start": 359.68,
+ "duration": 0.0,
+ "text": "to actually unravel it. Okay. Yeah, so that<00:05:59.880> that<00:06:00.120> that's<00:06:00.320> it."
+ },
+ {
+ "start": 361.63,
+ "duration": 0.0,
+ "text": "that that that's it."
+ },
+ {
+ "start": 361.64,
+ "duration": 0.0,
+ "text": "that that that's it. Okay.<00:06:02.080> And<00:06:02.240> also,<00:06:02.520> just<00:06:02.760> to<00:06:02.960> elaborate<00:06:03.520> a"
+ },
+ {
+ "start": 363.59,
+ "duration": 0.0,
+ "text": "Okay. And also, just to elaborate a"
+ },
+ {
+ "start": 363.6,
+ "duration": 0.0,
+ "text": "Okay. And also, just to elaborate a little<00:06:03.800> bit<00:06:03.920> more<00:06:04.320> on<00:06:04.640> the<00:06:04.760> difference"
+ },
+ {
+ "start": 365.35,
+ "duration": 0.0,
+ "text": "little bit more on the difference"
+ },
+ {
+ "start": 365.36,
+ "duration": 0.0,
+ "text": "little bit more on the difference between<00:06:06.240> structural<00:06:06.840> information<00:06:07.480> and"
+ },
+ {
+ "start": 367.75,
+ "duration": 0.0,
+ "text": "between structural information and"
+ },
+ {
+ "start": 367.76,
+ "duration": 0.0,
+ "text": "between structural information and random<00:06:08.120> information,<00:06:08.840> which<00:06:09.080> is<00:06:09.200> something<00:06:09.480> I"
+ },
+ {
+ "start": 369.55,
+ "duration": 0.0,
+ "text": "random information, which is something I"
+ },
+ {
+ "start": 369.56,
+ "duration": 0.0,
+ "text": "random information, which is something I alluded<00:06:09.960> to<00:06:10.160> when<00:06:10.360> I<00:06:10.440> said<00:06:10.880> that<00:06:11.720> we're<00:06:12.120> often"
+ },
+ {
+ "start": 372.43,
+ "duration": 0.0,
+ "text": "alluded to when I said that we're often"
+ },
+ {
+ "start": 372.44,
+ "duration": 0.0,
+ "text": "alluded to when I said that we're often not<00:06:12.640> targeting<00:06:13.080> useful<00:06:13.440> information<00:06:14.000> content"
+ },
+ {
+ "start": 374.59,
+ "duration": 0.0,
+ "text": "not targeting useful information content"
+ },
+ {
+ "start": 374.6,
+ "duration": 0.0,
+ "text": "not targeting useful information content and<00:06:14.720> that<00:06:14.920> can<00:06:15.720> um<00:06:15.920> lead<00:06:16.160> to<00:06:16.280> the<00:06:16.400> paradoxes"
+ },
+ {
+ "start": 377.07,
+ "duration": 0.0,
+ "text": "and that can um lead to the paradoxes"
+ },
+ {
+ "start": 377.08,
+ "duration": 0.0,
+ "text": "and that can um lead to the paradoxes that<00:06:17.360> we<00:06:17.480> presented.<00:06:18.560> Um"
+ },
+ {
+ "start": 379.63,
+ "duration": 0.0,
+ "text": "that we presented. Um"
+ },
+ {
+ "start": 379.64,
+ "duration": 0.0,
+ "text": "that we presented. Um we<00:06:19.800> can<00:06:19.920> imagine<00:06:20.360> in<00:06:20.440> this<00:06:20.640> first<00:06:20.960> row,<00:06:21.320> we"
+ },
+ {
+ "start": 381.63,
+ "duration": 0.0,
+ "text": "we can imagine in this first row, we"
+ },
+ {
+ "start": 381.64,
+ "duration": 0.0,
+ "text": "we can imagine in this first row, we have<00:06:22.040> just<00:06:22.240> a<00:06:22.320> simple<00:06:22.640> gradient<00:06:23.160> of<00:06:23.280> color."
+ },
+ {
+ "start": 383.75,
+ "duration": 0.0,
+ "text": "have just a simple gradient of color."
+ },
+ {
+ "start": 383.76,
+ "duration": 0.0,
+ "text": "have just a simple gradient of color. So,<00:06:23.960> this<00:06:24.240> has<00:06:24.400> got<00:06:24.680> very<00:06:24.920> simple<00:06:25.240> structure"
+ },
+ {
+ "start": 385.71,
+ "duration": 0.0,
+ "text": "So, this has got very simple structure"
+ },
+ {
+ "start": 385.72,
+ "duration": 0.0,
+ "text": "So, this has got very simple structure and<00:06:25.840> it's<00:06:26.000> not<00:06:26.200> very<00:06:26.440> noisy.<00:06:27.400> And<00:06:27.680> so,<00:06:27.920> this<00:06:28.120> is"
+ },
+ {
+ "start": 388.27,
+ "duration": 0.0,
+ "text": "and it's not very noisy. And so, this is"
+ },
+ {
+ "start": 388.28,
+ "duration": 0.0,
+ "text": "and it's not very noisy. And so, this is very<00:06:28.600> compressible.<00:06:29.800> Um"
+ },
+ {
+ "start": 391.11,
+ "duration": 0.0,
+ "text": "very compressible. Um"
+ },
+ {
+ "start": 391.12,
+ "duration": 0.0,
+ "text": "very compressible. Um and<00:06:31.800> uh"
+ },
+ {
+ "start": 392.39,
+ "duration": 0.0,
+ "text": "and uh"
+ },
+ {
+ "start": 392.4,
+ "duration": 0.0,
+ "text": "and uh in<00:06:32.520> the<00:06:32.600> middle<00:06:32.840> row,<00:06:33.160> we<00:06:33.440> have<00:06:33.720> natural"
+ },
+ {
+ "start": 394.19,
+ "duration": 0.0,
+ "text": "in the middle row, we have natural"
+ },
+ {
+ "start": 394.2,
+ "duration": 0.0,
+ "text": "in the middle row, we have natural images<00:06:34.920> and<00:06:35.240> some<00:06:35.640> structured<00:06:36.280> code.<00:06:37.200> Uh<00:06:37.440> so,"
+ },
+ {
+ "start": 397.59,
+ "duration": 0.0,
+ "text": "images and some structured code. Uh so,"
+ },
+ {
+ "start": 397.6,
+ "duration": 0.0,
+ "text": "images and some structured code. Uh so, this<00:06:37.880> data<00:06:38.840> is<00:06:39.080> going<00:06:39.320> to<00:06:39.440> be<00:06:39.880> very<00:06:40.400> useful<00:06:40.920> for"
+ },
+ {
+ "start": 401.07,
+ "duration": 0.0,
+ "text": "this data is going to be very useful for"
+ },
+ {
+ "start": 401.08,
+ "duration": 0.0,
+ "text": "this data is going to be very useful for training<00:06:41.600> a<00:06:41.680> model.<00:06:42.160> It<00:06:42.320> could<00:06:42.480> teach<00:06:42.800> our"
+ },
+ {
+ "start": 402.91,
+ "duration": 0.0,
+ "text": "training a model. It could teach our"
+ },
+ {
+ "start": 402.92,
+ "duration": 0.0,
+ "text": "training a model. It could teach our model<00:06:43.240> a<00:06:43.280> useful<00:06:43.640> representation<00:06:44.480> that<00:06:44.640> will"
+ },
+ {
+ "start": 404.75,
+ "duration": 0.0,
+ "text": "model a useful representation that will"
+ },
+ {
+ "start": 404.76,
+ "duration": 0.0,
+ "text": "model a useful representation that will make<00:06:45.520> um<00:06:45.760> predictions<00:06:46.520> on<00:06:46.840> downstream"
+ },
+ {
+ "start": 407.35,
+ "duration": 0.0,
+ "text": "make um predictions on downstream"
+ },
+ {
+ "start": 407.36,
+ "duration": 0.0,
+ "text": "make um predictions on downstream settings.<00:06:48.280> Um<00:06:48.640> it<00:06:49.000> has<00:06:49.840> uh<00:06:50.120> a<00:06:50.240> fair<00:06:50.480> amount<00:06:50.840> of"
+ },
+ {
+ "start": 410.95,
+ "duration": 0.0,
+ "text": "settings. Um it has uh a fair amount of"
+ },
+ {
+ "start": 410.96,
+ "duration": 0.0,
+ "text": "settings. Um it has uh a fair amount of structural<00:06:51.440> information<00:06:52.000> content<00:06:52.680> and<00:06:53.080> a"
+ },
+ {
+ "start": 413.11,
+ "duration": 0.0,
+ "text": "structural information content and a"
+ },
+ {
+ "start": 413.12,
+ "duration": 0.0,
+ "text": "structural information content and a little<00:06:53.360> bit<00:06:53.520> of<00:06:53.640> noise.<00:06:54.600> And<00:06:55.000> in<00:06:55.320> the<00:06:55.440> bottom"
+ },
+ {
+ "start": 415.87,
+ "duration": 0.0,
+ "text": "little bit of noise. And in the bottom"
+ },
+ {
+ "start": 415.88,
+ "duration": 0.0,
+ "text": "little bit of noise. And in the bottom row,<00:06:56.280> we<00:06:56.520> have<00:06:57.040> uh<00:06:57.280> just<00:06:57.600> white<00:06:57.920> noise,<00:06:58.440> which"
+ },
+ {
+ "start": 418.99,
+ "duration": 0.0,
+ "text": "row, we have uh just white noise, which"
+ },
+ {
+ "start": 419.0,
+ "duration": 0.0,
+ "text": "row, we have uh just white noise, which is<00:06:59.160> also<00:06:59.720> quite<00:07:00.080> incompressible,<00:07:01.280> but<00:07:01.480> it's"
+ },
+ {
+ "start": 421.63,
+ "duration": 0.0,
+ "text": "is also quite incompressible, but it's"
+ },
+ {
+ "start": 421.64,
+ "duration": 0.0,
+ "text": "is also quite incompressible, but it's not<00:07:01.840> going<00:07:01.960> to<00:07:02.040> teach<00:07:02.560> our<00:07:02.720> data<00:07:03.400> our<00:07:03.560> model"
+ },
+ {
+ "start": 423.95,
+ "duration": 0.0,
+ "text": "not going to teach our data our model"
+ },
+ {
+ "start": 423.96,
+ "duration": 0.0,
+ "text": "not going to teach our data our model anything<00:07:04.440> very<00:07:04.720> useful.<00:07:05.560> And<00:07:05.800> so,<00:07:05.960> this<00:07:06.160> has"
+ },
+ {
+ "start": 426.71,
+ "duration": 0.0,
+ "text": "anything very useful. And so, this has"
+ },
+ {
+ "start": 426.72,
+ "duration": 0.0,
+ "text": "anything very useful. And so, this has very<00:07:06.960> low<00:07:07.240> structural<00:07:07.760> information<00:07:08.360> content,"
+ },
+ {
+ "start": 429.47,
+ "duration": 0.0,
+ "text": "very low structural information content,"
+ },
+ {
+ "start": 429.48,
+ "duration": 0.0,
+ "text": "very low structural information content, um<00:07:09.880> but<00:07:10.480> uh<00:07:10.560> high<00:07:10.760> random<00:07:11.160> information"
+ },
+ {
+ "start": 431.75,
+ "duration": 0.0,
+ "text": "um but uh high random information"
+ },
+ {
+ "start": 431.76,
+ "duration": 0.0,
+ "text": "um but uh high random information content.<00:07:12.360> And<00:07:12.680> similarly,<00:07:13.200> in<00:07:13.320> this<00:07:13.480> code"
+ },
+ {
+ "start": 433.71,
+ "duration": 0.0,
+ "text": "content. And similarly, in this code"
+ },
+ {
+ "start": 433.72,
+ "duration": 0.0,
+ "text": "content. And similarly, in this code block,<00:07:14.080> we<00:07:14.160> just<00:07:14.400> have<00:07:14.560> sort<00:07:14.760> of<00:07:14.880> like<00:07:15.080> random"
+ },
+ {
+ "start": 435.39,
+ "duration": 0.0,
+ "text": "block, we just have sort of like random"
+ },
+ {
+ "start": 435.4,
+ "duration": 0.0,
+ "text": "block, we just have sort of like random hashes<00:07:15.840> and<00:07:15.960> things<00:07:16.160> like<00:07:16.360> this.<00:07:16.600> You"
+ },
+ {
+ "start": 436.67,
+ "duration": 0.0,
+ "text": "hashes and things like this. You"
+ },
+ {
+ "start": 436.68,
+ "duration": 0.0,
+ "text": "hashes and things like this. You basically<00:07:17.080> have<00:07:17.240> to<00:07:17.360> memorize<00:07:18.160> the<00:07:18.240> data."
+ },
+ {
+ "start": 438.59,
+ "duration": 0.0,
+ "text": "basically have to memorize the data."
+ },
+ {
+ "start": 438.6,
+ "duration": 0.0,
+ "text": "basically have to memorize the data. There<00:07:18.800> isn't<00:07:19.360> much<00:07:19.600> structure<00:07:20.040> that<00:07:20.200> we<00:07:20.320> can"
+ },
+ {
+ "start": 440.47,
+ "duration": 0.0,
+ "text": "There isn't much structure that we can"
+ },
+ {
+ "start": 440.48,
+ "duration": 0.0,
+ "text": "There isn't much structure that we can extract<00:07:20.960> from<00:07:21.120> that.<00:07:21.840> Um<00:07:22.200> Mark<00:07:22.520> is<00:07:22.640> going<00:07:22.760> to"
+ },
+ {
+ "start": 442.83,
+ "duration": 0.0,
+ "text": "extract from that. Um Mark is going to"
+ },
+ {
+ "start": 442.84,
+ "duration": 0.0,
+ "text": "extract from that. Um Mark is going to be<00:07:23.320> introducing<00:07:23.920> epiplexity<00:07:25.000> formally,<00:07:25.480> but"
+ },
+ {
+ "start": 445.71,
+ "duration": 0.0,
+ "text": "be introducing epiplexity formally, but"
+ },
+ {
+ "start": 445.72,
+ "duration": 0.0,
+ "text": "be introducing epiplexity formally, but just<00:07:26.000> as<00:07:26.320> like<00:07:26.640> a<00:07:26.720> teaser,<00:07:27.720> um<00:07:27.960> you<00:07:28.160> can"
+ },
+ {
+ "start": 448.71,
+ "duration": 0.0,
+ "text": "just as like a teaser, um you can"
+ },
+ {
+ "start": 448.72,
+ "duration": 0.0,
+ "text": "just as like a teaser, um you can heuristically<00:07:29.320> approximate<00:07:30.080> epiplexity<00:07:30.960> as"
+ },
+ {
+ "start": 451.15,
+ "duration": 0.0,
+ "text": "heuristically approximate epiplexity as"
+ },
+ {
+ "start": 451.16,
+ "duration": 0.0,
+ "text": "heuristically approximate epiplexity as the<00:07:31.320> area<00:07:31.760> under<00:07:32.040> the<00:07:32.760> uh<00:07:32.880> training<00:07:33.240> loss"
+ },
+ {
+ "start": 453.43,
+ "duration": 0.0,
+ "text": "the area under the uh training loss"
+ },
+ {
+ "start": 453.44,
+ "duration": 0.0,
+ "text": "the area under the uh training loss curve<00:07:33.840> above<00:07:34.200> the<00:07:34.320> final<00:07:34.680> value<00:07:35.200> of<00:07:35.400> the<00:07:35.520> loss."
+ },
+ {
+ "start": 456.27,
+ "duration": 0.0,
+ "text": "curve above the final value of the loss."
+ },
+ {
+ "start": 456.28,
+ "duration": 0.0,
+ "text": "curve above the final value of the loss. And<00:07:36.440> so,<00:07:36.560> we<00:07:36.680> can<00:07:36.840> see<00:07:36.960> this<00:07:37.120> first<00:07:37.320> system<00:07:37.600> is"
+ },
+ {
+ "start": 457.67,
+ "duration": 0.0,
+ "text": "And so, we can see this first system is"
+ },
+ {
+ "start": 457.68,
+ "duration": 0.0,
+ "text": "And so, we can see this first system is very<00:07:37.920> learnable,<00:07:38.520> but<00:07:38.680> there<00:07:38.800> isn't<00:07:39.040> very"
+ },
+ {
+ "start": 459.15,
+ "duration": 0.0,
+ "text": "very learnable, but there isn't very"
+ },
+ {
+ "start": 459.16,
+ "duration": 0.0,
+ "text": "very learnable, but there isn't very much<00:07:39.360> structure.<00:07:39.760> It<00:07:39.840> actually<00:07:40.080> has<00:07:40.240> low"
+ },
+ {
+ "start": 460.43,
+ "duration": 0.0,
+ "text": "much structure. It actually has low"
+ },
+ {
+ "start": 460.44,
+ "duration": 0.0,
+ "text": "much structure. It actually has low epiplexity<00:07:41.040> and<00:07:41.120> it<00:07:41.200> has<00:07:41.400> low<00:07:42.000> time-bounded"
+ },
+ {
+ "start": 462.71,
+ "duration": 0.0,
+ "text": "epiplexity and it has low time-bounded"
+ },
+ {
+ "start": 462.72,
+ "duration": 0.0,
+ "text": "epiplexity and it has low time-bounded entropy,<00:07:43.680> um<00:07:43.760> which<00:07:43.960> is<00:07:44.120> sort<00:07:44.280> of<00:07:44.440> what<00:07:44.760> is"
+ },
+ {
+ "start": 464.99,
+ "duration": 0.0,
+ "text": "entropy, um which is sort of what is"
+ },
+ {
+ "start": 465.0,
+ "duration": 0.0,
+ "text": "entropy, um which is sort of what is random<00:07:45.360> from<00:07:45.560> the<00:07:45.680> perspective<00:07:46.200> of<00:07:46.280> the"
+ },
+ {
+ "start": 466.35,
+ "duration": 0.0,
+ "text": "random from the perspective of the"
+ },
+ {
+ "start": 466.36,
+ "duration": 0.0,
+ "text": "random from the perspective of the model.<00:07:47.200> This<00:07:47.440> system<00:07:47.960> has<00:07:48.320> moderate"
+ },
+ {
+ "start": 468.83,
+ "duration": 0.0,
+ "text": "model. This system has moderate"
+ },
+ {
+ "start": 468.84,
+ "duration": 0.0,
+ "text": "model. This system has moderate epiplexity<00:07:49.720> and<00:07:50.280> relatively<00:07:50.800> low"
+ },
+ {
+ "start": 470.99,
+ "duration": 0.0,
+ "text": "epiplexity and relatively low"
+ },
+ {
+ "start": 471.0,
+ "duration": 0.0,
+ "text": "epiplexity and relatively low time-bounded<00:07:51.600> entropy.<00:07:52.400> And<00:07:52.520> this<00:07:52.680> bottom"
+ },
+ {
+ "start": 472.95,
+ "duration": 0.0,
+ "text": "time-bounded entropy. And this bottom"
+ },
+ {
+ "start": 472.96,
+ "duration": 0.0,
+ "text": "time-bounded entropy. And this bottom system<00:07:53.480> is<00:07:54.200> pretty<00:07:54.400> much<00:07:54.680> all<00:07:54.920> entropy<00:07:55.520> and<00:07:55.880> no"
+ },
+ {
+ "start": 476.35,
+ "duration": 0.0,
+ "text": "system is pretty much all entropy and no"
+ },
+ {
+ "start": 476.36,
+ "duration": 0.0,
+ "text": "system is pretty much all entropy and no epiplexity."
+ },
+ {
+ "start": 478.39,
+ "duration": 0.0,
+ "text": "epiplexity."
+ },
+ {
+ "start": 478.4,
+ "duration": 0.0,
+ "text": "epiplexity. Okay.<00:07:58.840> So,"
+ },
+ {
+ "start": 480.27,
+ "duration": 0.0,
+ "text": "Okay. So,"
+ },
+ {
+ "start": 480.28,
+ "duration": 0.0,
+ "text": "Okay. So, we<00:08:00.520> also<00:08:00.960> became<00:08:01.520> interested<00:08:02.320> in<00:08:02.560> some<00:08:02.800> of"
+ },
+ {
+ "start": 482.87,
+ "duration": 0.0,
+ "text": "we also became interested in some of"
+ },
+ {
+ "start": 482.88,
+ "duration": 0.0,
+ "text": "we also became interested in some of these<00:08:03.680> types<00:08:04.000> of<00:08:04.120> questions<00:08:04.760> because<00:08:05.880> in<00:08:06.040> our"
+ },
+ {
+ "start": 486.19,
+ "duration": 0.0,
+ "text": "these types of questions because in our"
+ },
+ {
+ "start": 486.2,
+ "duration": 0.0,
+ "text": "these types of questions because in our group,<00:08:06.760> we<00:08:06.960> had<00:08:07.160> observed<00:08:07.840> that<00:08:08.560> certain"
+ },
+ {
+ "start": 488.83,
+ "duration": 0.0,
+ "text": "group, we had observed that certain"
+ },
+ {
+ "start": 488.84,
+ "duration": 0.0,
+ "text": "group, we had observed that certain modalities<00:08:09.520> of<00:08:09.680> data<00:08:10.080> led<00:08:10.360> to"
+ },
+ {
+ "start": 490.47,
+ "duration": 0.0,
+ "text": "modalities of data led to"
+ },
+ {
+ "start": 490.48,
+ "duration": 0.0,
+ "text": "modalities of data led to representations<00:08:11.560> that<00:08:11.800> were<00:08:12.320> much<00:08:12.560> more"
+ },
+ {
+ "start": 492.71,
+ "duration": 0.0,
+ "text": "representations that were much more"
+ },
+ {
+ "start": 492.72,
+ "duration": 0.0,
+ "text": "representations that were much more transferable<00:08:13.440> than<00:08:13.680> others.<00:08:14.160> So,<00:08:14.840> uh<00:08:14.920> we<00:08:15.080> had"
+ },
+ {
+ "start": 495.23,
+ "duration": 0.0,
+ "text": "transferable than others. So, uh we had"
+ },
+ {
+ "start": 495.24,
+ "duration": 0.0,
+ "text": "transferable than others. So, uh we had this<00:08:15.480> paper<00:08:15.880> which<00:08:16.120> was<00:08:16.360> co-led<00:08:16.760> by<00:08:16.960> Mark"
+ },
+ {
+ "start": 497.39,
+ "duration": 0.0,
+ "text": "this paper which was co-led by Mark"
+ },
+ {
+ "start": 497.4,
+ "duration": 0.0,
+ "text": "this paper which was co-led by Mark called<00:08:17.960> LLM<00:08:18.400> time,<00:08:18.920> uh<00:08:19.000> large<00:08:19.280> language"
+ },
+ {
+ "start": 499.59,
+ "duration": 0.0,
+ "text": "called LLM time, uh large language"
+ },
+ {
+ "start": 499.6,
+ "duration": 0.0,
+ "text": "called LLM time, uh large language models<00:08:19.920> are<00:08:20.000> zero-shot<00:08:20.520> time<00:08:20.760> series"
+ },
+ {
+ "start": 501.03,
+ "duration": 0.0,
+ "text": "models are zero-shot time series"
+ },
+ {
+ "start": 501.04,
+ "duration": 0.0,
+ "text": "models are zero-shot time series forecasters.<00:08:22.320> Um<00:08:22.480> and<00:08:22.640> there<00:08:22.880> we<00:08:23.000> just<00:08:23.280> took"
+ },
+ {
+ "start": 503.91,
+ "duration": 0.0,
+ "text": "forecasters. Um and there we just took"
+ },
+ {
+ "start": 503.92,
+ "duration": 0.0,
+ "text": "forecasters. Um and there we just took an<00:08:24.200> LLM<00:08:24.640> that<00:08:24.840> had<00:08:24.960> been<00:08:25.200> pretrained<00:08:26.000> on<00:08:26.240> next"
+ },
+ {
+ "start": 506.47,
+ "duration": 0.0,
+ "text": "an LLM that had been pretrained on next"
+ },
+ {
+ "start": 506.48,
+ "duration": 0.0,
+ "text": "an LLM that had been pretrained on next word<00:08:26.600> prediction<00:08:27.160> off<00:08:27.400> the<00:08:27.480> shelf<00:08:28.000> and<00:08:28.160> then"
+ },
+ {
+ "start": 508.35,
+ "duration": 0.0,
+ "text": "word prediction off the shelf and then"
+ },
+ {
+ "start": 508.36,
+ "duration": 0.0,
+ "text": "word prediction off the shelf and then fed<00:08:28.600> it<00:08:29.080> string<00:08:29.400> token<00:08:30.000> Sorry,<00:08:30.280> uh<00:08:30.400> numbers<00:08:31.080> uh"
+ },
+ {
+ "start": 511.15,
+ "duration": 0.0,
+ "text": "fed it string token Sorry, uh numbers uh"
+ },
+ {
+ "start": 511.16,
+ "duration": 0.0,
+ "text": "fed it string token Sorry, uh numbers uh in<00:08:31.320> time<00:08:31.600> series<00:08:32.320> uh<00:08:32.440> naively<00:08:32.880> represented<00:08:33.479> as"
+ },
+ {
+ "start": 513.589,
+ "duration": 0.0,
+ "text": "in time series uh naively represented as"
+ },
+ {
+ "start": 513.599,
+ "duration": 0.0,
+ "text": "in time series uh naively represented as string<00:08:33.840> tokens<00:08:34.800> and<00:08:35.159> had<00:08:35.320> it<00:08:35.479> extrapolate"
+ },
+ {
+ "start": 516.19,
+ "duration": 0.0,
+ "text": "string tokens and had it extrapolate"
+ },
+ {
+ "start": 516.2,
+ "duration": 0.0,
+ "text": "string tokens and had it extrapolate like<00:08:36.320> the<00:08:36.400> next<00:08:36.599> sequence<00:08:37.000> of<00:08:37.080> string<00:08:37.320> tokens."
+ },
+ {
+ "start": 518.19,
+ "duration": 0.0,
+ "text": "like the next sequence of string tokens."
+ },
+ {
+ "start": 518.2,
+ "duration": 0.0,
+ "text": "like the next sequence of string tokens. And<00:08:38.479> in<00:08:38.640> some<00:08:38.800> cases,<00:08:39.280> this<00:08:39.479> could<00:08:39.680> work<00:08:40.039> as"
+ },
+ {
+ "start": 520.27,
+ "duration": 0.0,
+ "text": "And in some cases, this could work as"
+ },
+ {
+ "start": 520.28,
+ "duration": 0.0,
+ "text": "And in some cases, this could work as well<00:08:40.479> or<00:08:40.599> better<00:08:40.960> than<00:08:41.200> purpose-built<00:08:41.880> time"
+ },
+ {
+ "start": 522.11,
+ "duration": 0.0,
+ "text": "well or better than purpose-built time"
+ },
+ {
+ "start": 522.12,
+ "duration": 0.0,
+ "text": "well or better than purpose-built time series<00:08:42.479> models<00:08:42.840> that<00:08:43.000> had<00:08:43.120> specifically<00:08:44.120> been"
+ },
+ {
+ "start": 524.27,
+ "duration": 0.0,
+ "text": "series models that had specifically been"
+ },
+ {
+ "start": 524.28,
+ "duration": 0.0,
+ "text": "series models that had specifically been trained<00:08:44.760> on<00:08:45.000> this<00:08:45.120> time<00:08:45.360> series<00:08:45.680> data.<00:08:46.080> So,"
+ },
+ {
+ "start": 526.23,
+ "duration": 0.0,
+ "text": "trained on this time series data. So,"
+ },
+ {
+ "start": 526.24,
+ "duration": 0.0,
+ "text": "trained on this time series data. So, this<00:08:46.440> is<00:08:46.600> just<00:08:47.080> taking<00:08:47.400> a<00:08:47.440> next<00:08:47.680> word"
+ },
+ {
+ "start": 527.83,
+ "duration": 0.0,
+ "text": "this is just taking a next word"
+ },
+ {
+ "start": 527.84,
+ "duration": 0.0,
+ "text": "this is just taking a next word predictor,<00:08:48.280> completely<00:08:48.800> freezing<00:08:49.240> its"
+ },
+ {
+ "start": 529.35,
+ "duration": 0.0,
+ "text": "predictor, completely freezing its"
+ },
+ {
+ "start": 529.36,
+ "duration": 0.0,
+ "text": "predictor, completely freezing its representation,<00:08:50.120> and<00:08:50.240> having<00:08:50.560> it<00:08:51.040> make"
+ },
+ {
+ "start": 531.23,
+ "duration": 0.0,
+ "text": "representation, and having it make"
+ },
+ {
+ "start": 531.24,
+ "duration": 0.0,
+ "text": "representation, and having it make predictions<00:08:51.680> on<00:08:51.800> time<00:08:52.040> series<00:08:52.320> in<00:08:52.440> a"
+ },
+ {
+ "start": 532.47,
+ "duration": 0.0,
+ "text": "predictions on time series in a"
+ },
+ {
+ "start": 532.48,
+ "duration": 0.0,
+ "text": "predictions on time series in a zero-shot<00:08:52.960> setting.<00:08:53.200> It<00:08:53.320> can<00:08:53.400> do<00:08:53.480> that<00:08:53.600> quite"
+ },
+ {
+ "start": 533.83,
+ "duration": 0.0,
+ "text": "zero-shot setting. It can do that quite"
+ },
+ {
+ "start": 533.84,
+ "duration": 0.0,
+ "text": "zero-shot setting. It can do that quite well.<00:08:54.320> This<00:08:54.480> was<00:08:54.640> very<00:08:54.840> surprising.<00:08:55.920> Uh<00:08:56.120> we"
+ },
+ {
+ "start": 536.23,
+ "duration": 0.0,
+ "text": "well. This was very surprising. Uh we"
+ },
+ {
+ "start": 536.24,
+ "duration": 0.0,
+ "text": "well. This was very surprising. Uh we had<00:08:56.440> a<00:08:56.480> similar<00:08:56.880> result<00:08:57.360> in<00:08:57.520> a<00:08:57.600> different"
+ },
+ {
+ "start": 537.91,
+ "duration": 0.0,
+ "text": "had a similar result in a different"
+ },
+ {
+ "start": 537.92,
+ "duration": 0.0,
+ "text": "had a similar result in a different paper<00:08:58.440> on<00:08:58.640> generating<00:08:59.160> stable<00:08:59.600> inorganic"
+ },
+ {
+ "start": 540.35,
+ "duration": 0.0,
+ "text": "paper on generating stable inorganic"
+ },
+ {
+ "start": 540.36,
+ "duration": 0.0,
+ "text": "paper on generating stable inorganic crystals,<00:09:01.240> where<00:09:01.560> text-based<00:09:02.120> pretraining"
+ },
+ {
+ "start": 542.75,
+ "duration": 0.0,
+ "text": "crystals, where text-based pretraining"
+ },
+ {
+ "start": 542.76,
+ "duration": 0.0,
+ "text": "crystals, where text-based pretraining again<00:09:03.120> seemed<00:09:03.360> to<00:09:03.480> be<00:09:03.720> an<00:09:03.920> indispensable<00:09:04.720> part"
+ },
+ {
+ "start": 545.07,
+ "duration": 0.0,
+ "text": "again seemed to be an indispensable part"
+ },
+ {
+ "start": 545.08,
+ "duration": 0.0,
+ "text": "again seemed to be an indispensable part of<00:09:05.200> the<00:09:05.360> pipeline.<00:09:06.360> And<00:09:07.240> um<00:09:07.480> this<00:09:07.680> was<00:09:07.840> also"
+ },
+ {
+ "start": 548.19,
+ "duration": 0.0,
+ "text": "of the pipeline. And um this was also"
+ },
+ {
+ "start": 548.2,
+ "duration": 0.0,
+ "text": "of the pipeline. And um this was also kind<00:09:08.440> of<00:09:08.720> surprising.<00:09:09.800> Um<00:09:10.000> and<00:09:10.120> then<00:09:10.240> there"
+ },
+ {
+ "start": 550.39,
+ "duration": 0.0,
+ "text": "kind of surprising. Um and then there"
+ },
+ {
+ "start": 550.4,
+ "duration": 0.0,
+ "text": "kind of surprising. Um and then there are<00:09:10.640> neural<00:09:11.000> cellular<00:09:11.560> automata,<00:09:12.360> and<00:09:12.560> we'll"
+ },
+ {
+ "start": 552.67,
+ "duration": 0.0,
+ "text": "are neural cellular automata, and we'll"
+ },
+ {
+ "start": 552.68,
+ "duration": 0.0,
+ "text": "are neural cellular automata, and we'll be<00:09:12.800> talking<00:09:13.160> about<00:09:13.440> this<00:09:13.680> a<00:09:13.760> fair<00:09:13.920> bit<00:09:14.080> more<00:09:14.280> in"
+ },
+ {
+ "start": 554.39,
+ "duration": 0.0,
+ "text": "be talking about this a fair bit more in"
+ },
+ {
+ "start": 554.4,
+ "duration": 0.0,
+ "text": "be talking about this a fair bit more in a<00:09:14.440> moment,<00:09:15.240> um<00:09:15.600> which<00:09:16.440> uh<00:09:16.800> tend<00:09:17.040> to<00:09:17.120> be<00:09:17.280> useful"
+ },
+ {
+ "start": 557.71,
+ "duration": 0.0,
+ "text": "a moment, um which uh tend to be useful"
+ },
+ {
+ "start": 557.72,
+ "duration": 0.0,
+ "text": "a moment, um which uh tend to be useful for<00:09:17.880> quite<00:09:18.200> a<00:09:18.280> wide<00:09:18.600> array<00:09:19.040> of<00:09:19.440> understanding"
+ },
+ {
+ "start": 560.11,
+ "duration": 0.0,
+ "text": "for quite a wide array of understanding"
+ },
+ {
+ "start": 560.12,
+ "duration": 0.0,
+ "text": "for quite a wide array of understanding different<00:09:20.480> modalities<00:09:21.040> of<00:09:21.160> data<00:09:21.480> and"
+ },
+ {
+ "start": 561.59,
+ "duration": 0.0,
+ "text": "different modalities of data and"
+ },
+ {
+ "start": 561.6,
+ "duration": 0.0,
+ "text": "different modalities of data and different<00:09:21.840> types<00:09:22.120> of<00:09:22.240> problems.<00:09:22.880> And<00:09:23.080> so,"
+ },
+ {
+ "start": 563.59,
+ "duration": 0.0,
+ "text": "different types of problems. And so,"
+ },
+ {
+ "start": 563.6,
+ "duration": 0.0,
+ "text": "different types of problems. And so, there's<00:09:23.800> this<00:09:24.000> question<00:09:24.400> of<00:09:24.560> why<00:09:24.760> language"
+ },
+ {
+ "start": 565.19,
+ "duration": 0.0,
+ "text": "there's this question of why language"
+ },
+ {
+ "start": 565.2,
+ "duration": 0.0,
+ "text": "there's this question of why language data<00:09:25.520> and<00:09:25.680> other<00:09:25.880> types<00:09:26.160> of<00:09:26.320> data<00:09:27.280> can<00:09:27.440> be"
+ },
+ {
+ "start": 567.63,
+ "duration": 0.0,
+ "text": "data and other types of data can be"
+ },
+ {
+ "start": 567.64,
+ "duration": 0.0,
+ "text": "data and other types of data can be particularly<00:09:28.160> transferable,<00:09:28.960> whereas<00:09:29.400> like"
+ },
+ {
+ "start": 569.55,
+ "duration": 0.0,
+ "text": "particularly transferable, whereas like"
+ },
+ {
+ "start": 569.56,
+ "duration": 0.0,
+ "text": "particularly transferable, whereas like some<00:09:29.760> modalities<00:09:30.360> of<00:09:30.480> data<00:09:30.960> are<00:09:31.280> not<00:09:31.520> nearly"
+ },
+ {
+ "start": 571.91,
+ "duration": 0.0,
+ "text": "some modalities of data are not nearly"
+ },
+ {
+ "start": 571.92,
+ "duration": 0.0,
+ "text": "some modalities of data are not nearly as<00:09:32.160> transferable.<00:09:33.360> And<00:09:33.600> so,<00:09:34.000> what<00:09:34.240> is<00:09:34.400> it"
+ },
+ {
+ "start": 574.51,
+ "duration": 0.0,
+ "text": "as transferable. And so, what is it"
+ },
+ {
+ "start": 574.52,
+ "duration": 0.0,
+ "text": "as transferable. And so, what is it about<00:09:34.840> that<00:09:35.120> data<00:09:35.840> that<00:09:36.040> leads<00:09:36.280> the<00:09:36.360> model<00:09:36.760> to"
+ },
+ {
+ "start": 576.91,
+ "duration": 0.0,
+ "text": "about that data that leads the model to"
+ },
+ {
+ "start": 576.92,
+ "duration": 0.0,
+ "text": "about that data that leads the model to have<00:09:37.160> a<00:09:37.240> relatively<00:09:37.920> general"
+ },
+ {
+ "start": 578.39,
+ "duration": 0.0,
+ "text": "have a relatively general"
+ },
+ {
+ "start": 578.4,
+ "duration": 0.0,
+ "text": "have a relatively general representation?<00:09:39.600> And<00:09:39.760> how<00:09:39.920> should<00:09:40.120> we<00:09:40.240> be"
+ },
+ {
+ "start": 580.39,
+ "duration": 0.0,
+ "text": "representation? And how should we be"
+ },
+ {
+ "start": 580.4,
+ "duration": 0.0,
+ "text": "representation? And how should we be thinking<00:09:40.840> about<00:09:41.360> OOD<00:09:42.080> generalization<00:09:43.000> and"
+ },
+ {
+ "start": 583.19,
+ "duration": 0.0,
+ "text": "thinking about OOD generalization and"
+ },
+ {
+ "start": 583.2,
+ "duration": 0.0,
+ "text": "thinking about OOD generalization and data<00:09:43.480> selection<00:09:44.000> towards<00:09:44.680> OOD"
+ },
+ {
+ "start": 585.19,
+ "duration": 0.0,
+ "text": "data selection towards OOD"
+ },
+ {
+ "start": 585.2,
+ "duration": 0.0,
+ "text": "data selection towards OOD generalization?<00:09:46.480> And<00:09:46.640> so,<00:09:47.040> just<00:09:47.240> to<00:09:47.360> step"
+ },
+ {
+ "start": 587.59,
+ "duration": 0.0,
+ "text": "generalization? And so, just to step"
+ },
+ {
+ "start": 587.6,
+ "duration": 0.0,
+ "text": "generalization? And so, just to step back<00:09:47.840> a<00:09:47.880> little<00:09:48.120> bit,<00:09:48.640> uh<00:09:48.760> as<00:09:48.920> a<00:09:48.960> bit<00:09:49.080> of"
+ },
+ {
+ "start": 589.19,
+ "duration": 0.0,
+ "text": "back a little bit, uh as a bit of"
+ },
+ {
+ "start": 589.2,
+ "duration": 0.0,
+ "text": "back a little bit, uh as a bit of background,<00:09:50.200> there<00:09:50.480> are<00:09:50.880> many<00:09:51.120> different"
+ },
+ {
+ "start": 591.71,
+ "duration": 0.0,
+ "text": "background, there are many different"
+ },
+ {
+ "start": 591.72,
+ "duration": 0.0,
+ "text": "background, there are many different measures<00:09:52.360> of<00:09:52.640> information<00:09:53.320> and<00:09:53.480> theories<00:09:53.840> of"
+ },
+ {
+ "start": 593.95,
+ "duration": 0.0,
+ "text": "measures of information and theories of"
+ },
+ {
+ "start": 593.96,
+ "duration": 0.0,
+ "text": "measures of information and theories of information.<00:09:54.640> So,<00:09:54.800> there's<00:09:55.040> classical"
+ },
+ {
+ "start": 595.51,
+ "duration": 0.0,
+ "text": "information. So, there's classical"
+ },
+ {
+ "start": 595.52,
+ "duration": 0.0,
+ "text": "information. So, there's classical Shannon<00:09:55.840> information<00:09:56.400> theory<00:09:56.720> where"
+ },
+ {
+ "start": 596.83,
+ "duration": 0.0,
+ "text": "Shannon information theory where"
+ },
+ {
+ "start": 596.84,
+ "duration": 0.0,
+ "text": "Shannon information theory where information<00:09:57.360> is<00:09:57.520> the<00:09:57.640> surprisal<00:09:58.240> in<00:09:58.360> seeing"
+ },
+ {
+ "start": 598.59,
+ "duration": 0.0,
+ "text": "information is the surprisal in seeing"
+ },
+ {
+ "start": 598.6,
+ "duration": 0.0,
+ "text": "information is the surprisal in seeing the<00:09:58.680> value<00:09:59.000> of<00:09:59.080> a<00:09:59.120> random<00:09:59.440> variable.<00:10:00.320> There's"
+ },
+ {
+ "start": 600.51,
+ "duration": 0.0,
+ "text": "the value of a random variable. There's"
+ },
+ {
+ "start": 600.52,
+ "duration": 0.0,
+ "text": "the value of a random variable. There's also<00:10:00.880> algorithmic<00:10:01.440> information<00:10:02.000> theory,"
+ },
+ {
+ "start": 602.35,
+ "duration": 0.0,
+ "text": "also algorithmic information theory,"
+ },
+ {
+ "start": 602.36,
+ "duration": 0.0,
+ "text": "also algorithmic information theory, which<00:10:02.560> applies<00:10:02.960> to<00:10:03.120> non-random<00:10:03.680> variables"
+ },
+ {
+ "start": 604.27,
+ "duration": 0.0,
+ "text": "which applies to non-random variables"
+ },
+ {
+ "start": 604.28,
+ "duration": 0.0,
+ "text": "which applies to non-random variables and<00:10:04.800> often<00:10:05.040> measures<00:10:05.400> incompressibility<00:10:06.400> of"
+ },
+ {
+ "start": 606.87,
+ "duration": 0.0,
+ "text": "and often measures incompressibility of"
+ },
+ {
+ "start": 606.88,
+ "duration": 0.0,
+ "text": "and often measures incompressibility of data<00:10:07.240> through<00:10:07.480> things<00:10:07.720> like<00:10:07.920> Kolmogorov"
+ },
+ {
+ "start": 608.39,
+ "duration": 0.0,
+ "text": "data through things like Kolmogorov"
+ },
+ {
+ "start": 608.4,
+ "duration": 0.0,
+ "text": "data through things like Kolmogorov complexity."
+ },
+ {
+ "start": 609.63,
+ "duration": 0.0,
+ "text": "complexity."
+ },
+ {
+ "start": 609.64,
+ "duration": 0.0,
+ "text": "complexity. Uh<00:10:09.800> intuitively,<00:10:10.760> uh<00:10:10.960> useful<00:10:11.280> information"
+ },
+ {
+ "start": 612.27,
+ "duration": 0.0,
+ "text": "Uh intuitively, uh useful information"
+ },
+ {
+ "start": 612.28,
+ "duration": 0.0,
+ "text": "Uh intuitively, uh useful information ought<00:10:12.520> to<00:10:12.600> reduce<00:10:12.960> uncertainty<00:10:13.720> in<00:10:13.920> our"
+ },
+ {
+ "start": 614.03,
+ "duration": 0.0,
+ "text": "ought to reduce uncertainty in our"
+ },
+ {
+ "start": 614.04,
+ "duration": 0.0,
+ "text": "ought to reduce uncertainty in our predictions."
+ },
+ {
+ "start": 616.59,
+ "duration": 0.0,
+ "text": "predictions."
+ },
+ {
+ "start": 616.6,
+ "duration": 0.0,
+ "text": "predictions. So,<00:10:16.680> just<00:10:16.880> to<00:10:17.000> expand<00:10:17.360> a<00:10:17.400> little<00:10:17.560> bit<00:10:17.720> more,<00:10:18.280> so"
+ },
+ {
+ "start": 618.43,
+ "duration": 0.0,
+ "text": "So, just to expand a little bit more, so"
+ },
+ {
+ "start": 618.44,
+ "duration": 0.0,
+ "text": "So, just to expand a little bit more, so Shannon<00:10:18.800> information<00:10:19.960> is<00:10:20.240> represented<00:10:21.160> as"
+ },
+ {
+ "start": 621.63,
+ "duration": 0.0,
+ "text": "Shannon information is represented as"
+ },
+ {
+ "start": 621.64,
+ "duration": 0.0,
+ "text": "Shannon information is represented as log<00:10:21.880> base<00:10:22.240> two<00:10:22.760> of<00:10:23.000> one<00:10:23.200> over<00:10:23.760> the<00:10:23.880> probability"
+ },
+ {
+ "start": 624.75,
+ "duration": 0.0,
+ "text": "log base two of one over the probability"
+ },
+ {
+ "start": 624.76,
+ "duration": 0.0,
+ "text": "log base two of one over the probability distribution<00:10:25.440> associated<00:10:26.000> with<00:10:26.120> the<00:10:26.200> random"
+ },
+ {
+ "start": 626.51,
+ "duration": 0.0,
+ "text": "distribution associated with the random"
+ },
+ {
+ "start": 626.52,
+ "duration": 0.0,
+ "text": "distribution associated with the random variable<00:10:26.960> that<00:10:27.120> we're<00:10:27.240> considering.<00:10:28.040> This<00:10:28.200> is"
+ },
+ {
+ "start": 628.35,
+ "duration": 0.0,
+ "text": "variable that we're considering. This is"
+ },
+ {
+ "start": 628.36,
+ "duration": 0.0,
+ "text": "variable that we're considering. This is considered<00:10:28.800> the<00:10:28.920> surprisal<00:10:29.600> in<00:10:29.760> observing<00:10:30.800> uh"
+ },
+ {
+ "start": 631.43,
+ "duration": 0.0,
+ "text": "considered the surprisal in observing uh"
+ },
+ {
+ "start": 631.44,
+ "duration": 0.0,
+ "text": "considered the surprisal in observing uh the<00:10:31.600> value<00:10:31.920> of<00:10:32.000> this<00:10:32.160> random<00:10:32.440> variable<00:10:32.920> X.<00:10:33.680> The"
+ },
+ {
+ "start": 633.95,
+ "duration": 0.0,
+ "text": "the value of this random variable X. The"
+ },
+ {
+ "start": 633.96,
+ "duration": 0.0,
+ "text": "the value of this random variable X. The Shannon<00:10:34.280> entropy<00:10:34.720> is<00:10:34.920> the<00:10:35.120> average"
+ },
+ {
+ "start": 635.47,
+ "duration": 0.0,
+ "text": "Shannon entropy is the average"
+ },
+ {
+ "start": 635.48,
+ "duration": 0.0,
+ "text": "Shannon entropy is the average information<00:10:36.000> content<00:10:36.560> in<00:10:36.840> X,<00:10:37.600> and<00:10:37.840> the<00:10:37.920> mutual"
+ },
+ {
+ "start": 638.27,
+ "duration": 0.0,
+ "text": "information content in X, and the mutual"
+ },
+ {
+ "start": 638.28,
+ "duration": 0.0,
+ "text": "information content in X, and the mutual information<00:10:39.000> is<00:10:39.760> our<00:10:40.160> uncertainty<00:10:41.080> in<00:10:41.360> X"
+ },
+ {
+ "start": 641.63,
+ "duration": 0.0,
+ "text": "information is our uncertainty in X"
+ },
+ {
+ "start": 641.64,
+ "duration": 0.0,
+ "text": "information is our uncertainty in X after<00:10:42.080> our<00:10:42.600> the<00:10:42.680> reduction<00:10:43.160> in<00:10:43.240> our"
+ },
+ {
+ "start": 643.35,
+ "duration": 0.0,
+ "text": "after our the reduction in our"
+ },
+ {
+ "start": 643.36,
+ "duration": 0.0,
+ "text": "after our the reduction in our uncertainty<00:10:43.840> in<00:10:43.960> X<00:10:44.120> after<00:10:44.360> we<00:10:44.480> observe<00:10:45.040> Y."
+ },
+ {
+ "start": 645.95,
+ "duration": 0.0,
+ "text": "uncertainty in X after we observe Y."
+ },
+ {
+ "start": 645.96,
+ "duration": 0.0,
+ "text": "uncertainty in X after we observe Y. So,<00:10:46.760> Shannon<00:10:47.120> information<00:10:47.720> has<00:10:47.920> several"
+ },
+ {
+ "start": 648.31,
+ "duration": 0.0,
+ "text": "So, Shannon information has several"
+ },
+ {
+ "start": 648.32,
+ "duration": 0.0,
+ "text": "So, Shannon information has several really<00:10:48.560> key<00:10:48.840> properties.<00:10:49.480> Symmetry<00:10:49.920> of"
+ },
+ {
+ "start": 650.11,
+ "duration": 0.0,
+ "text": "really key properties. Symmetry of"
+ },
+ {
+ "start": 650.12,
+ "duration": 0.0,
+ "text": "really key properties. Symmetry of information,<00:10:50.760> so<00:10:50.880> this<00:10:51.040> is<00:10:51.200> related<00:10:51.600> to<00:10:51.680> that"
+ },
+ {
+ "start": 651.87,
+ "duration": 0.0,
+ "text": "information, so this is related to that"
+ },
+ {
+ "start": 651.88,
+ "duration": 0.0,
+ "text": "information, so this is related to that second<00:10:52.200> paradox<00:10:52.720> I<00:10:52.800> mentioned.<00:10:53.520> The"
+ },
+ {
+ "start": 653.59,
+ "duration": 0.0,
+ "text": "second paradox I mentioned. The"
+ },
+ {
+ "start": 653.6,
+ "duration": 0.0,
+ "text": "second paradox I mentioned. The information<00:10:54.080> that<00:10:54.200> we<00:10:54.320> get<00:10:54.640> in<00:10:55.120> predicting<00:10:55.520> X"
+ },
+ {
+ "start": 655.71,
+ "duration": 0.0,
+ "text": "information that we get in predicting X"
+ },
+ {
+ "start": 655.72,
+ "duration": 0.0,
+ "text": "information that we get in predicting X from<00:10:56.040> from<00:10:56.240> Y<00:10:56.520> is<00:10:56.680> the<00:10:56.760> same<00:10:56.960> as<00:10:57.080> predicting<00:10:57.440> Y"
+ },
+ {
+ "start": 657.59,
+ "duration": 0.0,
+ "text": "from from Y is the same as predicting Y"
+ },
+ {
+ "start": 657.6,
+ "duration": 0.0,
+ "text": "from from Y is the same as predicting Y from<00:10:58.320> X.<00:10:58.880> Um<00:10:59.400> deterministic<00:11:00.040> transformations"
+ },
+ {
+ "start": 660.79,
+ "duration": 0.0,
+ "text": "from X. Um deterministic transformations"
+ },
+ {
+ "start": 660.8,
+ "duration": 0.0,
+ "text": "from X. Um deterministic transformations don't<00:11:01.120> add<00:11:01.360> information,<00:11:01.920> so<00:11:02.080> if<00:11:02.200> we<00:11:02.320> have<00:11:02.880> a"
+ },
+ {
+ "start": 662.95,
+ "duration": 0.0,
+ "text": "don't add information, so if we have a"
+ },
+ {
+ "start": 662.96,
+ "duration": 0.0,
+ "text": "don't add information, so if we have a deterministic<00:11:03.560> transformation<00:11:04.240> F<00:11:04.520> operating"
+ },
+ {
+ "start": 664.95,
+ "duration": 0.0,
+ "text": "deterministic transformation F operating"
+ },
+ {
+ "start": 664.96,
+ "duration": 0.0,
+ "text": "deterministic transformation F operating on<00:11:05.160> X<00:11:05.400> to<00:11:05.480> give<00:11:05.640> us<00:11:05.800> Y,<00:11:06.360> the<00:11:06.480> entropy<00:11:06.880> of<00:11:07.000> Y"
+ },
+ {
+ "start": 667.19,
+ "duration": 0.0,
+ "text": "on X to give us Y, the entropy of Y"
+ },
+ {
+ "start": 667.2,
+ "duration": 0.0,
+ "text": "on X to give us Y, the entropy of Y given<00:11:07.480> X<00:11:07.680> is<00:11:08.000> zero,<00:11:08.560> and<00:11:08.920> as<00:11:09.080> a<00:11:09.120> corollary,<00:11:09.640> the"
+ },
+ {
+ "start": 670.19,
+ "duration": 0.0,
+ "text": "given X is zero, and as a corollary, the"
+ },
+ {
+ "start": 670.2,
+ "duration": 0.0,
+ "text": "given X is zero, and as a corollary, the entropy<00:11:10.560> of<00:11:10.680> f<00:11:10.800> of<00:11:10.920> X<00:11:11.160> is<00:11:11.400> always<00:11:11.680> less<00:11:11.839> than<00:11:11.960> or"
+ },
+ {
+ "start": 672.03,
+ "duration": 0.0,
+ "text": "entropy of f of X is always less than or"
+ },
+ {
+ "start": 672.04,
+ "duration": 0.0,
+ "text": "entropy of f of X is always less than or equal<00:11:12.400> to<00:11:12.680> the<00:11:12.760> entropy<00:11:13.120> of<00:11:13.280> X.<00:11:13.920> And<00:11:14.080> related"
+ },
+ {
+ "start": 674.43,
+ "duration": 0.0,
+ "text": "equal to the entropy of X. And related"
+ },
+ {
+ "start": 674.44,
+ "duration": 0.0,
+ "text": "equal to the entropy of X. And related to<00:11:14.560> that,<00:11:14.839> we<00:11:14.960> have<00:11:15.120> something<00:11:15.440> called<00:11:15.640> the"
+ },
+ {
+ "start": 675.95,
+ "duration": 0.0,
+ "text": "to that, we have something called the"
+ },
+ {
+ "start": 675.96,
+ "duration": 0.0,
+ "text": "to that, we have something called the data<00:11:16.080> processing<00:11:16.640> inequality.<00:11:17.520> If<00:11:17.720> Y<00:11:17.920> is"
+ },
+ {
+ "start": 678.03,
+ "duration": 0.0,
+ "text": "data processing inequality. If Y is"
+ },
+ {
+ "start": 678.04,
+ "duration": 0.0,
+ "text": "data processing inequality. If Y is obtained<00:11:18.520> from<00:11:18.760> X<00:11:18.960> through<00:11:19.160> some<00:11:19.400> processing,"
+ },
+ {
+ "start": 680.75,
+ "duration": 0.0,
+ "text": "obtained from X through some processing,"
+ },
+ {
+ "start": 680.76,
+ "duration": 0.0,
+ "text": "obtained from X through some processing, like<00:11:21.000> a<00:11:21.040> deterministic<00:11:21.600> transformation,<00:11:22.240> but"
+ },
+ {
+ "start": 682.39,
+ "duration": 0.0,
+ "text": "like a deterministic transformation, but"
+ },
+ {
+ "start": 682.4,
+ "duration": 0.0,
+ "text": "like a deterministic transformation, but not<00:11:22.560> necessarily,<00:11:23.600> and<00:11:23.760> similarly,<00:11:24.360> Z"
+ },
+ {
+ "start": 684.59,
+ "duration": 0.0,
+ "text": "not necessarily, and similarly, Z"
+ },
+ {
+ "start": 684.6,
+ "duration": 0.0,
+ "text": "not necessarily, and similarly, Z through<00:11:24.920> Y,<00:11:25.560> then<00:11:25.760> the<00:11:25.839> mutual<00:11:26.200> information"
+ },
+ {
+ "start": 686.75,
+ "duration": 0.0,
+ "text": "through Y, then the mutual information"
+ },
+ {
+ "start": 686.76,
+ "duration": 0.0,
+ "text": "through Y, then the mutual information between<00:11:27.200> X<00:11:27.440> and<00:11:27.560> Z<00:11:27.800> is<00:11:28.000> less<00:11:28.200> than<00:11:28.320> or<00:11:28.400> equal<00:11:28.800> to"
+ },
+ {
+ "start": 689.03,
+ "duration": 0.0,
+ "text": "between X and Z is less than or equal to"
+ },
+ {
+ "start": 689.04,
+ "duration": 0.0,
+ "text": "between X and Z is less than or equal to the<00:11:29.120> mutual<00:11:29.400> information<00:11:29.880> between<00:11:30.400> X<00:11:30.760> and<00:11:31.160> Y."
+ },
+ {
+ "start": 692.15,
+ "duration": 0.0,
+ "text": "the mutual information between X and Y."
+ },
+ {
+ "start": 692.16,
+ "duration": 0.0,
+ "text": "the mutual information between X and Y. Uh<00:11:32.400> objects<00:11:32.800> which<00:11:33.120> aren't<00:11:33.400> random<00:11:34.320> um<00:11:34.600> don't"
+ },
+ {
+ "start": 694.87,
+ "duration": 0.0,
+ "text": "Uh objects which aren't random um don't"
+ },
+ {
+ "start": 694.88,
+ "duration": 0.0,
+ "text": "Uh objects which aren't random um don't have<00:11:35.120> information<00:11:35.760> from<00:11:36.400> uh<00:11:36.560> the<00:11:36.680> perspective"
+ },
+ {
+ "start": 697.23,
+ "duration": 0.0,
+ "text": "have information from uh the perspective"
+ },
+ {
+ "start": 697.24,
+ "duration": 0.0,
+ "text": "have information from uh the perspective of<00:11:37.480> classical<00:11:37.960> Shannon<00:11:38.240> information<00:11:38.760> theory."
+ },
+ {
+ "start": 699.35,
+ "duration": 0.0,
+ "text": "of classical Shannon information theory."
+ },
+ {
+ "start": 699.36,
+ "duration": 0.0,
+ "text": "of classical Shannon information theory. This<00:11:39.560> is<00:11:39.680> different<00:11:40.040> than<00:11:40.360> algorithmic"
+ },
+ {
+ "start": 700.87,
+ "duration": 0.0,
+ "text": "This is different than algorithmic"
+ },
+ {
+ "start": 700.88,
+ "duration": 0.0,
+ "text": "This is different than algorithmic information<00:11:41.480> theory,<00:11:41.839> which<00:11:42.640> studies<00:11:43.120> the"
+ },
+ {
+ "start": 703.35,
+ "duration": 0.0,
+ "text": "information theory, which studies the"
+ },
+ {
+ "start": 703.36,
+ "duration": 0.0,
+ "text": "information theory, which studies the information<00:11:43.920> content<00:11:44.520> of<00:11:44.800> any<00:11:45.080> object,"
+ },
+ {
+ "start": 705.55,
+ "duration": 0.0,
+ "text": "information content of any object,"
+ },
+ {
+ "start": 705.56,
+ "duration": 0.0,
+ "text": "information content of any object, doesn't<00:11:45.839> have<00:11:46.000> to<00:11:46.080> be<00:11:46.200> random."
+ },
+ {
+ "start": 707.47,
+ "duration": 0.0,
+ "text": "doesn't have to be random."
+ },
+ {
+ "start": 707.48,
+ "duration": 0.0,
+ "text": "doesn't have to be random. In<00:11:47.839> algorithmic<00:11:48.280> information<00:11:48.800> theory,<00:11:49.120> the"
+ },
+ {
+ "start": 709.35,
+ "duration": 0.0,
+ "text": "In algorithmic information theory, the"
+ },
+ {
+ "start": 709.36,
+ "duration": 0.0,
+ "text": "In algorithmic information theory, the prefix<00:11:49.880> Kolmogorov<00:11:50.360> complexity<00:11:51.200> of<00:11:51.480> some"
+ },
+ {
+ "start": 711.67,
+ "duration": 0.0,
+ "text": "prefix Kolmogorov complexity of some"
+ },
+ {
+ "start": 711.68,
+ "duration": 0.0,
+ "text": "prefix Kolmogorov complexity of some object<00:11:52.120> X<00:11:52.839> is<00:11:53.160> the<00:11:53.280> shortest<00:11:53.920> self-delimiting"
+ },
+ {
+ "start": 714.91,
+ "duration": 0.0,
+ "text": "object X is the shortest self-delimiting"
+ },
+ {
+ "start": 714.92,
+ "duration": 0.0,
+ "text": "object X is the shortest self-delimiting program<00:11:55.360> that<00:11:55.560> outputs<00:11:56.040> X<00:11:56.360> and<00:11:56.560> then<00:11:56.920> halts."
+ },
+ {
+ "start": 717.99,
+ "duration": 0.0,
+ "text": "program that outputs X and then halts."
+ },
+ {
+ "start": 718.0,
+ "duration": 0.0,
+ "text": "program that outputs X and then halts. There's<00:11:58.240> also<00:11:58.520> a<00:11:58.600> similar<00:11:59.240> symmetry<00:11:59.680> of"
+ },
+ {
+ "start": 719.79,
+ "duration": 0.0,
+ "text": "There's also a similar symmetry of"
+ },
+ {
+ "start": 719.8,
+ "duration": 0.0,
+ "text": "There's also a similar symmetry of information<00:12:00.560> in"
+ },
+ {
+ "start": 722.19,
+ "duration": 0.0,
+ "text": "information in"
+ },
+ {
+ "start": 722.2,
+ "duration": 0.0,
+ "text": "information in algorithmic<00:12:02.680> information<00:12:03.240> theory<00:12:03.600> and<00:12:03.760> also"
+ },
+ {
+ "start": 723.99,
+ "duration": 0.0,
+ "text": "algorithmic information theory and also"
+ },
+ {
+ "start": 724.0,
+ "duration": 0.0,
+ "text": "algorithmic information theory and also an<00:12:04.120> information<00:12:05.040> non-increase<00:12:05.880> property"
+ },
+ {
+ "start": 726.35,
+ "duration": 0.0,
+ "text": "an information non-increase property"
+ },
+ {
+ "start": 726.36,
+ "duration": 0.0,
+ "text": "an information non-increase property through<00:12:06.680> deterministic<00:12:07.360> transformations<00:12:08.120> F."
+ },
+ {
+ "start": 728.95,
+ "duration": 0.0,
+ "text": "through deterministic transformations F."
+ },
+ {
+ "start": 728.96,
+ "duration": 0.0,
+ "text": "through deterministic transformations F. Like<00:12:09.400> Shannon<00:12:09.760> information,"
+ },
+ {
+ "start": 731.79,
+ "duration": 0.0,
+ "text": "Like Shannon information,"
+ },
+ {
+ "start": 731.8,
+ "duration": 0.0,
+ "text": "Like Shannon information, Kolmogorov<00:12:12.240> complexity<00:12:12.920> is<00:12:13.120> an<00:12:13.280> absolute"
+ },
+ {
+ "start": 733.67,
+ "duration": 0.0,
+ "text": "Kolmogorov complexity is an absolute"
+ },
+ {
+ "start": 733.68,
+ "duration": 0.0,
+ "text": "Kolmogorov complexity is an absolute measure<00:12:14.000> of<00:12:14.200> information<00:12:15.240> and<00:12:15.600> doesn't"
+ },
+ {
+ "start": 735.95,
+ "duration": 0.0,
+ "text": "measure of information and doesn't"
+ },
+ {
+ "start": 735.96,
+ "duration": 0.0,
+ "text": "measure of information and doesn't separate<00:12:17.120> useful<00:12:17.600> structure<00:12:18.080> from"
+ },
+ {
+ "start": 738.35,
+ "duration": 0.0,
+ "text": "separate useful structure from"
+ },
+ {
+ "start": 738.36,
+ "duration": 0.0,
+ "text": "separate useful structure from unpredictable<00:12:19.040> structure,<00:12:19.480> like<00:12:19.640> we<00:12:19.760> were"
+ },
+ {
+ "start": 739.91,
+ "duration": 0.0,
+ "text": "unpredictable structure, like we were"
+ },
+ {
+ "start": 739.92,
+ "duration": 0.0,
+ "text": "unpredictable structure, like we were considering<00:12:20.440> with<00:12:20.560> some<00:12:20.720> of<00:12:20.800> those<00:12:21.000> examples"
+ },
+ {
+ "start": 741.51,
+ "duration": 0.0,
+ "text": "considering with some of those examples"
+ },
+ {
+ "start": 741.52,
+ "duration": 0.0,
+ "text": "considering with some of those examples earlier<00:12:21.880> with<00:12:22.040> the<00:12:22.120> natural<00:12:22.520> images<00:12:23.040> and<00:12:23.280> and"
+ },
+ {
+ "start": 743.43,
+ "duration": 0.0,
+ "text": "earlier with the natural images and and"
+ },
+ {
+ "start": 743.44,
+ "duration": 0.0,
+ "text": "earlier with the natural images and and white<00:12:23.640> noise.<00:12:24.480> It's<00:12:24.640> incomputable.<00:12:25.839> Uh<00:12:26.000> we"
+ },
+ {
+ "start": 746.11,
+ "duration": 0.0,
+ "text": "white noise. It's incomputable. Uh we"
+ },
+ {
+ "start": 746.12,
+ "duration": 0.0,
+ "text": "white noise. It's incomputable. Uh we don't<00:12:26.320> know<00:12:26.440> what<00:12:26.600> the<00:12:26.680> shortest<00:12:27.040> program<00:12:27.440> is,"
+ },
+ {
+ "start": 747.67,
+ "duration": 0.0,
+ "text": "don't know what the shortest program is,"
+ },
+ {
+ "start": 747.68,
+ "duration": 0.0,
+ "text": "don't know what the shortest program is, but<00:12:28.320> it<00:12:28.440> can<00:12:28.560> be<00:12:28.680> upper<00:12:28.880> bounded<00:12:29.320> and<00:12:29.400> it<00:12:29.480> can"
+ },
+ {
+ "start": 749.59,
+ "duration": 0.0,
+ "text": "but it can be upper bounded and it can"
+ },
+ {
+ "start": 749.6,
+ "duration": 0.0,
+ "text": "but it can be upper bounded and it can still<00:12:29.760> be<00:12:29.880> very<00:12:30.120> useful.<00:12:30.480> And<00:12:30.600> so,<00:12:30.760> we<00:12:30.920> found"
+ },
+ {
+ "start": 751.11,
+ "duration": 0.0,
+ "text": "still be very useful. And so, we found"
+ },
+ {
+ "start": 751.12,
+ "duration": 0.0,
+ "text": "still be very useful. And so, we found Kolmogorov<00:12:31.600> complexity<00:12:32.600> very<00:12:33.120> useful<00:12:33.520> as<00:12:33.680> a"
+ },
+ {
+ "start": 753.87,
+ "duration": 0.0,
+ "text": "Kolmogorov complexity very useful as a"
+ },
+ {
+ "start": 753.88,
+ "duration": 0.0,
+ "text": "Kolmogorov complexity very useful as a concept<00:12:34.480> in<00:12:34.640> formulating<00:12:35.320> generalization"
+ },
+ {
+ "start": 756.03,
+ "duration": 0.0,
+ "text": "concept in formulating generalization"
+ },
+ {
+ "start": 756.04,
+ "duration": 0.0,
+ "text": "concept in formulating generalization bounds<00:12:36.400> for<00:12:36.520> large<00:12:36.920> neural<00:12:37.120> networks."
+ },
+ {
+ "start": 759.8,
+ "duration": 0.0,
+ "text": "There's<00:12:40.320> um<00:12:40.760> a<00:12:41.120> a<00:12:41.200> a<00:12:41.240> slightly<00:12:41.920> less"
+ },
+ {
+ "start": 762.19,
+ "duration": 0.0,
+ "text": "There's um a a a slightly less"
+ },
+ {
+ "start": 762.2,
+ "duration": 0.0,
+ "text": "There's um a a a slightly less well-known<00:12:42.760> concept<00:12:43.240> called<00:12:43.480> sophistication"
+ },
+ {
+ "start": 764.39,
+ "duration": 0.0,
+ "text": "well-known concept called sophistication"
+ },
+ {
+ "start": 764.4,
+ "duration": 0.0,
+ "text": "well-known concept called sophistication in<00:12:44.600> algorithmic<00:12:45.280> information<00:12:45.839> theory,<00:12:46.120> which"
+ },
+ {
+ "start": 766.39,
+ "duration": 0.0,
+ "text": "in algorithmic information theory, which"
+ },
+ {
+ "start": 766.4,
+ "duration": 0.0,
+ "text": "in algorithmic information theory, which is<00:12:46.600> the<00:12:46.800> smallest<00:12:47.320> Kolmogorov<00:12:47.800> complexity<00:12:48.440> of"
+ },
+ {
+ "start": 768.55,
+ "duration": 0.0,
+ "text": "is the smallest Kolmogorov complexity of"
+ },
+ {
+ "start": 768.56,
+ "duration": 0.0,
+ "text": "is the smallest Kolmogorov complexity of a<00:12:48.640> set<00:12:49.000> S<00:12:49.240> such<00:12:49.480> that<00:12:49.640> X<00:12:49.839> is<00:12:50.000> a<00:12:50.040> random<00:12:50.400> element"
+ },
+ {
+ "start": 770.75,
+ "duration": 0.0,
+ "text": "a set S such that X is a random element"
+ },
+ {
+ "start": 770.76,
+ "duration": 0.0,
+ "text": "a set S such that X is a random element from<00:12:50.920> that<00:12:51.120> set.<00:12:51.680> This<00:12:51.880> does<00:12:52.080> try<00:12:52.320> to<00:12:52.440> carve"
+ },
+ {
+ "start": 772.829,
+ "duration": 0.0,
+ "text": "from that set. This does try to carve"
+ },
+ {
+ "start": 772.839,
+ "duration": 0.0,
+ "text": "from that set. This does try to carve out<00:12:53.520> uh<00:12:54.040> structural<00:12:54.680> information<00:12:55.280> content"
+ },
+ {
+ "start": 775.75,
+ "duration": 0.0,
+ "text": "out uh structural information content"
+ },
+ {
+ "start": 775.76,
+ "duration": 0.0,
+ "text": "out uh structural information content from<00:12:56.040> random<00:12:56.360> information,<00:12:57.320> but<00:12:57.640> it's"
+ },
+ {
+ "start": 777.829,
+ "duration": 0.0,
+ "text": "from random information, but it's"
+ },
+ {
+ "start": 777.839,
+ "duration": 0.0,
+ "text": "from random information, but it's difficult<00:12:58.280> to<00:12:58.400> find<00:12:59.080> high<00:12:59.280> sophistication"
+ },
+ {
+ "start": 780.35,
+ "duration": 0.0,
+ "text": "difficult to find high sophistication"
+ },
+ {
+ "start": 780.36,
+ "duration": 0.0,
+ "text": "difficult to find high sophistication objects<00:13:01.120> due<00:13:01.320> to<00:13:01.680> Shannon's<00:13:02.120> incompleteness"
+ },
+ {
+ "start": 782.71,
+ "duration": 0.0,
+ "text": "objects due to Shannon's incompleteness"
+ },
+ {
+ "start": 782.72,
+ "duration": 0.0,
+ "text": "objects due to Shannon's incompleteness theorem."
+ },
+ {
+ "start": 783.67,
+ "duration": 0.0,
+ "text": "theorem."
+ },
+ {
+ "start": 783.68,
+ "duration": 0.0,
+ "text": "theorem. And"
+ },
+ {
+ "start": 785.35,
+ "duration": 0.0,
+ "text": "And"
+ },
+ {
+ "start": 785.36,
+ "duration": 0.0,
+ "text": "And since<00:13:05.680> it<00:13:06.000> is<00:13:06.200> not<00:13:06.480> considering<00:13:06.960> computation,"
+ },
+ {
+ "start": 787.87,
+ "duration": 0.0,
+ "text": "since it is not considering computation,"
+ },
+ {
+ "start": 787.88,
+ "duration": 0.0,
+ "text": "since it is not considering computation, typically<00:13:08.440> complex<00:13:08.960> objects<00:13:09.480> often<00:13:09.800> appear"
+ },
+ {
+ "start": 790.07,
+ "duration": 0.0,
+ "text": "typically complex objects often appear"
+ },
+ {
+ "start": 790.08,
+ "duration": 0.0,
+ "text": "typically complex objects often appear to<00:13:10.400> lose<00:13:10.680> their<00:13:10.960> complexity<00:13:11.560> when<00:13:11.720> measured"
+ },
+ {
+ "start": 792.07,
+ "duration": 0.0,
+ "text": "to lose their complexity when measured"
+ },
+ {
+ "start": 792.08,
+ "duration": 0.0,
+ "text": "to lose their complexity when measured by<00:13:12.360> sophistication,<00:13:13.600> and<00:13:13.800> it's<00:13:13.960> actually<00:13:14.520> not"
+ },
+ {
+ "start": 794.75,
+ "duration": 0.0,
+ "text": "by sophistication, and it's actually not"
+ },
+ {
+ "start": 794.76,
+ "duration": 0.0,
+ "text": "by sophistication, and it's actually not trivial<00:13:15.280> to<00:13:15.720> make<00:13:15.960> sophistication"
+ },
+ {
+ "start": 797.03,
+ "duration": 0.0,
+ "text": "trivial to make sophistication"
+ },
+ {
+ "start": 797.04,
+ "duration": 0.0,
+ "text": "trivial to make sophistication time-bounded.<00:13:17.680> So,<00:13:17.839> in<00:13:17.920> the<00:13:18.040> paper,<00:13:18.360> we<00:13:18.480> show"
+ },
+ {
+ "start": 798.67,
+ "duration": 0.0,
+ "text": "time-bounded. So, in the paper, we show"
+ },
+ {
+ "start": 798.68,
+ "duration": 0.0,
+ "text": "time-bounded. So, in the paper, we show that<00:13:18.839> it<00:13:19.080> becomes<00:13:19.440> essentially<00:13:19.920> constant<00:13:20.320> for"
+ },
+ {
+ "start": 800.43,
+ "duration": 0.0,
+ "text": "that it becomes essentially constant for"
+ },
+ {
+ "start": 800.44,
+ "duration": 0.0,
+ "text": "that it becomes essentially constant for all<00:13:20.640> strings<00:13:21.400> when<00:13:21.560> you<00:13:21.640> try<00:13:21.800> to<00:13:21.960> do<00:13:22.120> that."
+ },
+ {
+ "start": 803.11,
+ "duration": 0.0,
+ "text": "all strings when you try to do that."
+ },
+ {
+ "start": 803.12,
+ "duration": 0.0,
+ "text": "all strings when you try to do that. Uh<00:13:23.280> so,<00:13:23.480> it's<00:13:24.200> our<00:13:24.360> belief<00:13:24.760> that<00:13:25.240> really"
+ },
+ {
+ "start": 805.51,
+ "duration": 0.0,
+ "text": "Uh so, it's our belief that really"
+ },
+ {
+ "start": 805.52,
+ "duration": 0.0,
+ "text": "Uh so, it's our belief that really understanding<00:13:26.040> the<00:13:26.120> role<00:13:26.280> of<00:13:26.360> computation<00:13:27.040> is"
+ },
+ {
+ "start": 807.27,
+ "duration": 0.0,
+ "text": "understanding the role of computation is"
+ },
+ {
+ "start": 807.28,
+ "duration": 0.0,
+ "text": "understanding the role of computation is central<00:13:27.760> to<00:13:28.120> understanding<00:13:29.080> these<00:13:29.280> phenomena"
+ },
+ {
+ "start": 809.91,
+ "duration": 0.0,
+ "text": "central to understanding these phenomena"
+ },
+ {
+ "start": 809.92,
+ "duration": 0.0,
+ "text": "central to understanding these phenomena like<00:13:30.360> emergence<00:13:31.080> and<00:13:31.440> induction,<00:13:32.240> chaos,"
+ },
+ {
+ "start": 812.67,
+ "duration": 0.0,
+ "text": "like emergence and induction, chaos,"
+ },
+ {
+ "start": 812.68,
+ "duration": 0.0,
+ "text": "like emergence and induction, chaos, cryptography."
+ },
+ {
+ "start": 814.75,
+ "duration": 0.0,
+ "text": "cryptography."
+ },
+ {
+ "start": 814.76,
+ "duration": 0.0,
+ "text": "cryptography. And<00:13:34.880> I<00:13:34.920> thought<00:13:35.280> I<00:13:35.480> had<00:13:35.800> to<00:13:35.880> mention<00:13:36.440> Levin"
+ },
+ {
+ "start": 816.75,
+ "duration": 0.0,
+ "text": "And I thought I had to mention Levin"
+ },
+ {
+ "start": 816.76,
+ "duration": 0.0,
+ "text": "And I thought I had to mention Levin complexity<00:13:37.400> because<00:13:37.880> this<00:13:38.080> is<00:13:38.200> the<00:13:38.320> Levin"
+ },
+ {
+ "start": 818.67,
+ "duration": 0.0,
+ "text": "complexity because this is the Levin"
+ },
+ {
+ "start": 818.68,
+ "duration": 0.0,
+ "text": "complexity because this is the Levin group<00:13:39.000> that<00:13:39.560> introduced<00:13:40.120> Levin<00:13:40.400> complexity."
+ },
+ {
+ "start": 821.31,
+ "duration": 0.0,
+ "text": "group that introduced Levin complexity."
+ },
+ {
+ "start": 821.32,
+ "duration": 0.0,
+ "text": "group that introduced Levin complexity. I'm<00:13:41.440> just<00:13:41.600> kidding,<00:13:41.920> I<00:13:42.080> I<00:13:42.200> don't<00:13:42.440> think<00:13:42.600> that."
+ },
+ {
+ "start": 823.15,
+ "duration": 0.0,
+ "text": "I'm just kidding, I I don't think that."
+ },
+ {
+ "start": 823.16,
+ "duration": 0.0,
+ "text": "I'm just kidding, I I don't think that. Um"
+ },
+ {
+ "start": 824.31,
+ "duration": 0.0,
+ "text": "Um"
+ },
+ {
+ "start": 824.32,
+ "duration": 0.0,
+ "text": "Um uh<00:13:44.400> so,<00:13:44.520> Levin<00:13:44.800> complexity<00:13:45.320> is<00:13:45.520> a"
+ },
+ {
+ "start": 825.55,
+ "duration": 0.0,
+ "text": "uh so, Levin complexity is a"
+ },
+ {
+ "start": 825.56,
+ "duration": 0.0,
+ "text": "uh so, Levin complexity is a compute-limited<00:13:46.320> notion<00:13:46.640> of<00:13:46.760> Kolmogorov"
+ },
+ {
+ "start": 827.23,
+ "duration": 0.0,
+ "text": "compute-limited notion of Kolmogorov"
+ },
+ {
+ "start": 827.24,
+ "duration": 0.0,
+ "text": "compute-limited notion of Kolmogorov complexity.<00:13:48.320> It's<00:13:48.520> concerned<00:13:49.080> with<00:13:49.560> how"
+ },
+ {
+ "start": 829.99,
+ "duration": 0.0,
+ "text": "complexity. It's concerned with how"
+ },
+ {
+ "start": 830.0,
+ "duration": 0.0,
+ "text": "complexity. It's concerned with how compactly<00:13:50.560> you<00:13:50.680> can<00:13:50.839> generate<00:13:51.240> one<00:13:51.400> specific"
+ },
+ {
+ "start": 832.03,
+ "duration": 0.0,
+ "text": "compactly you can generate one specific"
+ },
+ {
+ "start": 832.04,
+ "duration": 0.0,
+ "text": "compactly you can generate one specific output,<00:13:52.880> rather<00:13:53.120> than<00:13:53.320> what<00:13:53.440> can<00:13:53.560> be"
+ },
+ {
+ "start": 833.63,
+ "duration": 0.0,
+ "text": "output, rather than what can be"
+ },
+ {
+ "start": 833.64,
+ "duration": 0.0,
+ "text": "output, rather than what can be extracted<00:13:54.080> from<00:13:54.200> a<00:13:54.240> distribution.<00:13:55.440> Um<00:13:55.839> but<00:13:56.160> it"
+ },
+ {
+ "start": 836.35,
+ "duration": 0.0,
+ "text": "extracted from a distribution. Um but it"
+ },
+ {
+ "start": 836.36,
+ "duration": 0.0,
+ "text": "extracted from a distribution. Um but it really<00:13:56.600> doesn't<00:13:56.960> do<00:13:57.240> what<00:13:57.600> we're<00:13:57.800> looking<00:13:58.200> for"
+ },
+ {
+ "start": 838.63,
+ "duration": 0.0,
+ "text": "really doesn't do what we're looking for"
+ },
+ {
+ "start": 838.64,
+ "duration": 0.0,
+ "text": "really doesn't do what we're looking for in<00:13:59.040> appiplexity.<00:14:00.160> Um<00:14:00.400> for<00:14:00.520> example,"
+ },
+ {
+ "start": 841.19,
+ "duration": 0.0,
+ "text": "in appiplexity. Um for example,"
+ },
+ {
+ "start": 841.2,
+ "duration": 0.0,
+ "text": "in appiplexity. Um for example, pseudo-random<00:14:01.800> numbers<00:14:02.280> would<00:14:02.440> be<00:14:02.560> treated"
+ },
+ {
+ "start": 843.03,
+ "duration": 0.0,
+ "text": "pseudo-random numbers would be treated"
+ },
+ {
+ "start": 843.04,
+ "duration": 0.0,
+ "text": "pseudo-random numbers would be treated as<00:14:03.200> simple<00:14:03.680> by<00:14:04.040> Levin<00:14:04.320> complexity<00:14:04.880> because"
+ },
+ {
+ "start": 845.31,
+ "duration": 0.0,
+ "text": "as simple by Levin complexity because"
+ },
+ {
+ "start": 845.32,
+ "duration": 0.0,
+ "text": "as simple by Levin complexity because there<00:14:05.520> is<00:14:05.760> a<00:14:05.800> short<00:14:06.080> program<00:14:06.560> that<00:14:06.800> can"
+ },
+ {
+ "start": 846.99,
+ "duration": 0.0,
+ "text": "there is a short program that can"
+ },
+ {
+ "start": 847.0,
+ "duration": 0.0,
+ "text": "there is a short program that can generate<00:14:07.440> them.<00:14:07.640> You<00:14:07.720> just<00:14:08.000> run<00:14:08.520> your"
+ },
+ {
+ "start": 848.63,
+ "duration": 0.0,
+ "text": "generate them. You just run your"
+ },
+ {
+ "start": 848.64,
+ "duration": 0.0,
+ "text": "generate them. You just run your generator<00:14:09.240> on<00:14:09.480> some<00:14:09.680> seed,<00:14:10.480> um<00:14:10.839> and<00:14:11.360> uh<00:14:11.720> that"
+ },
+ {
+ "start": 851.91,
+ "duration": 0.0,
+ "text": "generator on some seed, um and uh that"
+ },
+ {
+ "start": 851.92,
+ "duration": 0.0,
+ "text": "generator on some seed, um and uh that can<00:14:12.040> be<00:14:12.120> done<00:14:12.320> in<00:14:12.440> a<00:14:12.480> very<00:14:12.640> short<00:14:12.880> amount<00:14:13.079> of"
+ },
+ {
+ "start": 853.19,
+ "duration": 0.0,
+ "text": "can be done in a very short amount of"
+ },
+ {
+ "start": 853.2,
+ "duration": 0.0,
+ "text": "can be done in a very short amount of time.<00:14:14.000> Um<00:14:14.760> and<00:14:15.440> uh"
+ },
+ {
+ "start": 856.51,
+ "duration": 0.0,
+ "text": "time. Um and uh"
+ },
+ {
+ "start": 856.52,
+ "duration": 0.0,
+ "text": "time. Um and uh this<00:14:16.720> is<00:14:16.880> really,<00:14:17.280> you<00:14:17.400> know,<00:14:17.640> a<00:14:17.680> distinction"
+ },
+ {
+ "start": 858.19,
+ "duration": 0.0,
+ "text": "this is really, you know, a distinction"
+ },
+ {
+ "start": 858.2,
+ "duration": 0.0,
+ "text": "this is really, you know, a distinction that<00:14:18.400> we're<00:14:18.880> focused<00:14:19.320> on<00:14:19.680> in<00:14:19.880> this<00:14:20.160> this<00:14:20.360> work."
+ },
+ {
+ "start": 861.59,
+ "duration": 0.0,
+ "text": "that we're focused on in this this work."
+ },
+ {
+ "start": 861.6,
+ "duration": 0.0,
+ "text": "that we're focused on in this this work. Okay,<00:14:21.959> and<00:14:22.280> finally,<00:14:22.920> uh"
+ },
+ {
+ "start": 863.79,
+ "duration": 0.0,
+ "text": "Okay, and finally, uh"
+ },
+ {
+ "start": 863.8,
+ "duration": 0.0,
+ "text": "Okay, and finally, uh uh<00:14:24.079> we<00:14:24.240> can<00:14:24.400> sort<00:14:24.600> of<00:14:25.240> consider<00:14:25.680> what<00:14:25.880> it"
+ },
+ {
+ "start": 865.99,
+ "duration": 0.0,
+ "text": "uh we can sort of consider what it"
+ },
+ {
+ "start": 866.0,
+ "duration": 0.0,
+ "text": "uh we can sort of consider what it actually<00:14:26.320> means<00:14:26.560> to<00:14:26.680> be<00:14:26.920> random.<00:14:27.360> This<00:14:27.560> has"
+ },
+ {
+ "start": 867.75,
+ "duration": 0.0,
+ "text": "actually means to be random. This has"
+ },
+ {
+ "start": 867.76,
+ "duration": 0.0,
+ "text": "actually means to be random. This has been<00:14:28.280> uh"
+ },
+ {
+ "start": 868.829,
+ "duration": 0.0,
+ "text": "been uh"
+ },
+ {
+ "start": 868.839,
+ "duration": 0.0,
+ "text": "been uh something<00:14:29.440> a<00:14:29.520> discussion<00:14:30.040> of<00:14:30.240> of<00:14:30.400> great"
+ },
+ {
+ "start": 870.63,
+ "duration": 0.0,
+ "text": "something a discussion of of great"
+ },
+ {
+ "start": 870.64,
+ "duration": 0.0,
+ "text": "something a discussion of of great interest<00:14:31.040> to<00:14:31.240> mathematicians<00:14:32.160> throughout"
+ },
+ {
+ "start": 872.47,
+ "duration": 0.0,
+ "text": "interest to mathematicians throughout"
+ },
+ {
+ "start": 872.48,
+ "duration": 0.0,
+ "text": "interest to mathematicians throughout the<00:14:32.560> 20th<00:14:32.920> century.<00:14:33.720> Uh<00:14:33.959> so,<00:14:34.240> a<00:14:34.320> random"
+ },
+ {
+ "start": 874.59,
+ "duration": 0.0,
+ "text": "the 20th century. Uh so, a random"
+ },
+ {
+ "start": 874.6,
+ "duration": 0.0,
+ "text": "the 20th century. Uh so, a random variable<00:14:34.959> is<00:14:35.040> defined<00:14:35.440> as<00:14:35.560> a<00:14:35.600> map<00:14:35.920> from<00:14:36.320> a"
+ },
+ {
+ "start": 876.35,
+ "duration": 0.0,
+ "text": "variable is defined as a map from a"
+ },
+ {
+ "start": 876.36,
+ "duration": 0.0,
+ "text": "variable is defined as a map from a measurable<00:14:36.800> probability<00:14:37.320> space<00:14:37.600> to"
+ },
+ {
+ "start": 877.67,
+ "duration": 0.0,
+ "text": "measurable probability space to"
+ },
+ {
+ "start": 877.68,
+ "duration": 0.0,
+ "text": "measurable probability space to different<00:14:38.000> outcomes<00:14:39.079> with<00:14:39.240> probabilities"
+ },
+ {
+ "start": 879.71,
+ "duration": 0.0,
+ "text": "different outcomes with probabilities"
+ },
+ {
+ "start": 879.72,
+ "duration": 0.0,
+ "text": "different outcomes with probabilities corresponding<00:14:40.240> to<00:14:40.320> the<00:14:40.400> measure<00:14:40.720> of<00:14:40.800> that"
+ },
+ {
+ "start": 880.949,
+ "duration": 0.0,
+ "text": "corresponding to the measure of that"
+ },
+ {
+ "start": 880.959,
+ "duration": 0.0,
+ "text": "corresponding to the measure of that space<00:14:41.280> that<00:14:41.440> lead<00:14:41.600> to<00:14:41.680> a<00:14:41.760> certain<00:14:42.040> outcome.<00:14:43.079> In"
+ },
+ {
+ "start": 883.55,
+ "duration": 0.0,
+ "text": "space that lead to a certain outcome. In"
+ },
+ {
+ "start": 883.56,
+ "duration": 0.0,
+ "text": "space that lead to a certain outcome. In uh<00:14:43.760> the<00:14:43.839> mid-20th<00:14:44.400> century,<00:14:44.800> there<00:14:45.000> was"
+ },
+ {
+ "start": 885.31,
+ "duration": 0.0,
+ "text": "uh the mid-20th century, there was"
+ },
+ {
+ "start": 885.32,
+ "duration": 0.0,
+ "text": "uh the mid-20th century, there was interest<00:14:45.880> in<00:14:46.480> precisely<00:14:46.959> formalizing<00:14:47.680> what"
+ },
+ {
+ "start": 887.829,
+ "duration": 0.0,
+ "text": "interest in precisely formalizing what"
+ },
+ {
+ "start": 887.839,
+ "duration": 0.0,
+ "text": "interest in precisely formalizing what it<00:14:47.920> means<00:14:48.160> for<00:14:48.280> a<00:14:48.320> sample<00:14:48.680> to<00:14:48.839> be<00:14:49.280> a<00:14:49.440> random"
+ },
+ {
+ "start": 889.75,
+ "duration": 0.0,
+ "text": "it means for a sample to be a random"
+ },
+ {
+ "start": 889.76,
+ "duration": 0.0,
+ "text": "it means for a sample to be a random draw<00:14:50.040> from<00:14:50.240> a<00:14:50.280> distribution,<00:14:51.440> and"
+ },
+ {
+ "start": 892.63,
+ "duration": 0.0,
+ "text": "draw from a distribution, and"
+ },
+ {
+ "start": 892.64,
+ "duration": 0.0,
+ "text": "draw from a distribution, and central<00:14:53.040> to<00:14:53.160> their<00:14:53.360> considerations<00:14:54.560> um<00:14:55.000> was"
+ },
+ {
+ "start": 895.59,
+ "duration": 0.0,
+ "text": "central to their considerations um was"
+ },
+ {
+ "start": 895.6,
+ "duration": 0.0,
+ "text": "central to their considerations um was uh"
+ },
+ {
+ "start": 896.39,
+ "duration": 0.0,
+ "text": "uh"
+ },
+ {
+ "start": 896.4,
+ "duration": 0.0,
+ "text": "uh uh<00:14:56.480> sort<00:14:56.640> of<00:14:56.760> having"
+ },
+ {
+ "start": 897.63,
+ "duration": 0.0,
+ "text": "uh sort of having"
+ },
+ {
+ "start": 897.64,
+ "duration": 0.0,
+ "text": "uh sort of having uh<00:14:58.120> large<00:14:59.120> uh<00:14:59.400> uniform<00:15:00.400> sequences<00:15:01.280> uh<00:15:01.600> uh<00:15:01.839> for"
+ },
+ {
+ "start": 902.069,
+ "duration": 0.0,
+ "text": "uh large uh uniform sequences uh uh for"
+ },
+ {
+ "start": 902.079,
+ "duration": 0.0,
+ "text": "uh large uh uniform sequences uh uh for for<00:15:02.240> binary<00:15:02.560> numbers<00:15:03.440> uh<00:15:03.640> from<00:15:03.800> which<00:15:03.959> we<00:15:04.040> can"
+ },
+ {
+ "start": 904.23,
+ "duration": 0.0,
+ "text": "for binary numbers uh from which we can"
+ },
+ {
+ "start": 904.24,
+ "duration": 0.0,
+ "text": "for binary numbers uh from which we can construct<00:15:04.720> other<00:15:05.040> distributions.<00:15:06.280> And<00:15:06.640> if<00:15:06.760> we"
+ },
+ {
+ "start": 906.829,
+ "duration": 0.0,
+ "text": "construct other distributions. And if we"
+ },
+ {
+ "start": 906.839,
+ "duration": 0.0,
+ "text": "construct other distributions. And if we think<00:15:07.040> about<00:15:07.280> these<00:15:07.480> sequences,<00:15:08.079> we<00:15:08.280> could"
+ },
+ {
+ "start": 909.069,
+ "duration": 0.0,
+ "text": "think about these sequences, we could"
+ },
+ {
+ "start": 909.079,
+ "duration": 0.0,
+ "text": "think about these sequences, we could ask<00:15:09.720> um<00:15:10.440> whether<00:15:11.200> all<00:15:11.400> of<00:15:11.440> these<00:15:11.600> sequences"
+ },
+ {
+ "start": 912.069,
+ "duration": 0.0,
+ "text": "ask um whether all of these sequences"
+ },
+ {
+ "start": 912.079,
+ "duration": 0.0,
+ "text": "ask um whether all of these sequences are<00:15:12.200> equally<00:15:12.520> random<00:15:12.880> since<00:15:13.079> they're<00:15:13.240> equally"
+ },
+ {
+ "start": 913.59,
+ "duration": 0.0,
+ "text": "are equally random since they're equally"
+ },
+ {
+ "start": 913.6,
+ "duration": 0.0,
+ "text": "are equally random since they're equally likely.<00:15:14.040> So,<00:15:14.160> we<00:15:14.280> could<00:15:14.440> have<00:15:14.560> a<00:15:14.640> sequence<00:15:15.079> of"
+ },
+ {
+ "start": 915.19,
+ "duration": 0.0,
+ "text": "likely. So, we could have a sequence of"
+ },
+ {
+ "start": 915.2,
+ "duration": 0.0,
+ "text": "likely. So, we could have a sequence of just<00:15:15.440> repeating<00:15:15.880> ones,<00:15:16.120> for<00:15:16.240> example,<00:15:17.040> versus"
+ },
+ {
+ "start": 917.47,
+ "duration": 0.0,
+ "text": "just repeating ones, for example, versus"
+ },
+ {
+ "start": 917.48,
+ "duration": 0.0,
+ "text": "just repeating ones, for example, versus a<00:15:17.560> sequence<00:15:18.040> that<00:15:18.280> looks<00:15:18.920> much<00:15:19.120> more"
+ },
+ {
+ "start": 919.31,
+ "duration": 0.0,
+ "text": "a sequence that looks much more"
+ },
+ {
+ "start": 919.32,
+ "duration": 0.0,
+ "text": "a sequence that looks much more unpredictable,<00:15:20.120> like<00:15:20.360> 1001110"
+ },
+ {
+ "start": 921.949,
+ "duration": 0.0,
+ "text": "unpredictable, like 1001110"
+ },
+ {
+ "start": 921.959,
+ "duration": 0.0,
+ "text": "unpredictable, like 1001110 and<00:15:22.079> so<00:15:22.200> on.<00:15:22.920> Um<00:15:23.360> and<00:15:23.640> so,<00:15:24.440> uh<00:15:24.600> these<00:15:24.760> two"
+ },
+ {
+ "start": 924.91,
+ "duration": 0.0,
+ "text": "and so on. Um and so, uh these two"
+ },
+ {
+ "start": 924.92,
+ "duration": 0.0,
+ "text": "and so on. Um and so, uh these two sequences<00:15:25.640> have<00:15:25.920> the<00:15:26.040> same<00:15:26.360> probability"
+ },
+ {
+ "start": 926.99,
+ "duration": 0.0,
+ "text": "sequences have the same probability"
+ },
+ {
+ "start": 927.0,
+ "duration": 0.0,
+ "text": "sequences have the same probability mass,<00:15:28.000> um<00:15:28.480> and<00:15:28.680> so,<00:15:28.839> in<00:15:28.959> some<00:15:29.200> sense,<00:15:29.760> it<00:15:29.959> might"
+ },
+ {
+ "start": 930.19,
+ "duration": 0.0,
+ "text": "mass, um and so, in some sense, it might"
+ },
+ {
+ "start": 930.2,
+ "duration": 0.0,
+ "text": "mass, um and so, in some sense, it might seem<00:15:30.440> like<00:15:30.680> they're<00:15:30.920> equally<00:15:31.400> random,<00:15:32.160> but"
+ },
+ {
+ "start": 932.43,
+ "duration": 0.0,
+ "text": "seem like they're equally random, but"
+ },
+ {
+ "start": 932.44,
+ "duration": 0.0,
+ "text": "seem like they're equally random, but intuitively,<00:15:33.200> the<00:15:33.360> first<00:15:33.640> sequence<00:15:34.320> doesn't"
+ },
+ {
+ "start": 934.79,
+ "duration": 0.0,
+ "text": "intuitively, the first sequence doesn't"
+ },
+ {
+ "start": 934.8,
+ "duration": 0.0,
+ "text": "intuitively, the first sequence doesn't seem<00:15:35.040> as<00:15:35.240> random<00:15:35.720> as<00:15:36.040> the<00:15:36.160> second.<00:15:36.959> And<00:15:37.200> so,<00:15:37.640> to"
+ },
+ {
+ "start": 937.75,
+ "duration": 0.0,
+ "text": "seem as random as the second. And so, to"
+ },
+ {
+ "start": 937.76,
+ "duration": 0.0,
+ "text": "seem as random as the second. And so, to get<00:15:37.959> some<00:15:38.120> intuition<00:15:38.560> about<00:15:38.839> this,<00:15:39.040> we<00:15:39.160> could"
+ },
+ {
+ "start": 939.35,
+ "duration": 0.0,
+ "text": "get some intuition about this, we could"
+ },
+ {
+ "start": 939.36,
+ "duration": 0.0,
+ "text": "get some intuition about this, we could start<00:15:39.640> to<00:15:39.720> compute<00:15:40.480> statistics<00:15:41.079> of<00:15:41.200> these"
+ },
+ {
+ "start": 941.39,
+ "duration": 0.0,
+ "text": "start to compute statistics of these"
+ },
+ {
+ "start": 941.4,
+ "duration": 0.0,
+ "text": "start to compute statistics of these sequences,<00:15:42.160> look<00:15:42.360> at<00:15:42.480> things<00:15:42.720> like<00:15:42.920> the<00:15:43.000> law"
+ },
+ {
+ "start": 943.19,
+ "duration": 0.0,
+ "text": "sequences, look at things like the law"
+ },
+ {
+ "start": 943.2,
+ "duration": 0.0,
+ "text": "sequences, look at things like the law of<00:15:43.440> large<00:15:43.720> numbers,<00:15:44.440> which<00:15:44.640> would<00:15:44.800> say<00:15:44.959> that"
+ },
+ {
+ "start": 945.11,
+ "duration": 0.0,
+ "text": "of large numbers, which would say that"
+ },
+ {
+ "start": 945.12,
+ "duration": 0.0,
+ "text": "of large numbers, which would say that the<00:15:45.400> average<00:15:45.760> entry<00:15:46.480> of<00:15:46.640> this<00:15:46.800> sequence"
+ },
+ {
+ "start": 947.23,
+ "duration": 0.0,
+ "text": "the average entry of this sequence"
+ },
+ {
+ "start": 947.24,
+ "duration": 0.0,
+ "text": "the average entry of this sequence should<00:15:47.440> be<00:15:47.760> a<00:15:47.880> half,<00:15:48.320> which<00:15:48.880> would<00:15:49.560> clearly"
+ },
+ {
+ "start": 949.829,
+ "duration": 0.0,
+ "text": "should be a half, which would clearly"
+ },
+ {
+ "start": 949.839,
+ "duration": 0.0,
+ "text": "should be a half, which would clearly not<00:15:50.040> apply<00:15:50.360> to<00:15:50.520> the<00:15:50.640> first<00:15:50.880> sequence.<00:15:51.760> And"
+ },
+ {
+ "start": 952.03,
+ "duration": 0.0,
+ "text": "not apply to the first sequence. And"
+ },
+ {
+ "start": 952.04,
+ "duration": 0.0,
+ "text": "not apply to the first sequence. And Martin-Löf<00:15:52.760> randomness<00:15:53.440> uh<00:15:53.560> formalizes<00:15:54.240> this"
+ },
+ {
+ "start": 954.63,
+ "duration": 0.0,
+ "text": "Martin-Löf randomness uh formalizes this"
+ },
+ {
+ "start": 954.64,
+ "duration": 0.0,
+ "text": "Martin-Löf randomness uh formalizes this idea<00:15:55.440> that<00:15:55.720> a<00:15:55.800> sequence<00:15:56.360> ought<00:15:56.600> to<00:15:56.720> pass<00:15:57.240> all"
+ },
+ {
+ "start": 957.51,
+ "duration": 0.0,
+ "text": "idea that a sequence ought to pass all"
+ },
+ {
+ "start": 957.52,
+ "duration": 0.0,
+ "text": "idea that a sequence ought to pass all computable<00:15:58.320> tests,<00:15:59.200> but<00:15:59.520> this<00:15:59.720> doesn't"
+ },
+ {
+ "start": 960.31,
+ "duration": 0.0,
+ "text": "computable tests, but this doesn't"
+ },
+ {
+ "start": 960.32,
+ "duration": 0.0,
+ "text": "computable tests, but this doesn't account<00:16:00.839> also<00:16:01.240> for<00:16:01.720> computation.<00:16:02.839> There's"
+ },
+ {
+ "start": 963.069,
+ "duration": 0.0,
+ "text": "account also for computation. There's"
+ },
+ {
+ "start": 963.079,
+ "duration": 0.0,
+ "text": "account also for computation. There's also<00:16:03.360> a<00:16:03.400> notion<00:16:03.760> of<00:16:03.880> cryptographic"
+ },
+ {
+ "start": 964.59,
+ "duration": 0.0,
+ "text": "also a notion of cryptographic"
+ },
+ {
+ "start": 964.6,
+ "duration": 0.0,
+ "text": "also a notion of cryptographic randomness<00:16:05.440> um<00:16:05.640> where<00:16:05.800> sequences<00:16:06.360> must<00:16:06.640> pass"
+ },
+ {
+ "start": 967.03,
+ "duration": 0.0,
+ "text": "randomness um where sequences must pass"
+ },
+ {
+ "start": 967.04,
+ "duration": 0.0,
+ "text": "randomness um where sequences must pass polynomial-time<00:16:08.520> randomness<00:16:09.000> tests.<00:16:09.480> And<00:16:09.600> I"
+ },
+ {
+ "start": 969.63,
+ "duration": 0.0,
+ "text": "polynomial-time randomness tests. And I"
+ },
+ {
+ "start": 969.64,
+ "duration": 0.0,
+ "text": "polynomial-time randomness tests. And I think<00:16:09.880> Mark<00:16:10.079> might<00:16:10.240> have<00:16:10.360> a<00:16:10.400> few<00:16:10.680> few<00:16:10.839> thoughts"
+ },
+ {
+ "start": 971.11,
+ "duration": 0.0,
+ "text": "think Mark might have a few few thoughts"
+ },
+ {
+ "start": 971.12,
+ "duration": 0.0,
+ "text": "think Mark might have a few few thoughts on<00:16:11.200> this<00:16:11.360> as<00:16:11.520> well."
+ },
+ {
+ "start": 972.27,
+ "duration": 0.0,
+ "text": "on this as well."
+ },
+ {
+ "start": 972.28,
+ "duration": 0.0,
+ "text": "on this as well. Yeah,<00:16:12.760> and<00:16:13.160> just<00:16:13.440> to<00:16:13.520> motivate<00:16:14.120> why"
+ },
+ {
+ "start": 975.55,
+ "duration": 0.0,
+ "text": "Yeah, and just to motivate why"
+ },
+ {
+ "start": 975.56,
+ "duration": 0.0,
+ "text": "Yeah, and just to motivate why we<00:16:15.680> want<00:16:15.839> to<00:16:15.880> make<00:16:16.079> this<00:16:16.240> change<00:16:16.600> from<00:16:17.120> uh<00:16:17.240> you"
+ },
+ {
+ "start": 977.31,
+ "duration": 0.0,
+ "text": "we want to make this change from uh you"
+ },
+ {
+ "start": 977.32,
+ "duration": 0.0,
+ "text": "we want to make this change from uh you know,<00:16:17.560> why<00:16:18.079> it's<00:16:18.320> a<00:16:18.360> useful<00:16:19.000> uh<00:16:19.079> change<00:16:19.280> to<00:16:19.400> go"
+ },
+ {
+ "start": 979.51,
+ "duration": 0.0,
+ "text": "know, why it's a useful uh change to go"
+ },
+ {
+ "start": 979.52,
+ "duration": 0.0,
+ "text": "know, why it's a useful uh change to go from<00:16:19.680> this<00:16:19.920> Martin-Löf<00:16:20.320> randomness,<00:16:20.839> which"
+ },
+ {
+ "start": 981.03,
+ "duration": 0.0,
+ "text": "from this Martin-Löf randomness, which"
+ },
+ {
+ "start": 981.04,
+ "duration": 0.0,
+ "text": "from this Martin-Löf randomness, which is<00:16:21.160> this<00:16:21.720> this<00:16:21.839> more<00:16:22.000> accepted<00:16:22.680> uh<00:16:23.120> definition"
+ },
+ {
+ "start": 983.59,
+ "duration": 0.0,
+ "text": "is this this more accepted uh definition"
+ },
+ {
+ "start": 983.6,
+ "duration": 0.0,
+ "text": "is this this more accepted uh definition of<00:16:23.821> [clears throat]<00:16:23.839> randomness,<00:16:24.280> to<00:16:24.400> the"
+ },
+ {
+ "start": 984.51,
+ "duration": 0.0,
+ "text": "of [clears throat] randomness, to the"
+ },
+ {
+ "start": 984.52,
+ "duration": 0.0,
+ "text": "of [clears throat] randomness, to the one<00:16:24.720> that<00:16:25.000> cryptographers<00:16:25.640> use."
+ },
+ {
+ "start": 986.67,
+ "duration": 0.0,
+ "text": "one that cryptographers use."
+ },
+ {
+ "start": 986.68,
+ "duration": 0.0,
+ "text": "one that cryptographers use. Um"
+ },
+ {
+ "start": 987.63,
+ "duration": 0.0,
+ "text": "Um"
+ },
+ {
+ "start": 987.64,
+ "duration": 0.0,
+ "text": "Um take,<00:16:28.120> for<00:16:28.240> example,"
+ },
+ {
+ "start": 989.51,
+ "duration": 0.0,
+ "text": "take, for example,"
+ },
+ {
+ "start": 989.52,
+ "duration": 0.0,
+ "text": "take, for example, uh<00:16:30.360> rock,<00:16:30.520> paper,<00:16:30.760> scissors,<00:16:31.240> all<00:16:31.320> right,"
+ },
+ {
+ "start": 991.43,
+ "duration": 0.0,
+ "text": "uh rock, paper, scissors, all right,"
+ },
+ {
+ "start": 991.44,
+ "duration": 0.0,
+ "text": "uh rock, paper, scissors, all right, game,<00:16:32.000> where<00:16:32.839> we<00:16:32.959> all<00:16:33.079> know<00:16:33.360> what<00:16:33.640> the<00:16:34.079> Nash"
+ },
+ {
+ "start": 994.35,
+ "duration": 0.0,
+ "text": "game, where we all know what the Nash"
+ },
+ {
+ "start": 994.36,
+ "duration": 0.0,
+ "text": "game, where we all know what the Nash equilibrium<00:16:34.800> strategy<00:16:35.200> is<00:16:35.640> of<00:16:36.520> uh"
+ },
+ {
+ "start": 997.51,
+ "duration": 0.0,
+ "text": "equilibrium strategy is of uh"
+ },
+ {
+ "start": 997.52,
+ "duration": 0.0,
+ "text": "equilibrium strategy is of uh predicting<00:16:38.040> rock,<00:16:38.280> paper,<00:16:38.480> and<00:16:38.600> scissors"
+ },
+ {
+ "start": 999.23,
+ "duration": 0.0,
+ "text": "predicting rock, paper, and scissors"
+ },
+ {
+ "start": 999.24,
+ "duration": 0.0,
+ "text": "predicting rock, paper, and scissors with<00:16:39.520> probability<00:16:40.040> each<00:16:40.320> 1/3."
+ },
+ {
+ "start": 1001.75,
+ "duration": 0.0,
+ "text": "with probability each 1/3."
+ },
+ {
+ "start": 1001.76,
+ "duration": 0.0,
+ "text": "with probability each 1/3. But<00:16:41.880> how<00:16:41.959> do<00:16:42.040> we<00:16:42.120> actually<00:16:42.360> implement<00:16:42.760> that"
+ },
+ {
+ "start": 1002.91,
+ "duration": 0.0,
+ "text": "But how do we actually implement that"
+ },
+ {
+ "start": 1002.92,
+ "duration": 0.0,
+ "text": "But how do we actually implement that strategy,<00:16:43.839> whether<00:16:44.040> it's<00:16:44.160> on<00:16:44.280> a<00:16:44.320> computer<00:16:45.040> or"
+ },
+ {
+ "start": 1005.11,
+ "duration": 0.0,
+ "text": "strategy, whether it's on a computer or"
+ },
+ {
+ "start": 1005.12,
+ "duration": 0.0,
+ "text": "strategy, whether it's on a computer or on<00:16:45.200> a<00:16:45.240> human?"
+ },
+ {
+ "start": 1006.47,
+ "duration": 0.0,
+ "text": "on a human?"
+ },
+ {
+ "start": 1006.48,
+ "duration": 0.0,
+ "text": "on a human? In<00:16:46.520> fact,<00:16:47.400> the<00:16:47.520> Martin-Löf<00:16:47.959> random"
+ },
+ {
+ "start": 1008.19,
+ "duration": 0.0,
+ "text": "In fact, the Martin-Löf random"
+ },
+ {
+ "start": 1008.2,
+ "duration": 0.0,
+ "text": "In fact, the Martin-Löf random sequences,<00:16:48.760> they're<00:16:49.000> all<00:16:49.320> incomputable."
+ },
+ {
+ "start": 1010.949,
+ "duration": 0.0,
+ "text": "sequences, they're all incomputable."
+ },
+ {
+ "start": 1010.959,
+ "duration": 0.0,
+ "text": "sequences, they're all incomputable. So,<00:16:51.280> there<00:16:51.440> must<00:16:51.640> be<00:16:51.760> no<00:16:52.040> computer<00:16:52.400> program"
+ },
+ {
+ "start": 1012.949,
+ "duration": 0.0,
+ "text": "So, there must be no computer program"
+ },
+ {
+ "start": 1012.959,
+ "duration": 0.0,
+ "text": "So, there must be no computer program that<00:16:53.560> outputs<00:16:54.120> a<00:16:54.200> Martin-Löf<00:16:54.600> random"
+ },
+ {
+ "start": 1014.79,
+ "duration": 0.0,
+ "text": "that outputs a Martin-Löf random"
+ },
+ {
+ "start": 1014.8,
+ "duration": 0.0,
+ "text": "that outputs a Martin-Löf random sequence.<00:16:55.680> So,<00:16:55.800> how<00:16:55.880> do<00:16:55.959> we<00:16:56.040> do<00:16:56.200> it?"
+ },
+ {
+ "start": 1017.55,
+ "duration": 0.0,
+ "text": "sequence. So, how do we do it?"
+ },
+ {
+ "start": 1017.56,
+ "duration": 0.0,
+ "text": "sequence. So, how do we do it? Of<00:16:57.720> course,"
+ },
+ {
+ "start": 1019.27,
+ "duration": 0.0,
+ "text": "Of course,"
+ },
+ {
+ "start": 1019.28,
+ "duration": 0.0,
+ "text": "Of course, uh"
+ },
+ {
+ "start": 1020.59,
+ "duration": 0.0,
+ "text": "uh"
+ },
+ {
+ "start": 1020.6,
+ "duration": 0.0,
+ "text": "uh turns<00:17:00.800> out<00:17:00.959> you<00:17:01.040> don't<00:17:01.240> need<00:17:02.120> a<00:17:02.320> truly"
+ },
+ {
+ "start": 1023.11,
+ "duration": 0.0,
+ "text": "turns out you don't need a truly"
+ },
+ {
+ "start": 1023.12,
+ "duration": 0.0,
+ "text": "turns out you don't need a truly Martin-Löf<00:17:03.600> random<00:17:03.839> sequence."
+ },
+ {
+ "start": 1024.99,
+ "duration": 0.0,
+ "text": "Martin-Löf random sequence."
+ },
+ {
+ "start": 1025.0,
+ "duration": 0.0,
+ "text": "Martin-Löf random sequence. You<00:17:05.079> just<00:17:05.240> need<00:17:05.400> something<00:17:05.760> that<00:17:05.920> will<00:17:06.079> fool"
+ },
+ {
+ "start": 1026.51,
+ "duration": 0.0,
+ "text": "You just need something that will fool"
+ },
+ {
+ "start": 1026.52,
+ "duration": 0.0,
+ "text": "You just need something that will fool your<00:17:06.679> adversary."
+ },
+ {
+ "start": 1028.069,
+ "duration": 0.0,
+ "text": "your adversary."
+ },
+ {
+ "start": 1028.079,
+ "duration": 0.0,
+ "text": "your adversary. And<00:17:08.199> then<00:17:08.360> this<00:17:08.640> also<00:17:08.959> becomes<00:17:09.320> relevant<00:17:09.839> in"
+ },
+ {
+ "start": 1030.069,
+ "duration": 0.0,
+ "text": "And then this also becomes relevant in"
+ },
+ {
+ "start": 1030.079,
+ "duration": 0.0,
+ "text": "And then this also becomes relevant in the<00:17:10.240> actual<00:17:10.560> playing<00:17:11.040> of"
+ },
+ {
+ "start": 1032.03,
+ "duration": 0.0,
+ "text": "the actual playing of"
+ },
+ {
+ "start": 1032.04,
+ "duration": 0.0,
+ "text": "the actual playing of say<00:17:12.240> rock,<00:17:12.439> paper,<00:17:12.679> scissors<00:17:13.199> in<00:17:13.480> the"
+ },
+ {
+ "start": 1033.59,
+ "duration": 0.0,
+ "text": "say rock, paper, scissors in the"
+ },
+ {
+ "start": 1033.6,
+ "duration": 0.0,
+ "text": "say rock, paper, scissors in the competitions,<00:17:14.720> where<00:17:15.199> people<00:17:15.439> try<00:17:15.640> very<00:17:15.839> hard"
+ },
+ {
+ "start": 1036.429,
+ "duration": 0.0,
+ "text": "competitions, where people try very hard"
+ },
+ {
+ "start": 1036.439,
+ "duration": 0.0,
+ "text": "competitions, where people try very hard to<00:17:16.600> be<00:17:16.760> random,<00:17:17.280> and<00:17:17.400> it's<00:17:17.520> a<00:17:17.560> difficult<00:17:17.920> thing"
+ },
+ {
+ "start": 1038.47,
+ "duration": 0.0,
+ "text": "to be random, and it's a difficult thing"
+ },
+ {
+ "start": 1038.48,
+ "duration": 0.0,
+ "text": "to be random, and it's a difficult thing to<00:17:18.560> be<00:17:18.679> random,<00:17:19.040> but<00:17:19.240> they<00:17:19.360> just<00:17:19.600> need<00:17:19.839> to<00:17:19.959> fool"
+ },
+ {
+ "start": 1040.63,
+ "duration": 0.0,
+ "text": "to be random, but they just need to fool"
+ },
+ {
+ "start": 1040.64,
+ "duration": 0.0,
+ "text": "to be random, but they just need to fool their<00:17:20.760> opponents."
+ },
+ {
+ "start": 1042.27,
+ "duration": 0.0,
+ "text": "their opponents."
+ },
+ {
+ "start": 1042.28,
+ "duration": 0.0,
+ "text": "their opponents. And<00:17:22.839> from<00:17:23.079> the<00:17:23.199> game<00:17:23.480> setting,<00:17:24.079> you<00:17:24.199> know,<00:17:24.280> in"
+ },
+ {
+ "start": 1044.35,
+ "duration": 0.0,
+ "text": "And from the game setting, you know, in"
+ },
+ {
+ "start": 1044.36,
+ "duration": 0.0,
+ "text": "And from the game setting, you know, in this<00:17:24.520> kind<00:17:24.679> of<00:17:24.839> algorithmic<00:17:25.280> game<00:17:25.439> setting,"
+ },
+ {
+ "start": 1045.87,
+ "duration": 0.0,
+ "text": "this kind of algorithmic game setting,"
+ },
+ {
+ "start": 1045.88,
+ "duration": 0.0,
+ "text": "this kind of algorithmic game setting, okay,<00:17:26.040> that<00:17:26.720> that's<00:17:27.400> that's<00:17:27.600> one<00:17:27.760> frame."
+ },
+ {
+ "start": 1048.71,
+ "duration": 0.0,
+ "text": "okay, that that's that's one frame."
+ },
+ {
+ "start": 1048.72,
+ "duration": 0.0,
+ "text": "okay, that that's that's one frame. But<00:17:28.880> also,<00:17:29.640> even<00:17:30.000> for<00:17:30.679> um<00:17:31.520> our<00:17:31.679> use<00:17:32.040> of"
+ },
+ {
+ "start": 1052.19,
+ "duration": 0.0,
+ "text": "But also, even for um our use of"
+ },
+ {
+ "start": 1052.2,
+ "duration": 0.0,
+ "text": "But also, even for um our use of randomness,<00:17:32.800> say<00:17:33.040> in<00:17:33.160> randomized"
+ },
+ {
+ "start": 1053.55,
+ "duration": 0.0,
+ "text": "randomness, say in randomized"
+ },
+ {
+ "start": 1053.56,
+ "duration": 0.0,
+ "text": "randomness, say in randomized algorithms,<00:17:34.640> so,<00:17:35.120> you<00:17:35.240> might<00:17:35.480> consider<00:17:35.880> an"
+ },
+ {
+ "start": 1055.91,
+ "duration": 0.0,
+ "text": "algorithms, so, you might consider an"
+ },
+ {
+ "start": 1055.92,
+ "duration": 0.0,
+ "text": "algorithms, so, you might consider an algorithm<00:17:36.320> like<00:17:37.080> MCMC"
+ },
+ {
+ "start": 1058.47,
+ "duration": 0.0,
+ "text": "algorithm like MCMC"
+ },
+ {
+ "start": 1058.48,
+ "duration": 0.0,
+ "text": "algorithm like MCMC or<00:17:38.840> quicksort,<00:17:39.640> some<00:17:39.800> other<00:17:39.960> randomized"
+ },
+ {
+ "start": 1060.39,
+ "duration": 0.0,
+ "text": "or quicksort, some other randomized"
+ },
+ {
+ "start": 1060.4,
+ "duration": 0.0,
+ "text": "or quicksort, some other randomized algorithm."
+ },
+ {
+ "start": 1062.27,
+ "duration": 0.0,
+ "text": "algorithm."
+ },
+ {
+ "start": 1062.28,
+ "duration": 0.0,
+ "text": "algorithm. Well,"
+ },
+ {
+ "start": 1064.72,
+ "duration": 0.0,
+ "text": "how<00:17:44.880> does<00:17:45.240> your<00:17:45.440> algorithm<00:17:46.120> know?<00:17:46.560> I<00:17:46.600> mean,"
+ },
+ {
+ "start": 1067.27,
+ "duration": 0.0,
+ "text": "how does your algorithm know? I mean,"
+ },
+ {
+ "start": 1067.28,
+ "duration": 0.0,
+ "text": "how does your algorithm know? I mean, so,"
+ },
+ {
+ "start": 1068.27,
+ "duration": 0.0,
+ "text": "so,"
+ },
+ {
+ "start": 1068.28,
+ "duration": 0.0,
+ "text": "so, in<00:17:48.480> order"
+ },
+ {
+ "start": 1069.59,
+ "duration": 0.0,
+ "text": "in order"
+ },
+ {
+ "start": 1069.6,
+ "duration": 0.0,
+ "text": "in order for<00:17:50.000> your<00:17:50.240> algorithm<00:17:50.920> to<00:17:51.040> behave<00:17:51.440> differently"
+ },
+ {
+ "start": 1072.35,
+ "duration": 0.0,
+ "text": "for your algorithm to behave differently"
+ },
+ {
+ "start": 1072.36,
+ "duration": 0.0,
+ "text": "for your algorithm to behave differently on<00:17:52.960> truly<00:17:53.400> random<00:17:53.800> sequences<00:17:55.040> or"
+ },
+ {
+ "start": 1075.31,
+ "duration": 0.0,
+ "text": "on truly random sequences or"
+ },
+ {
+ "start": 1075.32,
+ "duration": 0.0,
+ "text": "on truly random sequences or cryptographically<00:17:56.080> random<00:17:56.360> sequences,<00:17:57.000> it"
+ },
+ {
+ "start": 1077.11,
+ "duration": 0.0,
+ "text": "cryptographically random sequences, it"
+ },
+ {
+ "start": 1077.12,
+ "duration": 0.0,
+ "text": "cryptographically random sequences, it would<00:17:57.280> need<00:17:57.640> to<00:17:57.760> actually<00:17:58.760> distinguish"
+ },
+ {
+ "start": 1079.27,
+ "duration": 0.0,
+ "text": "would need to actually distinguish"
+ },
+ {
+ "start": 1079.28,
+ "duration": 0.0,
+ "text": "would need to actually distinguish between<00:17:59.640> the<00:17:59.720> two."
+ },
+ {
+ "start": 1080.99,
+ "duration": 0.0,
+ "text": "between the two."
+ },
+ {
+ "start": 1081.0,
+ "duration": 0.0,
+ "text": "between the two. If<00:18:01.160> somehow<00:18:01.560> it's<00:18:01.720> just<00:18:01.880> going<00:18:02.200> to<00:18:03.080> obviously"
+ },
+ {
+ "start": 1083.63,
+ "duration": 0.0,
+ "text": "If somehow it's just going to obviously"
+ },
+ {
+ "start": 1083.64,
+ "duration": 0.0,
+ "text": "If somehow it's just going to obviously fail<00:18:04.600> with<00:18:05.600> your<00:18:05.720> cryptographic<00:18:06.520> random"
+ },
+ {
+ "start": 1086.79,
+ "duration": 0.0,
+ "text": "fail with your cryptographic random"
+ },
+ {
+ "start": 1086.8,
+ "duration": 0.0,
+ "text": "fail with your cryptographic random sequence"
+ },
+ {
+ "start": 1087.95,
+ "duration": 0.0,
+ "text": "sequence"
+ },
+ {
+ "start": 1087.96,
+ "duration": 0.0,
+ "text": "sequence versus<00:18:08.240> your<00:18:08.360> truly<00:18:08.600> random<00:18:08.840> sequence,<00:18:09.280> then"
+ },
+ {
+ "start": 1089.87,
+ "duration": 0.0,
+ "text": "versus your truly random sequence, then"
+ },
+ {
+ "start": 1089.88,
+ "duration": 0.0,
+ "text": "versus your truly random sequence, then your<00:18:10.040> random<00:18:10.720> your<00:18:11.240> your<00:18:11.480> your<00:18:11.679> cryptographic"
+ },
+ {
+ "start": 1092.23,
+ "duration": 0.0,
+ "text": "your random your your your cryptographic"
+ },
+ {
+ "start": 1092.24,
+ "duration": 0.0,
+ "text": "your random your your your cryptographic random<00:18:12.440> sequence<00:18:12.800> is<00:18:12.880> not<00:18:13.440> um"
+ },
+ {
+ "start": 1094.23,
+ "duration": 0.0,
+ "text": "random sequence is not um"
+ },
+ {
+ "start": 1094.24,
+ "duration": 0.0,
+ "text": "random sequence is not um actually<00:18:14.679> indistinguishable"
+ },
+ {
+ "start": 1095.23,
+ "duration": 0.0,
+ "text": "actually indistinguishable"
+ },
+ {
+ "start": 1095.24,
+ "duration": 0.0,
+ "text": "actually indistinguishable computationally<00:18:15.720> indistinguishable.<00:18:16.320> So,"
+ },
+ {
+ "start": 1097.71,
+ "duration": 0.0,
+ "text": "computationally indistinguishable. So,"
+ },
+ {
+ "start": 1097.72,
+ "duration": 0.0,
+ "text": "computationally indistinguishable. So, in<00:18:17.840> these<00:18:18.080> different<00:18:18.360> ways,"
+ },
+ {
+ "start": 1099.51,
+ "duration": 0.0,
+ "text": "in these different ways,"
+ },
+ {
+ "start": 1099.52,
+ "duration": 0.0,
+ "text": "in these different ways, um"
+ },
+ {
+ "start": 1100.51,
+ "duration": 0.0,
+ "text": "um"
+ },
+ {
+ "start": 1100.52,
+ "duration": 0.0,
+ "text": "um the"
+ },
+ {
+ "start": 1101.63,
+ "duration": 0.0,
+ "text": "the"
+ },
+ {
+ "start": 1101.64,
+ "duration": 0.0,
+ "text": "the the<00:18:21.880> the<00:18:22.040> weaker<00:18:22.320> notion<00:18:22.679> of<00:18:22.800> cryptographic"
+ },
+ {
+ "start": 1103.31,
+ "duration": 0.0,
+ "text": "the the weaker notion of cryptographic"
+ },
+ {
+ "start": 1103.32,
+ "duration": 0.0,
+ "text": "the the weaker notion of cryptographic randomness<00:18:23.760> is<00:18:23.840> essentially<00:18:24.160> the<00:18:24.280> one<00:18:24.440> that"
+ },
+ {
+ "start": 1104.59,
+ "duration": 0.0,
+ "text": "randomness is essentially the one that"
+ },
+ {
+ "start": 1104.6,
+ "duration": 0.0,
+ "text": "randomness is essentially the one that is"
+ },
+ {
+ "start": 1105.47,
+ "duration": 0.0,
+ "text": "is"
+ },
+ {
+ "start": 1105.48,
+ "duration": 0.0,
+ "text": "is uh<00:18:25.640> more<00:18:25.840> relevant<00:18:26.760> um<00:18:26.880> to<00:18:27.080> us.<00:18:27.360> And<00:18:27.640> there<00:18:27.800> are"
+ },
+ {
+ "start": 1107.909,
+ "duration": 0.0,
+ "text": "uh more relevant um to us. And there are"
+ },
+ {
+ "start": 1107.919,
+ "duration": 0.0,
+ "text": "uh more relevant um to us. And there are some<00:18:28.840> uh<00:18:29.200> some<00:18:29.360> important<00:18:29.919> ties<00:18:30.320> to<00:18:30.840> say"
+ },
+ {
+ "start": 1111.11,
+ "duration": 0.0,
+ "text": "some uh some important ties to say"
+ },
+ {
+ "start": 1111.12,
+ "duration": 0.0,
+ "text": "some uh some important ties to say complexity<00:18:31.640> theory.<00:18:32.400> Say<00:18:32.720> uh"
+ },
+ {
+ "start": 1113.31,
+ "duration": 0.0,
+ "text": "complexity theory. Say uh"
+ },
+ {
+ "start": 1113.32,
+ "duration": 0.0,
+ "text": "complexity theory. Say uh the<00:18:33.679> um<00:18:34.159> you<00:18:34.240> know,<00:18:34.360> conjectured<00:18:35.040> equivalence"
+ },
+ {
+ "start": 1115.59,
+ "duration": 0.0,
+ "text": "the um you know, conjectured equivalence"
+ },
+ {
+ "start": 1115.6,
+ "duration": 0.0,
+ "text": "the um you know, conjectured equivalence of"
+ },
+ {
+ "start": 1116.39,
+ "duration": 0.0,
+ "text": "of"
+ },
+ {
+ "start": 1116.4,
+ "duration": 0.0,
+ "text": "of uh<00:18:36.480> bounded<00:18:36.840> error<00:18:37.400> polynomial<00:18:37.840> time<00:18:38.800> uh"
+ },
+ {
+ "start": 1119.63,
+ "duration": 0.0,
+ "text": "uh bounded error polynomial time uh"
+ },
+ {
+ "start": 1119.64,
+ "duration": 0.0,
+ "text": "uh bounded error polynomial time uh and<00:18:40.080> just<00:18:40.320> ordinary"
+ },
+ {
+ "start": 1121.51,
+ "duration": 0.0,
+ "text": "and just ordinary"
+ },
+ {
+ "start": 1121.52,
+ "duration": 0.0,
+ "text": "and just ordinary polynomial<00:18:41.840> time.<00:18:42.640> Um<00:18:43.159> so,<00:18:43.440> anyways,<00:18:43.760> just<00:18:44.000> a"
+ },
+ {
+ "start": 1124.149,
+ "duration": 0.0,
+ "text": "polynomial time. Um so, anyways, just a"
+ },
+ {
+ "start": 1124.159,
+ "duration": 0.0,
+ "text": "polynomial time. Um so, anyways, just a a<00:18:44.200> few<00:18:44.560> notes<00:18:44.800> there<00:18:45.000> that<00:18:45.200> actually<00:18:45.520> this"
+ },
+ {
+ "start": 1126.43,
+ "duration": 0.0,
+ "text": "a few notes there that actually this"
+ },
+ {
+ "start": 1126.44,
+ "duration": 0.0,
+ "text": "a few notes there that actually this though<00:18:47.159> less"
+ },
+ {
+ "start": 1128.31,
+ "duration": 0.0,
+ "text": "though less"
+ },
+ {
+ "start": 1128.32,
+ "duration": 0.0,
+ "text": "though less uh"
+ },
+ {
+ "start": 1129.909,
+ "duration": 0.0,
+ "text": "uh"
+ },
+ {
+ "start": 1129.919,
+ "duration": 0.0,
+ "text": "uh uh"
+ },
+ {
+ "start": 1130.59,
+ "duration": 0.0,
+ "text": "uh"
+ },
+ {
+ "start": 1130.6,
+ "duration": 0.0,
+ "text": "uh you<00:18:50.679> know,<00:18:51.080> thought<00:18:51.280> about"
+ },
+ {
+ "start": 1132.23,
+ "duration": 0.0,
+ "text": "you know, thought about"
+ },
+ {
+ "start": 1132.24,
+ "duration": 0.0,
+ "text": "you know, thought about with<00:18:52.520> yeah,<00:18:53.080> less<00:18:53.480> obviously<00:18:53.960> the"
+ },
+ {
+ "start": 1134.11,
+ "duration": 0.0,
+ "text": "with yeah, less obviously the"
+ },
+ {
+ "start": 1134.12,
+ "duration": 0.0,
+ "text": "with yeah, less obviously the theoretical<00:18:54.600> notion,<00:18:55.040> there<00:18:55.320> are<00:18:55.400> some<00:18:55.560> good"
+ },
+ {
+ "start": 1135.71,
+ "duration": 0.0,
+ "text": "theoretical notion, there are some good"
+ },
+ {
+ "start": 1135.72,
+ "duration": 0.0,
+ "text": "theoretical notion, there are some good reasons<00:18:56.080> to<00:18:56.200> think<00:18:56.440> that<00:18:56.679> this<00:18:56.880> cryptographic"
+ },
+ {
+ "start": 1137.51,
+ "duration": 0.0,
+ "text": "reasons to think that this cryptographic"
+ },
+ {
+ "start": 1137.52,
+ "duration": 0.0,
+ "text": "reasons to think that this cryptographic randomness<00:18:58.000> is<00:18:58.800> um"
+ },
+ {
+ "start": 1139.51,
+ "duration": 0.0,
+ "text": "randomness is um"
+ },
+ {
+ "start": 1139.52,
+ "duration": 0.0,
+ "text": "randomness is um the<00:19:00.040> the<00:19:00.159> more<00:19:00.320> relevant<00:19:00.640> notion<00:19:00.880> to<00:19:01.040> us."
+ },
+ {
+ "start": 1144.04,
+ "duration": 0.0,
+ "text": "Right.<00:19:04.440> And<00:19:04.720> so,<00:19:05.120> following<00:19:05.560> on<00:19:05.919> on<00:19:06.080> this<00:19:06.400> and"
+ },
+ {
+ "start": 1146.87,
+ "duration": 0.0,
+ "text": "Right. And so, following on on this and"
+ },
+ {
+ "start": 1146.88,
+ "duration": 0.0,
+ "text": "Right. And so, following on on this and the<00:19:07.080> importance<00:19:07.600> of<00:19:07.720> computation,<00:19:08.480> we<00:19:08.679> can"
+ },
+ {
+ "start": 1149.35,
+ "duration": 0.0,
+ "text": "the importance of computation, we can"
+ },
+ {
+ "start": 1149.36,
+ "duration": 0.0,
+ "text": "the importance of computation, we can further<00:19:09.679> consider<00:19:10.600> cryptographically"
+ },
+ {
+ "start": 1151.39,
+ "duration": 0.0,
+ "text": "further consider cryptographically"
+ },
+ {
+ "start": 1151.4,
+ "duration": 0.0,
+ "text": "further consider cryptographically secure<00:19:11.880> pseudo-random<00:19:12.919> number<00:19:13.240> generators."
+ },
+ {
+ "start": 1154.11,
+ "duration": 0.0,
+ "text": "secure pseudo-random number generators."
+ },
+ {
+ "start": 1154.12,
+ "duration": 0.0,
+ "text": "secure pseudo-random number generators. Uh<00:19:14.320> so,<00:19:14.480> the<00:19:14.679> outputs<00:19:15.280> of<00:19:15.800> these<00:19:16.440> um"
+ },
+ {
+ "start": 1156.909,
+ "duration": 0.0,
+ "text": "Uh so, the outputs of these um"
+ },
+ {
+ "start": 1156.919,
+ "duration": 0.0,
+ "text": "Uh so, the outputs of these um generators<00:19:17.600> are<00:19:17.760> going<00:19:18.040> to<00:19:18.159> be<00:19:18.320> statistically"
+ },
+ {
+ "start": 1158.99,
+ "duration": 0.0,
+ "text": "generators are going to be statistically"
+ },
+ {
+ "start": 1159.0,
+ "duration": 0.0,
+ "text": "generators are going to be statistically indistinguishable<00:19:19.919> from<00:19:20.800> actual<00:19:21.159> random"
+ },
+ {
+ "start": 1161.47,
+ "duration": 0.0,
+ "text": "indistinguishable from actual random"
+ },
+ {
+ "start": 1161.48,
+ "duration": 0.0,
+ "text": "indistinguishable from actual random numbers<00:19:21.960> if<00:19:22.200> we<00:19:22.360> only<00:19:22.640> have<00:19:23.440> polynomial-time"
+ },
+ {
+ "start": 1164.47,
+ "duration": 0.0,
+ "text": "numbers if we only have polynomial-time"
+ },
+ {
+ "start": 1164.48,
+ "duration": 0.0,
+ "text": "numbers if we only have polynomial-time computation.<00:19:25.960> Um<00:19:26.480> there's<00:19:26.720> a<00:19:26.760> closely"
+ },
+ {
+ "start": 1167.149,
+ "duration": 0.0,
+ "text": "computation. Um there's a closely"
+ },
+ {
+ "start": 1167.159,
+ "duration": 0.0,
+ "text": "computation. Um there's a closely related<00:19:27.520> concept<00:19:28.000> that<00:19:28.120> we<00:19:28.240> make<00:19:28.480> use<00:19:28.720> of"
+ },
+ {
+ "start": 1169.19,
+ "duration": 0.0,
+ "text": "related concept that we make use of"
+ },
+ {
+ "start": 1169.2,
+ "duration": 0.0,
+ "text": "related concept that we make use of throughout<00:19:29.520> the<00:19:29.640> paper<00:19:30.640> um<00:19:30.880> called<00:19:31.360> a<00:19:31.440> one-way"
+ },
+ {
+ "start": 1171.83,
+ "duration": 0.0,
+ "text": "throughout the paper um called a one-way"
+ },
+ {
+ "start": 1171.84,
+ "duration": 0.0,
+ "text": "throughout the paper um called a one-way function,<00:19:32.520> um<00:19:32.800> which<00:19:33.120> is<00:19:33.560> uh"
+ },
+ {
+ "start": 1174.23,
+ "duration": 0.0,
+ "text": "function, um which is uh"
+ },
+ {
+ "start": 1174.24,
+ "duration": 0.0,
+ "text": "function, um which is uh very<00:19:34.480> important<00:19:35.000> in<00:19:35.400> cryptography.<00:19:36.679> Uh<00:19:36.880> these"
+ },
+ {
+ "start": 1177.11,
+ "duration": 0.0,
+ "text": "very important in cryptography. Uh these"
+ },
+ {
+ "start": 1177.12,
+ "duration": 0.0,
+ "text": "very important in cryptography. Uh these one-way<00:19:37.440> functions<00:19:38.080> are<00:19:38.720> easy<00:19:39.200> or"
+ },
+ {
+ "start": 1179.39,
+ "duration": 0.0,
+ "text": "one-way functions are easy or"
+ },
+ {
+ "start": 1179.4,
+ "duration": 0.0,
+ "text": "one-way functions are easy or computationally<00:19:40.440> inexpensive<00:19:41.080> to<00:19:41.200> evaluate"
+ },
+ {
+ "start": 1181.75,
+ "duration": 0.0,
+ "text": "computationally inexpensive to evaluate"
+ },
+ {
+ "start": 1181.76,
+ "duration": 0.0,
+ "text": "computationally inexpensive to evaluate in<00:19:41.880> one<00:19:42.040> direction,<00:19:42.480> but<00:19:42.679> very"
+ },
+ {
+ "start": 1183.03,
+ "duration": 0.0,
+ "text": "in one direction, but very"
+ },
+ {
+ "start": 1183.04,
+ "duration": 0.0,
+ "text": "in one direction, but very computationally<00:19:43.720> expensive<00:19:44.360> to<00:19:45.200> invert.<00:19:45.880> And"
+ },
+ {
+ "start": 1186.11,
+ "duration": 0.0,
+ "text": "computationally expensive to invert. And"
+ },
+ {
+ "start": 1186.12,
+ "duration": 0.0,
+ "text": "computationally expensive to invert. And so,<00:19:46.720> cryptography<00:19:47.679> is<00:19:47.880> an<00:19:48.080> area<00:19:48.480> which<00:19:48.800> has<00:19:49.400> um"
+ },
+ {
+ "start": 1189.71,
+ "duration": 0.0,
+ "text": "so, cryptography is an area which has um"
+ },
+ {
+ "start": 1189.72,
+ "duration": 0.0,
+ "text": "so, cryptography is an area which has um really<00:19:49.960> considered<00:19:50.520> computational"
+ },
+ {
+ "start": 1191.27,
+ "duration": 0.0,
+ "text": "really considered computational"
+ },
+ {
+ "start": 1191.28,
+ "duration": 0.0,
+ "text": "really considered computational constraints<00:19:52.200> quite<00:19:52.480> extensively,<00:19:53.440> but<00:19:53.960> this"
+ },
+ {
+ "start": 1194.15,
+ "duration": 0.0,
+ "text": "constraints quite extensively, but this"
+ },
+ {
+ "start": 1194.16,
+ "duration": 0.0,
+ "text": "constraints quite extensively, but this is<00:19:54.240> something<00:19:54.520> that<00:19:54.640> has<00:19:54.880> not<00:19:55.200> been"
+ },
+ {
+ "start": 1195.51,
+ "duration": 0.0,
+ "text": "is something that has not been"
+ },
+ {
+ "start": 1195.52,
+ "duration": 0.0,
+ "text": "is something that has not been considered<00:19:55.960> as<00:19:56.120> much<00:19:56.440> in<00:19:56.600> learning<00:19:56.880> theory<00:19:57.360> or"
+ },
+ {
+ "start": 1197.55,
+ "duration": 0.0,
+ "text": "considered as much in learning theory or"
+ },
+ {
+ "start": 1197.56,
+ "duration": 0.0,
+ "text": "considered as much in learning theory or information<00:19:58.160> theory.<00:19:59.000> And<00:19:59.360> this<00:19:59.600> can<00:19:59.720> be"
+ },
+ {
+ "start": 1199.83,
+ "duration": 0.0,
+ "text": "information theory. And this can be"
+ },
+ {
+ "start": 1199.84,
+ "duration": 0.0,
+ "text": "information theory. And this can be quite<00:20:00.200> important<00:20:00.720> for<00:20:01.160> explaining<00:20:01.880> um"
+ },
+ {
+ "start": 1202.15,
+ "duration": 0.0,
+ "text": "quite important for explaining um"
+ },
+ {
+ "start": 1202.16,
+ "duration": 0.0,
+ "text": "quite important for explaining um behavior<00:20:02.760> of<00:20:03.040> AI<00:20:03.240> systems.<00:20:04.120> So,<00:20:04.400> we<00:20:04.600> can,<00:20:04.760> for"
+ },
+ {
+ "start": 1204.87,
+ "duration": 0.0,
+ "text": "behavior of AI systems. So, we can, for"
+ },
+ {
+ "start": 1204.88,
+ "duration": 0.0,
+ "text": "behavior of AI systems. So, we can, for example,<00:20:05.760> look<00:20:06.160> at<00:20:06.360> the<00:20:06.440> Shannon<00:20:06.840> information"
+ },
+ {
+ "start": 1207.59,
+ "duration": 0.0,
+ "text": "example, look at the Shannon information"
+ },
+ {
+ "start": 1207.6,
+ "duration": 0.0,
+ "text": "example, look at the Shannon information associated<00:20:08.320> with<00:20:09.120> uh<00:20:09.560> the<00:20:09.760> output<00:20:10.080> of<00:20:10.240> a"
+ },
+ {
+ "start": 1210.27,
+ "duration": 0.0,
+ "text": "associated with uh the output of a"
+ },
+ {
+ "start": 1210.28,
+ "duration": 0.0,
+ "text": "associated with uh the output of a random<00:20:10.600> number<00:20:10.840> generator.<00:20:11.520> Uh<00:20:11.880> so,<00:20:12.560> uh<00:20:12.880> these"
+ },
+ {
+ "start": 1213.07,
+ "duration": 0.0,
+ "text": "random number generator. Uh so, uh these"
+ },
+ {
+ "start": 1213.08,
+ "duration": 0.0,
+ "text": "random number generator. Uh so, uh these are<00:20:13.160> just<00:20:13.360> deterministic<00:20:13.960> transformations"
+ },
+ {
+ "start": 1214.99,
+ "duration": 0.0,
+ "text": "are just deterministic transformations"
+ },
+ {
+ "start": 1215.0,
+ "duration": 0.0,
+ "text": "are just deterministic transformations um"
+ },
+ {
+ "start": 1215.67,
+ "duration": 0.0,
+ "text": "um"
+ },
+ {
+ "start": 1215.68,
+ "duration": 0.0,
+ "text": "um due<00:20:15.840> to<00:20:15.960> the<00:20:16.160> data<00:20:16.400> processing<00:20:17.000> inequality,"
+ },
+ {
+ "start": 1217.83,
+ "duration": 0.0,
+ "text": "due to the data processing inequality,"
+ },
+ {
+ "start": 1217.84,
+ "duration": 0.0,
+ "text": "due to the data processing inequality, we're<00:20:18.000> not<00:20:18.360> actually<00:20:18.880> increasing<00:20:19.440> the"
+ },
+ {
+ "start": 1219.55,
+ "duration": 0.0,
+ "text": "we're not actually increasing the"
+ },
+ {
+ "start": 1219.56,
+ "duration": 0.0,
+ "text": "we're not actually increasing the information<00:20:20.480> content<00:20:21.400> um"
+ },
+ {
+ "start": 1221.99,
+ "duration": 0.0,
+ "text": "information content um"
+ },
+ {
+ "start": 1222.0,
+ "duration": 0.0,
+ "text": "information content um uh<00:20:22.200> according<00:20:22.560> to<00:20:22.680> Shannon<00:20:22.920> information,<00:20:23.880> and"
+ },
+ {
+ "start": 1224.07,
+ "duration": 0.0,
+ "text": "uh according to Shannon information, and"
+ },
+ {
+ "start": 1224.08,
+ "duration": 0.0,
+ "text": "uh according to Shannon information, and we<00:20:24.200> can<00:20:24.520> get<00:20:24.720> a<00:20:24.760> similar<00:20:25.320> result<00:20:25.840> from"
+ },
+ {
+ "start": 1226.51,
+ "duration": 0.0,
+ "text": "we can get a similar result from"
+ },
+ {
+ "start": 1226.52,
+ "duration": 0.0,
+ "text": "we can get a similar result from algorithmic<00:20:27.000> information<00:20:27.560> theory<00:20:27.840> with"
+ },
+ {
+ "start": 1228.07,
+ "duration": 0.0,
+ "text": "algorithmic information theory with"
+ },
+ {
+ "start": 1228.08,
+ "duration": 0.0,
+ "text": "algorithmic information theory with Kolmogorov<00:20:28.760> complexity.<00:20:30.000> And<00:20:30.280> so,<00:20:31.080> uh<00:20:31.960> this"
+ },
+ {
+ "start": 1232.59,
+ "duration": 0.0,
+ "text": "Kolmogorov complexity. And so, uh this"
+ },
+ {
+ "start": 1232.6,
+ "duration": 0.0,
+ "text": "Kolmogorov complexity. And so, uh this leads<00:20:32.840> to<00:20:32.920> this<00:20:33.080> question<00:20:33.480> of<00:20:33.880> like<00:20:34.360> um"
+ },
+ {
+ "start": 1235.91,
+ "duration": 0.0,
+ "text": "leads to this question of like um"
+ },
+ {
+ "start": 1235.92,
+ "duration": 0.0,
+ "text": "leads to this question of like um you<00:20:35.960> know,<00:20:36.080> how<00:20:36.280> can<00:20:36.440> pseudo<00:20:36.680> random<00:20:36.960> numbers"
+ },
+ {
+ "start": 1237.31,
+ "duration": 0.0,
+ "text": "you know, how can pseudo random numbers"
+ },
+ {
+ "start": 1237.32,
+ "duration": 0.0,
+ "text": "you know, how can pseudo random numbers then<00:20:37.560> actually<00:20:37.920> be"
+ },
+ {
+ "start": 1238.91,
+ "duration": 0.0,
+ "text": "then actually be"
+ },
+ {
+ "start": 1238.92,
+ "duration": 0.0,
+ "text": "then actually be uh<00:20:39.640> uh"
+ },
+ {
+ "start": 1240.23,
+ "duration": 0.0,
+ "text": "uh uh"
+ },
+ {
+ "start": 1240.24,
+ "duration": 0.0,
+ "text": "uh uh useful?<00:20:41.000> Uh"
+ },
+ {
+ "start": 1241.79,
+ "duration": 0.0,
+ "text": "useful? Uh"
+ },
+ {
+ "start": 1241.8,
+ "duration": 0.0,
+ "text": "useful? Uh uh<00:20:42.320> they're<00:20:42.760> indistinguishable<00:20:43.600> from<00:20:43.800> actual"
+ },
+ {
+ "start": 1244.11,
+ "duration": 0.0,
+ "text": "uh they're indistinguishable from actual"
+ },
+ {
+ "start": 1244.12,
+ "duration": 0.0,
+ "text": "uh they're indistinguishable from actual random<00:20:44.440> numbers,<00:20:45.080> um<00:20:45.760> uh<00:20:46.120> but<00:20:46.680> they<00:20:46.920> don't"
+ },
+ {
+ "start": 1247.31,
+ "duration": 0.0,
+ "text": "random numbers, um uh but they don't"
+ },
+ {
+ "start": 1247.32,
+ "duration": 0.0,
+ "text": "random numbers, um uh but they don't seem<00:20:47.520> to<00:20:47.640> add<00:20:47.840> information.<00:20:48.960> Um<00:20:49.160> and<00:20:49.320> so,<00:20:49.800> how"
+ },
+ {
+ "start": 1249.99,
+ "duration": 0.0,
+ "text": "seem to add information. Um and so, how"
+ },
+ {
+ "start": 1250.0,
+ "duration": 0.0,
+ "text": "seem to add information. Um and so, how can<00:20:50.160> we<00:20:50.560> really<00:20:50.840> accommodate<00:20:51.400> this<00:20:51.720> in"
+ },
+ {
+ "start": 1252.11,
+ "duration": 0.0,
+ "text": "can we really accommodate this in"
+ },
+ {
+ "start": 1252.12,
+ "duration": 0.0,
+ "text": "can we really accommodate this in rethinking<00:20:52.680> how<00:20:52.840> we<00:20:52.960> measure<00:20:53.320> information?"
+ },
+ {
+ "start": 1254.59,
+ "duration": 0.0,
+ "text": "rethinking how we measure information?"
+ },
+ {
+ "start": 1254.6,
+ "duration": 0.0,
+ "text": "rethinking how we measure information? Um<00:20:55.320> we've<00:20:55.560> also<00:20:56.480> made<00:20:56.800> use<00:20:57.160> of<00:20:57.640> elementary"
+ },
+ {
+ "start": 1258.15,
+ "duration": 0.0,
+ "text": "Um we've also made use of elementary"
+ },
+ {
+ "start": 1258.16,
+ "duration": 0.0,
+ "text": "Um we've also made use of elementary cellular<00:20:58.720> automata<00:20:59.760> as<00:20:59.960> a<00:21:00.040> mechanism<00:21:00.720> for"
+ },
+ {
+ "start": 1261.59,
+ "duration": 0.0,
+ "text": "cellular automata as a mechanism for"
+ },
+ {
+ "start": 1261.6,
+ "duration": 0.0,
+ "text": "cellular automata as a mechanism for reasoning<00:21:02.000> about<00:21:02.240> the<00:21:02.360> role<00:21:02.600> of<00:21:02.680> computation"
+ },
+ {
+ "start": 1263.67,
+ "duration": 0.0,
+ "text": "reasoning about the role of computation"
+ },
+ {
+ "start": 1263.68,
+ "duration": 0.0,
+ "text": "reasoning about the role of computation and<00:21:04.000> emergent<00:21:04.480> structure<00:21:04.960> and<00:21:05.120> deterministic"
+ },
+ {
+ "start": 1265.75,
+ "duration": 0.0,
+ "text": "and emergent structure and deterministic"
+ },
+ {
+ "start": 1265.76,
+ "duration": 0.0,
+ "text": "and emergent structure and deterministic transformations.<00:21:06.640> So,<00:21:06.800> just<00:21:07.040> as<00:21:07.160> a<00:21:07.200> little"
+ },
+ {
+ "start": 1267.35,
+ "duration": 0.0,
+ "text": "transformations. So, just as a little"
+ },
+ {
+ "start": 1267.36,
+ "duration": 0.0,
+ "text": "transformations. So, just as a little bit<00:21:07.480> of<00:21:07.600> background,<00:21:08.680> um<00:21:09.080> ECA<00:21:09.720> are<00:21:10.280> uh<00:21:10.600> 1D"
+ },
+ {
+ "start": 1271.07,
+ "duration": 0.0,
+ "text": "bit of background, um ECA are uh 1D"
+ },
+ {
+ "start": 1271.08,
+ "duration": 0.0,
+ "text": "bit of background, um ECA are uh 1D array<00:21:11.520> of<00:21:11.760> binary<00:21:12.200> cells."
+ },
+ {
+ "start": 1274.03,
+ "duration": 0.0,
+ "text": "array of binary cells."
+ },
+ {
+ "start": 1274.04,
+ "duration": 0.0,
+ "text": "array of binary cells. Each<00:21:14.280> cell's<00:21:15.120> next<00:21:15.480> value<00:21:16.080> at<00:21:16.280> the<00:21:16.360> next"
+ },
+ {
+ "start": 1276.63,
+ "duration": 0.0,
+ "text": "Each cell's next value at the next"
+ },
+ {
+ "start": 1276.64,
+ "duration": 0.0,
+ "text": "Each cell's next value at the next iteration<00:21:17.240> depends<00:21:17.760> only<00:21:18.120> on<00:21:18.560> its<00:21:19.240> own<00:21:19.480> value"
+ },
+ {
+ "start": 1280.35,
+ "duration": 0.0,
+ "text": "iteration depends only on its own value"
+ },
+ {
+ "start": 1280.36,
+ "duration": 0.0,
+ "text": "iteration depends only on its own value plus<00:21:20.720> the<00:21:20.840> value<00:21:21.320> of<00:21:21.520> its<00:21:21.800> two<00:21:22.000> neighbors."
+ },
+ {
+ "start": 1283.31,
+ "duration": 0.0,
+ "text": "plus the value of its two neighbors."
+ },
+ {
+ "start": 1283.32,
+ "duration": 0.0,
+ "text": "plus the value of its two neighbors. And<00:21:23.480> so,<00:21:23.600> this<00:21:23.800> means<00:21:24.000> there<00:21:24.160> going<00:21:24.360> to<00:21:24.520> be"
+ },
+ {
+ "start": 1285.19,
+ "duration": 0.0,
+ "text": "And so, this means there going to be"
+ },
+ {
+ "start": 1285.2,
+ "duration": 0.0,
+ "text": "And so, this means there going to be eight<00:21:25.360> possible<00:21:25.920> local<00:21:26.520> neighborhoods<00:21:27.120> that"
+ },
+ {
+ "start": 1287.35,
+ "duration": 0.0,
+ "text": "eight possible local neighborhoods that"
+ },
+ {
+ "start": 1287.36,
+ "duration": 0.0,
+ "text": "eight possible local neighborhoods that will<00:21:28.080> determine<00:21:28.640> the<00:21:28.760> state<00:21:29.080> of<00:21:29.280> a<00:21:29.560> cell<00:21:29.800> at"
+ },
+ {
+ "start": 1289.91,
+ "duration": 0.0,
+ "text": "will determine the state of a cell at"
+ },
+ {
+ "start": 1289.92,
+ "duration": 0.0,
+ "text": "will determine the state of a cell at the<00:21:30.000> next<00:21:30.280> time<00:21:30.480> step.<00:21:31.320> And<00:21:31.880> each<00:21:32.120> of<00:21:32.200> these"
+ },
+ {
+ "start": 1292.35,
+ "duration": 0.0,
+ "text": "the next time step. And each of these"
+ },
+ {
+ "start": 1292.36,
+ "duration": 0.0,
+ "text": "the next time step. And each of these local<00:21:32.680> neighborhoods<00:21:33.280> can<00:21:33.520> have<00:21:33.960> a<00:21:34.040> rule"
+ },
+ {
+ "start": 1294.31,
+ "duration": 0.0,
+ "text": "local neighborhoods can have a rule"
+ },
+ {
+ "start": 1294.32,
+ "duration": 0.0,
+ "text": "local neighborhoods can have a rule associated<00:21:34.920> with<00:21:35.080> them.<00:21:35.360> So,<00:21:35.520> that<00:21:35.760> means"
+ },
+ {
+ "start": 1296.03,
+ "duration": 0.0,
+ "text": "associated with them. So, that means"
+ },
+ {
+ "start": 1296.04,
+ "duration": 0.0,
+ "text": "associated with them. So, that means that<00:21:36.200> there<00:21:36.520> are<00:21:36.920> two<00:21:37.080> to<00:21:37.160> the<00:21:37.320> eight<00:21:37.560> or<00:21:37.680> 256"
+ },
+ {
+ "start": 1299.11,
+ "duration": 0.0,
+ "text": "that there are two to the eight or 256"
+ },
+ {
+ "start": 1299.12,
+ "duration": 0.0,
+ "text": "that there are two to the eight or 256 different<00:21:39.440> possible<00:21:40.160> ECA<00:21:40.800> rules."
+ },
+ {
+ "start": 1301.99,
+ "duration": 0.0,
+ "text": "different possible ECA rules."
+ },
+ {
+ "start": 1302.0,
+ "duration": 0.0,
+ "text": "different possible ECA rules. And<00:21:42.240> these<00:21:42.520> rules<00:21:43.040> give<00:21:43.320> rise<00:21:43.680> to<00:21:44.160> very"
+ },
+ {
+ "start": 1304.43,
+ "duration": 0.0,
+ "text": "And these rules give rise to very"
+ },
+ {
+ "start": 1304.44,
+ "duration": 0.0,
+ "text": "And these rules give rise to very different<00:21:44.760> complexities<00:21:45.680> and<00:21:46.440> structures."
+ },
+ {
+ "start": 1307.43,
+ "duration": 0.0,
+ "text": "different complexities and structures."
+ },
+ {
+ "start": 1307.44,
+ "duration": 0.0,
+ "text": "different complexities and structures. And<00:21:47.680> so,<00:21:48.080> in<00:21:48.240> these<00:21:48.520> figures,<00:21:49.640> we<00:21:49.840> have<00:21:50.240> time"
+ },
+ {
+ "start": 1310.87,
+ "duration": 0.0,
+ "text": "And so, in these figures, we have time"
+ },
+ {
+ "start": 1310.88,
+ "duration": 0.0,
+ "text": "And so, in these figures, we have time running<00:21:51.240> from<00:21:51.600> top<00:21:51.920> to<00:21:52.040> bottom<00:21:52.600> in<00:21:52.800> the"
+ },
+ {
+ "start": 1312.91,
+ "duration": 0.0,
+ "text": "running from top to bottom in the"
+ },
+ {
+ "start": 1312.92,
+ "duration": 0.0,
+ "text": "running from top to bottom in the evolution<00:21:53.480> of<00:21:53.760> data<00:21:54.400> um"
+ },
+ {
+ "start": 1315.79,
+ "duration": 0.0,
+ "text": "evolution of data um"
+ },
+ {
+ "start": 1315.8,
+ "duration": 0.0,
+ "text": "evolution of data um which<00:21:55.960> is<00:21:56.080> generated<00:21:56.560> from<00:21:56.720> these<00:21:56.960> rules.<00:21:57.880> In"
+ },
+ {
+ "start": 1318.03,
+ "duration": 0.0,
+ "text": "which is generated from these rules. In"
+ },
+ {
+ "start": 1318.04,
+ "duration": 0.0,
+ "text": "which is generated from these rules. In the<00:21:58.120> left<00:21:58.400> panel<00:21:58.679> here,<00:21:58.920> we<00:21:59.040> have<00:21:59.160> an<00:21:59.280> example"
+ },
+ {
+ "start": 1320.03,
+ "duration": 0.0,
+ "text": "the left panel here, we have an example"
+ },
+ {
+ "start": 1320.04,
+ "duration": 0.0,
+ "text": "the left panel here, we have an example of<00:22:00.520> rule<00:22:00.840> 30.<00:22:01.400> So,<00:22:01.679> 111<00:22:02.280> here<00:22:02.520> maps<00:22:02.760> to<00:22:02.880> zero,"
+ },
+ {
+ "start": 1323.19,
+ "duration": 0.0,
+ "text": "of rule 30. So, 111 here maps to zero,"
+ },
+ {
+ "start": 1323.2,
+ "duration": 0.0,
+ "text": "of rule 30. So, 111 here maps to zero, 110<00:22:03.800> to<00:22:03.920> zero,<00:22:04.240> and<00:22:04.400> so<00:22:04.560> on."
+ },
+ {
+ "start": 1325.47,
+ "duration": 0.0,
+ "text": "110 to zero, and so on."
+ },
+ {
+ "start": 1325.48,
+ "duration": 0.0,
+ "text": "110 to zero, and so on. Um"
+ },
+ {
+ "start": 1326.71,
+ "duration": 0.0,
+ "text": "Um"
+ },
+ {
+ "start": 1326.72,
+ "duration": 0.0,
+ "text": "Um we<00:22:06.920> can"
+ },
+ {
+ "start": 1328.71,
+ "duration": 0.0,
+ "text": "we can"
+ },
+ {
+ "start": 1328.72,
+ "duration": 0.0,
+ "text": "we can see<00:22:08.960> that<00:22:09.480> for<00:22:09.640> certain<00:22:09.960> rules,<00:22:10.320> there<00:22:10.560> are"
+ },
+ {
+ "start": 1330.669,
+ "duration": 0.0,
+ "text": "see that for certain rules, there are"
+ },
+ {
+ "start": 1330.679,
+ "duration": 0.0,
+ "text": "see that for certain rules, there are very<00:22:11.400> simple<00:22:11.800> structures<00:22:12.360> that<00:22:12.480> arise,<00:22:12.960> like"
+ },
+ {
+ "start": 1333.27,
+ "duration": 0.0,
+ "text": "very simple structures that arise, like"
+ },
+ {
+ "start": 1333.28,
+ "duration": 0.0,
+ "text": "very simple structures that arise, like rule<00:22:13.520> 15.<00:22:14.600> Um<00:22:14.760> for<00:22:15.000> others,<00:22:15.360> like<00:22:15.600> rule<00:22:15.880> 30,<00:22:16.360> we"
+ },
+ {
+ "start": 1336.99,
+ "duration": 0.0,
+ "text": "rule 15. Um for others, like rule 30, we"
+ },
+ {
+ "start": 1337.0,
+ "duration": 0.0,
+ "text": "rule 15. Um for others, like rule 30, we effectively<00:22:17.679> have<00:22:18.240> random<00:22:18.600> structure.<00:22:19.160> And"
+ },
+ {
+ "start": 1339.31,
+ "duration": 0.0,
+ "text": "effectively have random structure. And"
+ },
+ {
+ "start": 1339.32,
+ "duration": 0.0,
+ "text": "effectively have random structure. And then,<00:22:19.520> rule<00:22:19.720> 54<00:22:20.320> is<00:22:20.440> kind<00:22:20.720> of<00:22:21.240> in<00:22:21.400> between.<00:22:21.880> It"
+ },
+ {
+ "start": 1342.03,
+ "duration": 0.0,
+ "text": "then, rule 54 is kind of in between. It"
+ },
+ {
+ "start": 1342.04,
+ "duration": 0.0,
+ "text": "then, rule 54 is kind of in between. It seems<00:22:22.280> to<00:22:22.400> have<00:22:22.760> structural<00:22:23.280> complexity,<00:22:24.520> um"
+ },
+ {
+ "start": 1344.91,
+ "duration": 0.0,
+ "text": "seems to have structural complexity, um"
+ },
+ {
+ "start": 1344.92,
+ "duration": 0.0,
+ "text": "seems to have structural complexity, um but<00:22:25.280> it's<00:22:25.679> still<00:22:25.960> relatively<00:22:26.880> predictable<00:22:27.920> as"
+ },
+ {
+ "start": 1348.07,
+ "duration": 0.0,
+ "text": "but it's still relatively predictable as"
+ },
+ {
+ "start": 1348.08,
+ "duration": 0.0,
+ "text": "but it's still relatively predictable as long<00:22:28.240> as<00:22:28.360> you<00:22:28.480> have<00:22:28.640> enough<00:22:28.840> computation.<00:22:30.120> Uh"
+ },
+ {
+ "start": 1350.31,
+ "duration": 0.0,
+ "text": "long as you have enough computation. Uh"
+ },
+ {
+ "start": 1350.32,
+ "duration": 0.0,
+ "text": "long as you have enough computation. Uh superimposed<00:22:31.080> on<00:22:31.200> these<00:22:31.400> images,<00:22:31.960> we<00:22:32.200> have<00:22:32.679> uh"
+ },
+ {
+ "start": 1352.79,
+ "duration": 0.0,
+ "text": "superimposed on these images, we have uh"
+ },
+ {
+ "start": 1352.8,
+ "duration": 0.0,
+ "text": "superimposed on these images, we have uh figures<00:22:33.360> of<00:22:34.040> uh<00:22:34.200> coffee<00:22:34.600> mixing<00:22:34.960> with<00:22:35.160> cream."
+ },
+ {
+ "start": 1355.59,
+ "duration": 0.0,
+ "text": "figures of uh coffee mixing with cream."
+ },
+ {
+ "start": 1355.6,
+ "duration": 0.0,
+ "text": "figures of uh coffee mixing with cream. And<00:22:35.800> so,<00:22:36.000> this<00:22:36.240> is<00:22:36.440> inspired<00:22:36.960> by<00:22:37.360> a<00:22:37.440> blog<00:22:37.720> post"
+ },
+ {
+ "start": 1358.23,
+ "duration": 0.0,
+ "text": "And so, this is inspired by a blog post"
+ },
+ {
+ "start": 1358.24,
+ "duration": 0.0,
+ "text": "And so, this is inspired by a blog post from<00:22:38.880> Scott<00:22:39.200> Aaronson<00:22:39.920> uh<00:22:40.440> around<00:22:40.760> 2010,"
+ },
+ {
+ "start": 1361.75,
+ "duration": 0.0,
+ "text": "from Scott Aaronson uh around 2010,"
+ },
+ {
+ "start": 1361.76,
+ "duration": 0.0,
+ "text": "from Scott Aaronson uh around 2010, where<00:22:42.360> he's<00:22:42.600> imagining<00:22:43.080> that<00:22:43.240> you<00:22:43.600> initially"
+ },
+ {
+ "start": 1364.03,
+ "duration": 0.0,
+ "text": "where he's imagining that you initially"
+ },
+ {
+ "start": 1364.04,
+ "duration": 0.0,
+ "text": "where he's imagining that you initially have<00:22:44.280> this<00:22:44.440> system<00:22:44.800> of<00:22:44.920> separated<00:22:45.440> coffee<00:22:45.760> and"
+ },
+ {
+ "start": 1365.87,
+ "duration": 0.0,
+ "text": "have this system of separated coffee and"
+ },
+ {
+ "start": 1365.88,
+ "duration": 0.0,
+ "text": "have this system of separated coffee and cream,<00:22:46.240> and<00:22:46.360> you<00:22:46.440> start<00:22:46.760> mixing<00:22:47.080> them"
+ },
+ {
+ "start": 1367.23,
+ "duration": 0.0,
+ "text": "cream, and you start mixing them"
+ },
+ {
+ "start": 1367.24,
+ "duration": 0.0,
+ "text": "cream, and you start mixing them together.<00:22:48.080> And<00:22:48.200> as<00:22:48.360> you<00:22:48.480> do<00:22:48.679> this,<00:22:48.880> the"
+ },
+ {
+ "start": 1368.99,
+ "duration": 0.0,
+ "text": "together. And as you do this, the"
+ },
+ {
+ "start": 1369.0,
+ "duration": 0.0,
+ "text": "together. And as you do this, the entropy<00:22:49.440> of<00:22:49.560> the<00:22:49.640> system<00:22:50.160> continues<00:22:50.640> to"
+ },
+ {
+ "start": 1370.87,
+ "duration": 0.0,
+ "text": "entropy of the system continues to"
+ },
+ {
+ "start": 1370.88,
+ "duration": 0.0,
+ "text": "entropy of the system continues to increase,<00:22:51.480> but<00:22:51.720> intuitively,<00:22:53.080> the"
+ },
+ {
+ "start": 1373.27,
+ "duration": 0.0,
+ "text": "increase, but intuitively, the"
+ },
+ {
+ "start": 1373.28,
+ "duration": 0.0,
+ "text": "increase, but intuitively, the sophistication<00:22:54.120> of<00:22:54.200> the<00:22:54.320> system<00:22:54.720> is"
+ },
+ {
+ "start": 1374.95,
+ "duration": 0.0,
+ "text": "sophistication of the system is"
+ },
+ {
+ "start": 1374.96,
+ "duration": 0.0,
+ "text": "sophistication of the system is non-monotonic.<00:22:56.000> So,<00:22:56.600> uh<00:22:56.840> at<00:22:56.960> the<00:22:57.040> beginning,"
+ },
+ {
+ "start": 1377.75,
+ "duration": 0.0,
+ "text": "non-monotonic. So, uh at the beginning,"
+ },
+ {
+ "start": 1377.76,
+ "duration": 0.0,
+ "text": "non-monotonic. So, uh at the beginning, you<00:22:57.880> don't<00:22:58.120> really<00:22:58.360> have<00:22:58.600> much<00:22:58.920> intuitive"
+ },
+ {
+ "start": 1379.51,
+ "duration": 0.0,
+ "text": "you don't really have much intuitive"
+ },
+ {
+ "start": 1379.52,
+ "duration": 0.0,
+ "text": "you don't really have much intuitive complexity.<00:23:00.600> In<00:23:01.000> the<00:23:01.120> middle,<00:23:01.520> you<00:23:01.720> have<00:23:02.080> some"
+ },
+ {
+ "start": 1382.31,
+ "duration": 0.0,
+ "text": "complexity. In the middle, you have some"
+ },
+ {
+ "start": 1382.32,
+ "duration": 0.0,
+ "text": "complexity. In the middle, you have some maximum<00:23:02.840> of<00:23:02.960> complexity,<00:23:03.640> and<00:23:03.760> then<00:23:03.880> at<00:23:03.960> the"
+ },
+ {
+ "start": 1384.11,
+ "duration": 0.0,
+ "text": "maximum of complexity, and then at the"
+ },
+ {
+ "start": 1384.12,
+ "duration": 0.0,
+ "text": "maximum of complexity, and then at the end,<00:23:04.679> you<00:23:04.840> actually<00:23:05.080> don't<00:23:05.240> have<00:23:05.400> any"
+ },
+ {
+ "start": 1385.55,
+ "duration": 0.0,
+ "text": "end, you actually don't have any"
+ },
+ {
+ "start": 1385.56,
+ "duration": 0.0,
+ "text": "end, you actually don't have any interesting<00:23:06.000> complexity<00:23:06.640> anymore.<00:23:07.480> And<00:23:07.679> so,"
+ },
+ {
+ "start": 1388.07,
+ "duration": 0.0,
+ "text": "interesting complexity anymore. And so,"
+ },
+ {
+ "start": 1388.08,
+ "duration": 0.0,
+ "text": "interesting complexity anymore. And so, this<00:23:08.280> is<00:23:08.440> exactly<00:23:09.000> what<00:23:09.240> we're<00:23:09.880> intending<00:23:10.360> to"
+ },
+ {
+ "start": 1390.47,
+ "duration": 0.0,
+ "text": "this is exactly what we're intending to"
+ },
+ {
+ "start": 1390.48,
+ "duration": 0.0,
+ "text": "this is exactly what we're intending to capture<00:23:11.000> with<00:23:11.720> appiplexity."
+ },
+ {
+ "start": 1393.99,
+ "duration": 0.0,
+ "text": "capture with appiplexity."
+ },
+ {
+ "start": 1394.0,
+ "duration": 0.0,
+ "text": "capture with appiplexity. These<00:23:14.880> ECA<00:23:15.400> systems<00:23:16.000> are<00:23:16.200> also<00:23:17.320> really"
+ },
+ {
+ "start": 1397.63,
+ "duration": 0.0,
+ "text": "These ECA systems are also really"
+ },
+ {
+ "start": 1397.64,
+ "duration": 0.0,
+ "text": "These ECA systems are also really interesting<00:23:18.280> because<00:23:18.760> they<00:23:19.040> allow<00:23:19.400> us<00:23:19.560> to"
+ },
+ {
+ "start": 1399.71,
+ "duration": 0.0,
+ "text": "interesting because they allow us to"
+ },
+ {
+ "start": 1399.72,
+ "duration": 0.0,
+ "text": "interesting because they allow us to study<00:23:20.040> the<00:23:20.120> emergent<00:23:20.560> phenomena.<00:23:21.520> Like,<00:23:21.679> if"
+ },
+ {
+ "start": 1401.83,
+ "duration": 0.0,
+ "text": "study the emergent phenomena. Like, if"
+ },
+ {
+ "start": 1401.84,
+ "duration": 0.0,
+ "text": "study the emergent phenomena. Like, if you<00:23:22.320> could<00:23:22.440> just<00:23:22.679> reverse<00:23:23.080> engineer<00:23:23.640> the"
+ },
+ {
+ "start": 1403.83,
+ "duration": 0.0,
+ "text": "you could just reverse engineer the"
+ },
+ {
+ "start": 1403.84,
+ "duration": 0.0,
+ "text": "you could just reverse engineer the rules<00:23:24.280> behind<00:23:25.120> the<00:23:25.240> data,<00:23:25.760> then<00:23:26.000> you<00:23:26.120> could"
+ },
+ {
+ "start": 1406.35,
+ "duration": 0.0,
+ "text": "rules behind the data, then you could"
+ },
+ {
+ "start": 1406.36,
+ "duration": 0.0,
+ "text": "rules behind the data, then you could predict<00:23:26.679> ahead<00:23:27.040> very<00:23:27.440> easily,<00:23:27.840> and<00:23:27.960> this"
+ },
+ {
+ "start": 1408.11,
+ "duration": 0.0,
+ "text": "predict ahead very easily, and this"
+ },
+ {
+ "start": 1408.12,
+ "duration": 0.0,
+ "text": "predict ahead very easily, and this would<00:23:28.240> have<00:23:28.360> a<00:23:28.440> very<00:23:28.640> short<00:23:29.000> description"
+ },
+ {
+ "start": 1409.51,
+ "duration": 0.0,
+ "text": "would have a very short description"
+ },
+ {
+ "start": 1409.52,
+ "duration": 0.0,
+ "text": "would have a very short description length,<00:23:29.800> and<00:23:30.280> actually<00:23:30.600> wouldn't"
+ },
+ {
+ "start": 1410.83,
+ "duration": 0.0,
+ "text": "length, and actually wouldn't"
+ },
+ {
+ "start": 1410.84,
+ "duration": 0.0,
+ "text": "length, and actually wouldn't necessarily<00:23:31.360> be<00:23:31.480> very<00:23:31.800> interesting<00:23:32.360> from<00:23:32.560> the"
+ },
+ {
+ "start": 1412.63,
+ "duration": 0.0,
+ "text": "necessarily be very interesting from the"
+ },
+ {
+ "start": 1412.64,
+ "duration": 0.0,
+ "text": "necessarily be very interesting from the perspective<00:23:33.200> of<00:23:33.320> downstream"
+ },
+ {
+ "start": 1414.15,
+ "duration": 0.0,
+ "text": "perspective of downstream"
+ },
+ {
+ "start": 1414.16,
+ "duration": 0.0,
+ "text": "perspective of downstream generalization.<00:23:35.360> But<00:23:35.520> because<00:23:35.960> it's<00:23:36.440> very,"
+ },
+ {
+ "start": 1416.71,
+ "duration": 0.0,
+ "text": "generalization. But because it's very,"
+ },
+ {
+ "start": 1416.72,
+ "duration": 0.0,
+ "text": "generalization. But because it's very, very<00:23:36.920> difficult<00:23:37.480> for<00:23:37.600> a<00:23:37.679> model<00:23:38.000> to<00:23:38.160> do<00:23:38.440> that,"
+ },
+ {
+ "start": 1419.11,
+ "duration": 0.0,
+ "text": "very difficult for a model to do that,"
+ },
+ {
+ "start": 1419.12,
+ "duration": 0.0,
+ "text": "very difficult for a model to do that, it<00:23:39.280> instead<00:23:39.800> learns<00:23:40.160> emergent<00:23:40.640> structures<00:23:41.600> of"
+ },
+ {
+ "start": 1421.75,
+ "duration": 0.0,
+ "text": "it instead learns emergent structures of"
+ },
+ {
+ "start": 1421.76,
+ "duration": 0.0,
+ "text": "it instead learns emergent structures of floaters<00:23:42.240> and<00:23:42.360> things<00:23:42.600> like<00:23:42.800> this<00:23:43.040> that<00:23:43.160> it"
+ },
+ {
+ "start": 1423.27,
+ "duration": 0.0,
+ "text": "floaters and things like this that it"
+ },
+ {
+ "start": 1423.28,
+ "duration": 0.0,
+ "text": "floaters and things like this that it can<00:23:43.440> use<00:23:43.679> to<00:23:43.760> predict<00:23:44.200> the<00:23:44.280> next<00:23:44.520> state.<00:23:44.840> So,"
+ },
+ {
+ "start": 1424.95,
+ "duration": 0.0,
+ "text": "can use to predict the next state. So,"
+ },
+ {
+ "start": 1424.96,
+ "duration": 0.0,
+ "text": "can use to predict the next state. So, in<00:23:45.080> some<00:23:45.280> sense,<00:23:45.520> it's<00:23:45.720> actually<00:23:46.040> going"
+ },
+ {
+ "start": 1426.35,
+ "duration": 0.0,
+ "text": "in some sense, it's actually going"
+ },
+ {
+ "start": 1426.36,
+ "duration": 0.0,
+ "text": "in some sense, it's actually going beyond<00:23:47.120> the<00:23:47.200> data<00:23:47.480> generating<00:23:48.360> process.<00:23:49.120> And"
+ },
+ {
+ "start": 1429.63,
+ "duration": 0.0,
+ "text": "beyond the data generating process. And"
+ },
+ {
+ "start": 1429.64,
+ "duration": 0.0,
+ "text": "beyond the data generating process. And this<00:23:49.800> is<00:23:49.960> something<00:23:50.280> that<00:23:50.400> we<00:23:50.560> can<00:23:51.000> capture"
+ },
+ {
+ "start": 1431.39,
+ "duration": 0.0,
+ "text": "this is something that we can capture"
+ },
+ {
+ "start": 1431.4,
+ "duration": 0.0,
+ "text": "this is something that we can capture with<00:23:51.560> appiplexity.<00:23:52.280> So,<00:23:52.800> now<00:23:52.960> Mark's<00:23:53.280> going"
+ },
+ {
+ "start": 1433.39,
+ "duration": 0.0,
+ "text": "with appiplexity. So, now Mark's going"
+ },
+ {
+ "start": 1433.4,
+ "duration": 0.0,
+ "text": "with appiplexity. So, now Mark's going to<00:23:53.720> properly<00:23:54.120> introduce<00:23:54.560> appiplexity<00:23:55.360> and<00:23:55.600> go"
+ },
+ {
+ "start": 1435.79,
+ "duration": 0.0,
+ "text": "to properly introduce appiplexity and go"
+ },
+ {
+ "start": 1435.8,
+ "duration": 0.0,
+ "text": "to properly introduce appiplexity and go through<00:23:56.480> how<00:23:56.679> it<00:23:56.880> can<00:23:57.240> help<00:23:57.520> resolve<00:23:57.880> these"
+ },
+ {
+ "start": 1438.07,
+ "duration": 0.0,
+ "text": "through how it can help resolve these"
+ },
+ {
+ "start": 1438.08,
+ "duration": 0.0,
+ "text": "through how it can help resolve these paradoxes<00:23:58.720> that<00:23:58.800> we've<00:23:59.000> introduced."
+ },
+ {
+ "start": 1443.4,
+ "duration": 0.0,
+ "text": "All<00:24:03.720> right."
+ },
+ {
+ "start": 1451.92,
+ "duration": 0.0,
+ "text": "So,<00:24:12.480> with<00:24:12.640> that<00:24:13.040> intuition<00:24:14.000> um<00:24:14.160> setting<00:24:14.480> the"
+ },
+ {
+ "start": 1454.59,
+ "duration": 0.0,
+ "text": "So, with that intuition um setting the"
+ },
+ {
+ "start": 1454.6,
+ "duration": 0.0,
+ "text": "So, with that intuition um setting the stage,"
+ },
+ {
+ "start": 1455.71,
+ "duration": 0.0,
+ "text": "stage,"
+ },
+ {
+ "start": 1455.72,
+ "duration": 0.0,
+ "text": "stage, I<00:24:15.760> hope<00:24:15.960> everyone<00:24:16.240> can<00:24:16.520> see<00:24:17.040> all<00:24:17.280> right."
+ },
+ {
+ "start": 1458.31,
+ "duration": 0.0,
+ "text": "I hope everyone can see all right."
+ },
+ {
+ "start": 1458.32,
+ "duration": 0.0,
+ "text": "I hope everyone can see all right. Let<00:24:18.400> me<00:24:18.520> just<00:24:18.800> move<00:24:19.080> this."
+ },
+ {
+ "start": 1460.51,
+ "duration": 0.0,
+ "text": "Let me just move this."
+ },
+ {
+ "start": 1460.52,
+ "duration": 0.0,
+ "text": "Let me just move this. Looks<00:24:20.720> good."
+ },
+ {
+ "start": 1462.669,
+ "duration": 0.0,
+ "text": "Looks good."
+ },
+ {
+ "start": 1462.679,
+ "duration": 0.0,
+ "text": "Looks good. Uh"
+ },
+ {
+ "start": 1464.63,
+ "duration": 0.0,
+ "text": "Uh"
+ },
+ {
+ "start": 1464.64,
+ "duration": 0.0,
+ "text": "Uh yeah,<00:24:24.840> so<00:24:24.960> with<00:24:25.080> that<00:24:25.560> intuition<00:24:26.080> setting<00:24:26.360> the"
+ },
+ {
+ "start": 1466.43,
+ "duration": 0.0,
+ "text": "yeah, so with that intuition setting the"
+ },
+ {
+ "start": 1466.44,
+ "duration": 0.0,
+ "text": "yeah, so with that intuition setting the stage,<00:24:27.080> now<00:24:27.280> we'll<00:24:27.480> actually<00:24:28.480> define<00:24:29.760> our"
+ },
+ {
+ "start": 1470.51,
+ "duration": 0.0,
+ "text": "stage, now we'll actually define our"
+ },
+ {
+ "start": 1470.52,
+ "duration": 0.0,
+ "text": "stage, now we'll actually define our appiplexity.<00:24:31.720> So,<00:24:31.880> the<00:24:31.960> starting<00:24:32.320> point,<00:24:33.200> as"
+ },
+ {
+ "start": 1473.75,
+ "duration": 0.0,
+ "text": "appiplexity. So, the starting point, as"
+ },
+ {
+ "start": 1473.76,
+ "duration": 0.0,
+ "text": "appiplexity. So, the starting point, as Andrew's<00:24:34.160> been<00:24:34.320> alluding<00:24:34.679> to,<00:24:35.160> is"
+ },
+ {
+ "start": 1476.11,
+ "duration": 0.0,
+ "text": "Andrew's been alluding to, is"
+ },
+ {
+ "start": 1476.12,
+ "duration": 0.0,
+ "text": "Andrew's been alluding to, is restricting<00:24:36.679> the<00:24:36.800> computation<00:24:37.600> available<00:24:38.400> to"
+ },
+ {
+ "start": 1478.51,
+ "duration": 0.0,
+ "text": "restricting the computation available to"
+ },
+ {
+ "start": 1478.52,
+ "duration": 0.0,
+ "text": "restricting the computation available to the<00:24:38.600> model."
+ },
+ {
+ "start": 1480.03,
+ "duration": 0.0,
+ "text": "the model."
+ },
+ {
+ "start": 1480.04,
+ "duration": 0.0,
+ "text": "the model. And<00:24:40.240> here,<00:24:40.840> what<00:24:40.960> we<00:24:41.080> mean<00:24:41.280> by<00:24:41.440> model<00:24:42.160> is<00:24:42.720> a"
+ },
+ {
+ "start": 1482.79,
+ "duration": 0.0,
+ "text": "And here, what we mean by model is a"
+ },
+ {
+ "start": 1482.8,
+ "duration": 0.0,
+ "text": "And here, what we mean by model is a probabilistic<00:24:43.400> model.<00:24:44.240> It's<00:24:44.400> going<00:24:44.520> to<00:24:44.600> be"
+ },
+ {
+ "start": 1484.87,
+ "duration": 0.0,
+ "text": "probabilistic model. It's going to be"
+ },
+ {
+ "start": 1484.88,
+ "duration": 0.0,
+ "text": "probabilistic model. It's going to be taking<00:24:45.160> the<00:24:45.240> place<00:24:45.560> of<00:24:45.720> our<00:24:46.040> machine<00:24:46.280> learning"
+ },
+ {
+ "start": 1486.47,
+ "duration": 0.0,
+ "text": "taking the place of our machine learning"
+ },
+ {
+ "start": 1486.48,
+ "duration": 0.0,
+ "text": "taking the place of our machine learning model<00:24:46.840> that<00:24:47.000> is<00:24:47.120> looking<00:24:47.360> at<00:24:47.440> this<00:24:47.560> data,"
+ },
+ {
+ "start": 1488.19,
+ "duration": 0.0,
+ "text": "model that is looking at this data,"
+ },
+ {
+ "start": 1488.2,
+ "duration": 0.0,
+ "text": "model that is looking at this data, trying<00:24:48.480> to<00:24:48.560> understand<00:24:48.960> it."
+ },
+ {
+ "start": 1489.87,
+ "duration": 0.0,
+ "text": "trying to understand it."
+ },
+ {
+ "start": 1489.88,
+ "duration": 0.0,
+ "text": "trying to understand it. Trying<00:24:50.360> to<00:24:51.400> provide<00:24:51.720> a<00:24:51.760> short<00:24:52.000> code<00:24:52.679> to"
+ },
+ {
+ "start": 1492.75,
+ "duration": 0.0,
+ "text": "Trying to provide a short code to"
+ },
+ {
+ "start": 1492.76,
+ "duration": 0.0,
+ "text": "Trying to provide a short code to produce<00:24:53.000> that<00:24:53.120> model."
+ },
+ {
+ "start": 1494.23,
+ "duration": 0.0,
+ "text": "produce that model."
+ },
+ {
+ "start": 1494.24,
+ "duration": 0.0,
+ "text": "produce that model. So,<00:24:54.400> we<00:24:54.880> write<00:24:55.800> PT<00:24:56.560> as<00:24:57.200> set<00:24:57.480> of<00:24:57.560> programs<00:24:58.240> that"
+ },
+ {
+ "start": 1498.51,
+ "duration": 0.0,
+ "text": "So, we write PT as set of programs that"
+ },
+ {
+ "start": 1498.52,
+ "duration": 0.0,
+ "text": "So, we write PT as set of programs that implement<00:24:59.160> normalized<00:24:59.640> probability"
+ },
+ {
+ "start": 1499.91,
+ "duration": 0.0,
+ "text": "implement normalized probability"
+ },
+ {
+ "start": 1499.92,
+ "duration": 0.0,
+ "text": "implement normalized probability distributions<00:25:01.120> on<00:25:01.320> just<00:25:02.160> a<00:25:02.240> binary<00:25:02.600> string<00:25:03.120> of"
+ },
+ {
+ "start": 1503.23,
+ "duration": 0.0,
+ "text": "distributions on just a binary string of"
+ },
+ {
+ "start": 1503.24,
+ "duration": 0.0,
+ "text": "distributions on just a binary string of length<00:25:03.480> n,"
+ },
+ {
+ "start": 1504.63,
+ "duration": 0.0,
+ "text": "length n,"
+ },
+ {
+ "start": 1504.64,
+ "duration": 0.0,
+ "text": "length n, where<00:25:05.240> both<00:25:06.120> sampling<00:25:07.200> and<00:25:07.480> probability"
+ },
+ {
+ "start": 1507.91,
+ "duration": 0.0,
+ "text": "where both sampling and probability"
+ },
+ {
+ "start": 1507.92,
+ "duration": 0.0,
+ "text": "where both sampling and probability estimation<00:25:08.600> can<00:25:08.760> be<00:25:08.840> done<00:25:09.280> in<00:25:09.400> time<00:25:09.760> T<00:25:10.000> of<00:25:10.120> n."
+ },
+ {
+ "start": 1510.43,
+ "duration": 0.0,
+ "text": "estimation can be done in time T of n."
+ },
+ {
+ "start": 1510.44,
+ "duration": 0.0,
+ "text": "estimation can be done in time T of n. So,<00:25:10.600> T<00:25:10.720> is<00:25:10.840> going<00:25:10.960> to<00:25:11.000> be<00:25:11.080> a<00:25:11.120> function.<00:25:11.920> Could"
+ },
+ {
+ "start": 1512.07,
+ "duration": 0.0,
+ "text": "So, T is going to be a function. Could"
+ },
+ {
+ "start": 1512.08,
+ "duration": 0.0,
+ "text": "So, T is going to be a function. Could be<00:25:12.200> n<00:25:12.320> squared,<00:25:13.120> could<00:25:13.280> be,<00:25:13.440> you<00:25:13.520> know,<00:25:13.640> some"
+ },
+ {
+ "start": 1513.83,
+ "duration": 0.0,
+ "text": "be n squared, could be, you know, some"
+ },
+ {
+ "start": 1513.84,
+ "duration": 0.0,
+ "text": "be n squared, could be, you know, some constant,<00:25:14.160> you<00:25:14.240> know,<00:25:14.400> some<00:25:14.520> linear"
+ },
+ {
+ "start": 1514.75,
+ "duration": 0.0,
+ "text": "constant, you know, some linear"
+ },
+ {
+ "start": 1514.76,
+ "duration": 0.0,
+ "text": "constant, you know, some linear function,"
+ },
+ {
+ "start": 1515.87,
+ "duration": 0.0,
+ "text": "function,"
+ },
+ {
+ "start": 1515.88,
+ "duration": 0.0,
+ "text": "function, and<00:25:16.000> whatnot."
+ },
+ {
+ "start": 1517.669,
+ "duration": 0.0,
+ "text": "and whatnot."
+ },
+ {
+ "start": 1517.679,
+ "duration": 0.0,
+ "text": "and whatnot. And<00:25:17.800> that's<00:25:18.000> how<00:25:18.120> we're<00:25:18.200> going<00:25:18.320> to<00:25:18.400> restrict"
+ },
+ {
+ "start": 1519.07,
+ "duration": 0.0,
+ "text": "And that's how we're going to restrict"
+ },
+ {
+ "start": 1519.08,
+ "duration": 0.0,
+ "text": "And that's how we're going to restrict the<00:25:19.160> computation."
+ },
+ {
+ "start": 1521.55,
+ "duration": 0.0,
+ "text": "the computation."
+ },
+ {
+ "start": 1521.56,
+ "duration": 0.0,
+ "text": "the computation. So,<00:25:22.040> yeah,<00:25:22.400> m-<00:25:22.640> note<00:25:22.840> here,<00:25:23.280> this<00:25:23.480> is<00:25:23.600> just<00:25:24.040> for"
+ },
+ {
+ "start": 1524.31,
+ "duration": 0.0,
+ "text": "So, yeah, m- note here, this is just for"
+ },
+ {
+ "start": 1524.32,
+ "duration": 0.0,
+ "text": "So, yeah, m- note here, this is just for discrete<00:25:24.720> data."
+ },
+ {
+ "start": 1525.59,
+ "duration": 0.0,
+ "text": "discrete data."
+ },
+ {
+ "start": 1525.6,
+ "duration": 0.0,
+ "text": "discrete data. So,<00:25:25.760> with<00:25:25.880> that<00:25:26.120> in<00:25:26.280> mind,<00:25:26.960> we<00:25:27.440> define"
+ },
+ {
+ "start": 1527.95,
+ "duration": 0.0,
+ "text": "So, with that in mind, we define"
+ },
+ {
+ "start": 1527.96,
+ "duration": 0.0,
+ "text": "So, with that in mind, we define appiplexity<00:25:29.280> and<00:25:29.400> time-bounded<00:25:29.840> entropy<00:25:30.560> in"
+ },
+ {
+ "start": 1530.669,
+ "duration": 0.0,
+ "text": "appiplexity and time-bounded entropy in"
+ },
+ {
+ "start": 1530.679,
+ "duration": 0.0,
+ "text": "appiplexity and time-bounded entropy in terms<00:25:31.280> of<00:25:31.520> this"
+ },
+ {
+ "start": 1532.75,
+ "duration": 0.0,
+ "text": "terms of this"
+ },
+ {
+ "start": 1532.76,
+ "duration": 0.0,
+ "text": "terms of this uh<00:25:33.000> you<00:25:33.080> know,<00:25:33.160> related<00:25:33.440> to<00:25:33.520> this<00:25:33.679> minimum"
+ },
+ {
+ "start": 1534.03,
+ "duration": 0.0,
+ "text": "uh you know, related to this minimum"
+ },
+ {
+ "start": 1534.04,
+ "duration": 0.0,
+ "text": "uh you know, related to this minimum description<00:25:34.520> length<00:25:34.720> principle."
+ },
+ {
+ "start": 1535.79,
+ "duration": 0.0,
+ "text": "description length principle."
+ },
+ {
+ "start": 1535.8,
+ "duration": 0.0,
+ "text": "description length principle. So,<00:25:36.640> we<00:25:36.880> consider<00:25:37.280> this<00:25:37.440> quantity,<00:25:37.960> which<00:25:38.200> is"
+ },
+ {
+ "start": 1538.31,
+ "duration": 0.0,
+ "text": "So, we consider this quantity, which is"
+ },
+ {
+ "start": 1538.32,
+ "duration": 0.0,
+ "text": "So, we consider this quantity, which is the<00:25:38.400> sum<00:25:39.080> of<00:25:39.360> the<00:25:39.480> program<00:25:39.840> size,<00:25:40.880> measured<00:25:41.160> in"
+ },
+ {
+ "start": 1541.27,
+ "duration": 0.0,
+ "text": "the sum of the program size, measured in"
+ },
+ {
+ "start": 1541.28,
+ "duration": 0.0,
+ "text": "the sum of the program size, measured in bits,"
+ },
+ {
+ "start": 1542.39,
+ "duration": 0.0,
+ "text": "bits,"
+ },
+ {
+ "start": 1542.4,
+ "duration": 0.0,
+ "text": "bits, and<00:25:42.560> then<00:25:43.120> this<00:25:44.040> um"
+ },
+ {
+ "start": 1545.07,
+ "duration": 0.0,
+ "text": "and then this um"
+ },
+ {
+ "start": 1545.08,
+ "duration": 0.0,
+ "text": "and then this um uh<00:25:45.560> negative<00:25:45.920> log<00:25:46.080> likelihood,<00:25:46.600> expected"
+ },
+ {
+ "start": 1546.95,
+ "duration": 0.0,
+ "text": "uh negative log likelihood, expected"
+ },
+ {
+ "start": 1546.96,
+ "duration": 0.0,
+ "text": "uh negative log likelihood, expected negative<00:25:47.240> log<00:25:47.360> likelihood,<00:25:48.160> of<00:25:48.600> the<00:25:48.679> data"
+ },
+ {
+ "start": 1549.43,
+ "duration": 0.0,
+ "text": "negative log likelihood, of the data"
+ },
+ {
+ "start": 1549.44,
+ "duration": 0.0,
+ "text": "negative log likelihood, of the data under<00:25:50.080> the<00:25:50.160> probability<00:25:50.440> distribution"
+ },
+ {
+ "start": 1551.39,
+ "duration": 0.0,
+ "text": "under the probability distribution"
+ },
+ {
+ "start": 1551.4,
+ "duration": 0.0,
+ "text": "under the probability distribution determined<00:25:51.800> by<00:25:51.920> that<00:25:52.080> program."
+ },
+ {
+ "start": 1553.63,
+ "duration": 0.0,
+ "text": "determined by that program."
+ },
+ {
+ "start": 1553.64,
+ "duration": 0.0,
+ "text": "determined by that program. Um<00:25:54.480> we<00:25:54.600> can<00:25:54.720> think<00:25:54.920> of<00:25:55.040> this<00:25:55.280> whole<00:25:55.520> quantity"
+ },
+ {
+ "start": 1556.03,
+ "duration": 0.0,
+ "text": "Um we can think of this whole quantity"
+ },
+ {
+ "start": 1556.04,
+ "duration": 0.0,
+ "text": "Um we can think of this whole quantity as<00:25:56.520> within<00:25:56.840> a<00:25:56.880> constant<00:25:58.000> to<00:25:59.000> the<00:25:59.960> uh"
+ },
+ {
+ "start": 1561.39,
+ "duration": 0.0,
+ "text": "as within a constant to the uh"
+ },
+ {
+ "start": 1561.4,
+ "duration": 0.0,
+ "text": "as within a constant to the uh the<00:26:01.600> code<00:26:01.920> length<00:26:02.560> of<00:26:02.679> the<00:26:02.760> data<00:26:03.520> using<00:26:03.880> the"
+ },
+ {
+ "start": 1563.95,
+ "duration": 0.0,
+ "text": "the code length of the data using the"
+ },
+ {
+ "start": 1563.96,
+ "duration": 0.0,
+ "text": "the code length of the data using the model<00:26:04.520> as<00:26:04.720> the<00:26:04.800> compressor."
+ },
+ {
+ "start": 1566.95,
+ "duration": 0.0,
+ "text": "model as the compressor."
+ },
+ {
+ "start": 1566.96,
+ "duration": 0.0,
+ "text": "model as the compressor. So,<00:26:07.120> thinking<00:26:07.440> about<00:26:08.240> this"
+ },
+ {
+ "start": 1569.43,
+ "duration": 0.0,
+ "text": "So, thinking about this"
+ },
+ {
+ "start": 1569.44,
+ "duration": 0.0,
+ "text": "So, thinking about this uh<00:26:10.120> search<00:26:11.200> over"
+ },
+ {
+ "start": 1572.43,
+ "duration": 0.0,
+ "text": "uh search over"
+ },
+ {
+ "start": 1572.44,
+ "duration": 0.0,
+ "text": "uh search over different<00:26:12.760> models,"
+ },
+ {
+ "start": 1574.11,
+ "duration": 0.0,
+ "text": "different models,"
+ },
+ {
+ "start": 1574.12,
+ "duration": 0.0,
+ "text": "different models, consider<00:26:14.480> these<00:26:14.640> different,<00:26:15.360> you<00:26:15.440> know,<00:26:15.600> the"
+ },
+ {
+ "start": 1575.75,
+ "duration": 0.0,
+ "text": "consider these different, you know, the"
+ },
+ {
+ "start": 1575.76,
+ "duration": 0.0,
+ "text": "consider these different, you know, the this<00:26:15.960> different<00:26:16.480> uh<00:26:16.880> description<00:26:17.360> length,"
+ },
+ {
+ "start": 1578.23,
+ "duration": 0.0,
+ "text": "this different uh description length,"
+ },
+ {
+ "start": 1578.24,
+ "duration": 0.0,
+ "text": "this different uh description length, and<00:26:18.360> we<00:26:18.520> want<00:26:18.760> to<00:26:18.840> take<00:26:19.080> the<00:26:19.200> one<00:26:19.520> that"
+ },
+ {
+ "start": 1579.669,
+ "duration": 0.0,
+ "text": "and we want to take the one that"
+ },
+ {
+ "start": 1579.679,
+ "duration": 0.0,
+ "text": "and we want to take the one that minimizes<00:26:20.240> it,<00:26:20.520> so<00:26:20.679> with<00:26:20.800> the<00:26:20.880> shortest"
+ },
+ {
+ "start": 1581.19,
+ "duration": 0.0,
+ "text": "minimizes it, so with the shortest"
+ },
+ {
+ "start": 1581.2,
+ "duration": 0.0,
+ "text": "minimizes it, so with the shortest description<00:26:21.600> length"
+ },
+ {
+ "start": 1582.51,
+ "duration": 0.0,
+ "text": "description length"
+ },
+ {
+ "start": 1582.52,
+ "duration": 0.0,
+ "text": "description length in<00:26:22.800> this<00:26:23.040> set<00:26:23.440> of<00:26:23.560> time-bounded<00:26:24.040> probability"
+ },
+ {
+ "start": 1584.35,
+ "duration": 0.0,
+ "text": "in this set of time-bounded probability"
+ },
+ {
+ "start": 1584.36,
+ "duration": 0.0,
+ "text": "in this set of time-bounded probability distributions.<00:26:25.480> Call<00:26:25.600> that<00:26:25.760> P<00:26:25.880> star."
+ },
+ {
+ "start": 1586.91,
+ "duration": 0.0,
+ "text": "distributions. Call that P star."
+ },
+ {
+ "start": 1586.92,
+ "duration": 0.0,
+ "text": "distributions. Call that P star. Then,<00:26:27.800> we<00:26:27.920> have<00:26:28.080> these<00:26:28.320> two<00:26:28.520> quantities.<00:26:29.480> This"
+ },
+ {
+ "start": 1589.63,
+ "duration": 0.0,
+ "text": "Then, we have these two quantities. This"
+ },
+ {
+ "start": 1589.64,
+ "duration": 0.0,
+ "text": "Then, we have these two quantities. This is<00:26:29.760> how<00:26:29.880> we're<00:26:29.960> going<00:26:30.080> to<00:26:30.160> separate<00:26:30.600> out<00:26:30.800> the"
+ },
+ {
+ "start": 1590.87,
+ "duration": 0.0,
+ "text": "is how we're going to separate out the"
+ },
+ {
+ "start": 1590.88,
+ "duration": 0.0,
+ "text": "is how we're going to separate out the structure<00:26:31.800> and<00:26:31.920> the<00:26:32.000> randomness.<00:26:32.760> The"
+ },
+ {
+ "start": 1592.83,
+ "duration": 0.0,
+ "text": "structure and the randomness. The"
+ },
+ {
+ "start": 1592.84,
+ "duration": 0.0,
+ "text": "structure and the randomness. The structure<00:26:33.880> is<00:26:34.240> just<00:26:34.600> the<00:26:34.720> size<00:26:35.240> of<00:26:35.320> this"
+ },
+ {
+ "start": 1595.47,
+ "duration": 0.0,
+ "text": "structure is just the size of this"
+ },
+ {
+ "start": 1595.48,
+ "duration": 0.0,
+ "text": "structure is just the size of this program<00:26:35.800> P<00:26:35.960> star."
+ },
+ {
+ "start": 1597.63,
+ "duration": 0.0,
+ "text": "program P star."
+ },
+ {
+ "start": 1597.64,
+ "duration": 0.0,
+ "text": "program P star. And<00:26:37.800> the<00:26:37.920> randomness,<00:26:39.040> the<00:26:39.160> time-bounded,"
+ },
+ {
+ "start": 1599.669,
+ "duration": 0.0,
+ "text": "And the randomness, the time-bounded,"
+ },
+ {
+ "start": 1599.679,
+ "duration": 0.0,
+ "text": "And the randomness, the time-bounded, what<00:26:39.800> we<00:26:39.880> call<00:26:40.120> time-bounded<00:26:40.640> entropy,"
+ },
+ {
+ "start": 1601.75,
+ "duration": 0.0,
+ "text": "what we call time-bounded entropy,"
+ },
+ {
+ "start": 1601.76,
+ "duration": 0.0,
+ "text": "what we call time-bounded entropy, is<00:26:42.000> going<00:26:42.160> to<00:26:42.240> be<00:26:42.720> this"
+ },
+ {
+ "start": 1603.83,
+ "duration": 0.0,
+ "text": "is going to be this"
+ },
+ {
+ "start": 1603.84,
+ "duration": 0.0,
+ "text": "is going to be this uh<00:26:44.560> cross<00:26:44.800> entropy.<00:26:45.760> Um<00:26:45.960> just<00:26:46.240> the<00:26:46.280> expected"
+ },
+ {
+ "start": 1607.39,
+ "duration": 0.0,
+ "text": "uh cross entropy. Um just the expected"
+ },
+ {
+ "start": 1607.4,
+ "duration": 0.0,
+ "text": "uh cross entropy. Um just the expected uh<00:26:48.000> right,<00:26:48.440> uh<00:26:48.880> log<00:26:49.840> uh<00:26:50.320> negative<00:26:50.640> log"
+ },
+ {
+ "start": 1610.79,
+ "duration": 0.0,
+ "text": "uh right, uh log uh negative log"
+ },
+ {
+ "start": 1610.8,
+ "duration": 0.0,
+ "text": "uh right, uh log uh negative log likelihood<00:26:51.640> of<00:26:52.280> that<00:26:52.440> data."
+ },
+ {
+ "start": 1613.79,
+ "duration": 0.0,
+ "text": "likelihood of that data."
+ },
+ {
+ "start": 1613.8,
+ "duration": 0.0,
+ "text": "likelihood of that data. We<00:26:53.920> should<00:26:54.120> think<00:26:54.360> of<00:26:54.520> this<00:26:54.760> data<00:26:55.040> this<00:26:55.400> X<00:26:56.080> as"
+ },
+ {
+ "start": 1616.19,
+ "duration": 0.0,
+ "text": "We should think of this data this X as"
+ },
+ {
+ "start": 1616.2,
+ "duration": 0.0,
+ "text": "We should think of this data this X as not,<00:26:56.720> say,<00:26:57.000> an<00:26:57.120> individual<00:26:57.600> example,<00:26:58.000> but<00:26:58.160> the"
+ },
+ {
+ "start": 1618.23,
+ "duration": 0.0,
+ "text": "not, say, an individual example, but the"
+ },
+ {
+ "start": 1618.24,
+ "duration": 0.0,
+ "text": "not, say, an individual example, but the entire<00:26:58.520> data<00:26:58.760> set<00:26:59.200> that<00:26:59.360> we're<00:26:59.760> considering"
+ },
+ {
+ "start": 1620.91,
+ "duration": 0.0,
+ "text": "entire data set that we're considering"
+ },
+ {
+ "start": 1620.92,
+ "duration": 0.0,
+ "text": "entire data set that we're considering uh<00:27:01.120> training<00:27:01.440> on.<00:27:01.960> And<00:27:02.080> this<00:27:02.280> P<00:27:03.280> um<00:27:03.760> could"
+ },
+ {
+ "start": 1623.99,
+ "duration": 0.0,
+ "text": "uh training on. And this P um could"
+ },
+ {
+ "start": 1624.0,
+ "duration": 0.0,
+ "text": "uh training on. And this P um could involve<00:27:04.640> a<00:27:04.679> very<00:27:04.880> complex<00:27:05.320> procedure<00:27:06.560> for"
+ },
+ {
+ "start": 1626.669,
+ "duration": 0.0,
+ "text": "involve a very complex procedure for"
+ },
+ {
+ "start": 1626.679,
+ "duration": 0.0,
+ "text": "involve a very complex procedure for running<00:27:06.960> it,<00:27:07.200> where<00:27:07.440> maybe<00:27:07.840> actually<00:27:08.200> this<00:27:08.400> is"
+ },
+ {
+ "start": 1628.55,
+ "duration": 0.0,
+ "text": "running it, where maybe actually this is"
+ },
+ {
+ "start": 1628.56,
+ "duration": 0.0,
+ "text": "running it, where maybe actually this is very<00:27:08.760> complex<00:27:09.400> compressed,<00:27:10.080> and<00:27:10.240> we<00:27:10.880> are"
+ },
+ {
+ "start": 1631.03,
+ "duration": 0.0,
+ "text": "very complex compressed, and we are"
+ },
+ {
+ "start": 1631.04,
+ "duration": 0.0,
+ "text": "very complex compressed, and we are going<00:27:11.400> to<00:27:11.760> use<00:27:12.120> some<00:27:12.280> of<00:27:12.400> the<00:27:12.480> compute<00:27:13.160> in<00:27:13.560> a"
+ },
+ {
+ "start": 1633.63,
+ "duration": 0.0,
+ "text": "going to use some of the compute in a"
+ },
+ {
+ "start": 1633.64,
+ "duration": 0.0,
+ "text": "going to use some of the compute in a lot<00:27:13.880> of<00:27:13.960> to<00:27:14.080> us<00:27:14.240> in<00:27:14.320> this<00:27:14.480> time<00:27:14.720> bound<00:27:15.360> to<00:27:15.520> do"
+ },
+ {
+ "start": 1635.75,
+ "duration": 0.0,
+ "text": "lot of to us in this time bound to do"
+ },
+ {
+ "start": 1635.76,
+ "duration": 0.0,
+ "text": "lot of to us in this time bound to do decompression<00:27:16.840> as<00:27:17.000> well<00:27:17.240> as<00:27:17.880> inference."
+ },
+ {
+ "start": 1639.95,
+ "duration": 0.0,
+ "text": "decompression as well as inference."
+ },
+ {
+ "start": 1639.96,
+ "duration": 0.0,
+ "text": "decompression as well as inference. Right.<00:27:20.138> [clears throat]<00:27:20.200> So,<00:27:20.720> that's<00:27:20.960> where"
+ },
+ {
+ "start": 1641.03,
+ "duration": 0.0,
+ "text": "Right. [clears throat] So, that's where"
+ },
+ {
+ "start": 1641.04,
+ "duration": 0.0,
+ "text": "Right. [clears throat] So, that's where this<00:27:21.240> time<00:27:21.480> bound<00:27:21.679> comes<00:27:21.920> in,<00:27:22.280> S<00:27:23.080> for"
+ },
+ {
+ "start": 1643.27,
+ "duration": 0.0,
+ "text": "this time bound comes in, S for"
+ },
+ {
+ "start": 1643.28,
+ "duration": 0.0,
+ "text": "this time bound comes in, S for structure.<00:27:24.360> Um<00:27:24.800> so,<00:27:24.960> this<00:27:25.120> is<00:27:25.240> the"
+ },
+ {
+ "start": 1645.31,
+ "duration": 0.0,
+ "text": "structure. Um so, this is the"
+ },
+ {
+ "start": 1645.32,
+ "duration": 0.0,
+ "text": "structure. Um so, this is the appiplexity<00:27:26.000> of<00:27:26.200> X<00:27:26.679> given<00:27:26.960> time<00:27:27.160> bound<00:27:27.360> T.<00:27:28.120> And"
+ },
+ {
+ "start": 1648.27,
+ "duration": 0.0,
+ "text": "appiplexity of X given time bound T. And"
+ },
+ {
+ "start": 1648.28,
+ "duration": 0.0,
+ "text": "appiplexity of X given time bound T. And this<00:27:28.480> would<00:27:28.600> be<00:27:29.160> the<00:27:29.240> time-bounded<00:27:29.640> entropy"
+ },
+ {
+ "start": 1650.43,
+ "duration": 0.0,
+ "text": "this would be the time-bounded entropy"
+ },
+ {
+ "start": 1650.44,
+ "duration": 0.0,
+ "text": "this would be the time-bounded entropy of<00:27:30.679> X<00:27:31.600> um<00:27:32.200> given<00:27:32.440> time<00:27:32.600> bound<00:27:32.800> T.<00:27:33.560> And<00:27:33.880> again,"
+ },
+ {
+ "start": 1654.43,
+ "duration": 0.0,
+ "text": "of X um given time bound T. And again,"
+ },
+ {
+ "start": 1654.44,
+ "duration": 0.0,
+ "text": "of X um given time bound T. And again, it's<00:27:34.640> defined<00:27:35.000> on<00:27:35.160> random<00:27:35.440> variables,<00:27:36.080> unlike"
+ },
+ {
+ "start": 1656.63,
+ "duration": 0.0,
+ "text": "it's defined on random variables, unlike"
+ },
+ {
+ "start": 1656.64,
+ "duration": 0.0,
+ "text": "it's defined on random variables, unlike um<00:27:37.000> yeah,<00:27:37.200> so<00:27:37.800> uh<00:27:37.880> not<00:27:38.120> not<00:27:38.400> like<00:27:38.760> uh"
+ },
+ {
+ "start": 1658.79,
+ "duration": 0.0,
+ "text": "um yeah, so uh not not like uh"
+ },
+ {
+ "start": 1658.8,
+ "duration": 0.0,
+ "text": "um yeah, so uh not not like uh Kolmogorov<00:27:39.120> complexity.<00:27:40.080> Okay."
+ },
+ {
+ "start": 1662.72,
+ "duration": 0.0,
+ "text": "So,<00:27:42.960> going<00:27:43.280> through<00:27:43.920> this<00:27:44.120> picture,"
+ },
+ {
+ "start": 1665.15,
+ "duration": 0.0,
+ "text": "So, going through this picture,"
+ },
+ {
+ "start": 1665.16,
+ "duration": 0.0,
+ "text": "So, going through this picture, um<00:27:45.920> which"
+ },
+ {
+ "start": 1667.35,
+ "duration": 0.0,
+ "text": "um which"
+ },
+ {
+ "start": 1667.36,
+ "duration": 0.0,
+ "text": "um which uh<00:27:48.280> Andrew<00:27:49.040> um"
+ },
+ {
+ "start": 1669.87,
+ "duration": 0.0,
+ "text": "uh Andrew um"
+ },
+ {
+ "start": 1669.88,
+ "duration": 0.0,
+ "text": "uh Andrew um uh<00:27:50.160> walked<00:27:50.400> you<00:27:50.480> through<00:27:50.560> earlier,<00:27:51.160> now<00:27:51.440> we'll"
+ },
+ {
+ "start": 1671.59,
+ "duration": 0.0,
+ "text": "uh walked you through earlier, now we'll"
+ },
+ {
+ "start": 1671.6,
+ "duration": 0.0,
+ "text": "uh walked you through earlier, now we'll just"
+ },
+ {
+ "start": 1672.669,
+ "duration": 0.0,
+ "text": "just"
+ },
+ {
+ "start": 1672.679,
+ "duration": 0.0,
+ "text": "just go<00:27:52.840> through<00:27:53.160> how<00:27:54.120> actually<00:27:55.040> uh<00:27:55.560> the"
+ },
+ {
+ "start": 1675.87,
+ "duration": 0.0,
+ "text": "go through how actually uh the"
+ },
+ {
+ "start": 1675.88,
+ "duration": 0.0,
+ "text": "go through how actually uh the appiplexity<00:27:56.480> and<00:27:56.560> time-bounded<00:27:56.920> entropy"
+ },
+ {
+ "start": 1677.15,
+ "duration": 0.0,
+ "text": "appiplexity and time-bounded entropy"
+ },
+ {
+ "start": 1677.16,
+ "duration": 0.0,
+ "text": "appiplexity and time-bounded entropy looks<00:27:57.560> for<00:27:57.720> each<00:27:57.880> of<00:27:57.920> these."
+ },
+ {
+ "start": 1679.51,
+ "duration": 0.0,
+ "text": "looks for each of these."
+ },
+ {
+ "start": 1679.52,
+ "duration": 0.0,
+ "text": "looks for each of these. So,<00:27:59.760> for<00:27:59.880> this<00:28:00.040> very<00:28:00.200> repetitive<00:28:00.679> code,"
+ },
+ {
+ "start": 1682.11,
+ "duration": 0.0,
+ "text": "So, for this very repetitive code,"
+ },
+ {
+ "start": 1682.12,
+ "duration": 0.0,
+ "text": "So, for this very repetitive code, we<00:28:02.240> can<00:28:02.360> have<00:28:02.480> a<00:28:02.520> very<00:28:02.760> simple<00:28:03.120> pro-<00:28:03.360> like,"
+ },
+ {
+ "start": 1683.669,
+ "duration": 0.0,
+ "text": "we can have a very simple pro- like,"
+ },
+ {
+ "start": 1683.679,
+ "duration": 0.0,
+ "text": "we can have a very simple pro- like, imagine<00:28:04.080> we<00:28:04.200> have<00:28:04.320> an<00:28:04.360> entire<00:28:04.640> data<00:28:04.880> set"
+ },
+ {
+ "start": 1685.669,
+ "duration": 0.0,
+ "text": "imagine we have an entire data set"
+ },
+ {
+ "start": 1685.679,
+ "duration": 0.0,
+ "text": "imagine we have an entire data set filled<00:28:06.520> with<00:28:06.720> just<00:28:07.320> boilerplate<00:28:08.160> super"
+ },
+ {
+ "start": 1688.75,
+ "duration": 0.0,
+ "text": "filled with just boilerplate super"
+ },
+ {
+ "start": 1688.76,
+ "duration": 0.0,
+ "text": "filled with just boilerplate super repetitive<00:28:09.240> code."
+ },
+ {
+ "start": 1691.63,
+ "duration": 0.0,
+ "text": "repetitive code."
+ },
+ {
+ "start": 1691.64,
+ "duration": 0.0,
+ "text": "repetitive code. An<00:28:11.800> LLM"
+ },
+ {
+ "start": 1693.75,
+ "duration": 0.0,
+ "text": "An LLM"
+ },
+ {
+ "start": 1693.76,
+ "duration": 0.0,
+ "text": "An LLM can<00:28:14.560> we<00:28:14.720> can,<00:28:15.000> with<00:28:15.160> a<00:28:15.200> very<00:28:15.400> small<00:28:15.760> LLM,"
+ },
+ {
+ "start": 1696.99,
+ "duration": 0.0,
+ "text": "can we can, with a very small LLM,"
+ },
+ {
+ "start": 1697.0,
+ "duration": 0.0,
+ "text": "can we can, with a very small LLM, do<00:28:17.160> a<00:28:17.200> very<00:28:17.400> good<00:28:17.600> job<00:28:18.120> at<00:28:18.280> predicting"
+ },
+ {
+ "start": 1699.83,
+ "duration": 0.0,
+ "text": "do a very good job at predicting"
+ },
+ {
+ "start": 1699.84,
+ "duration": 0.0,
+ "text": "do a very good job at predicting the<00:28:20.000> code<00:28:20.480> here.<00:28:21.120> We<00:28:21.240> don't<00:28:21.520> need<00:28:22.040> a<00:28:22.120> large<00:28:22.440> LLM"
+ },
+ {
+ "start": 1703.11,
+ "duration": 0.0,
+ "text": "the code here. We don't need a large LLM"
+ },
+ {
+ "start": 1703.12,
+ "duration": 0.0,
+ "text": "the code here. We don't need a large LLM to<00:28:23.240> do<00:28:23.600> those<00:28:23.800> good<00:28:23.960> predictions."
+ },
+ {
+ "start": 1705.19,
+ "duration": 0.0,
+ "text": "to do those good predictions."
+ },
+ {
+ "start": 1705.2,
+ "duration": 0.0,
+ "text": "to do those good predictions. And<00:28:25.360> because<00:28:25.679> we<00:28:25.800> pay<00:28:26.000> for<00:28:26.120> the<00:28:26.200> cost<00:28:26.800> of<00:28:26.919> the"
+ },
+ {
+ "start": 1707.03,
+ "duration": 0.0,
+ "text": "And because we pay for the cost of the"
+ },
+ {
+ "start": 1707.04,
+ "duration": 0.0,
+ "text": "And because we pay for the cost of the LLM<00:28:27.679> in<00:28:27.919> the<00:28:28.040> total<00:28:28.240> description<00:28:28.679> length,"
+ },
+ {
+ "start": 1709.71,
+ "duration": 0.0,
+ "text": "LLM in the total description length,"
+ },
+ {
+ "start": 1709.72,
+ "duration": 0.0,
+ "text": "LLM in the total description length, then<00:28:30.120> we<00:28:30.280> are<00:28:30.320> incentivized<00:28:31.120> in<00:28:31.240> the<00:28:31.360> search"
+ },
+ {
+ "start": 1712.03,
+ "duration": 0.0,
+ "text": "then we are incentivized in the search"
+ },
+ {
+ "start": 1712.04,
+ "duration": 0.0,
+ "text": "then we are incentivized in the search to<00:28:32.120> use<00:28:32.280> a<00:28:32.360> small<00:28:32.679> LLM"
+ },
+ {
+ "start": 1713.669,
+ "duration": 0.0,
+ "text": "to use a small LLM"
+ },
+ {
+ "start": 1713.679,
+ "duration": 0.0,
+ "text": "to use a small LLM or<00:28:33.880> other<00:28:34.120> probabilistic<00:28:34.679> model."
+ },
+ {
+ "start": 1716.23,
+ "duration": 0.0,
+ "text": "or other probabilistic model."
+ },
+ {
+ "start": 1716.24,
+ "duration": 0.0,
+ "text": "or other probabilistic model. And<00:28:36.440> so,<00:28:36.800> we<00:28:37.040> would<00:28:37.240> find<00:28:37.880> low<00:28:38.360> appiplexity,"
+ },
+ {
+ "start": 1719.909,
+ "duration": 0.0,
+ "text": "And so, we would find low appiplexity,"
+ },
+ {
+ "start": 1719.919,
+ "duration": 0.0,
+ "text": "And so, we would find low appiplexity, um<00:28:40.200> and<00:28:40.360> also<00:28:40.679> low<00:28:40.840> time-bounded<00:28:41.280> entropy,"
+ },
+ {
+ "start": 1721.95,
+ "duration": 0.0,
+ "text": "um and also low time-bounded entropy,"
+ },
+ {
+ "start": 1721.96,
+ "duration": 0.0,
+ "text": "um and also low time-bounded entropy, because<00:28:42.360> the<00:28:42.480> loss<00:28:43.000> would<00:28:43.120> be<00:28:43.200> small.<00:28:43.960> And<00:28:44.040> the"
+ },
+ {
+ "start": 1724.11,
+ "duration": 0.0,
+ "text": "because the loss would be small. And the"
+ },
+ {
+ "start": 1724.12,
+ "duration": 0.0,
+ "text": "because the loss would be small. And the same<00:28:44.320> thing<00:28:44.560> for,<00:28:44.760> say,<00:28:44.880> this<00:28:45.080> image<00:28:45.320> data."
+ },
+ {
+ "start": 1726.11,
+ "duration": 0.0,
+ "text": "same thing for, say, this image data."
+ },
+ {
+ "start": 1726.12,
+ "duration": 0.0,
+ "text": "same thing for, say, this image data. And<00:28:46.240> you<00:28:46.320> can<00:28:46.480> see<00:28:46.679> it<00:28:47.440> to<00:28:47.520> some<00:28:47.720> extent<00:28:48.159> in<00:28:48.280> the"
+ },
+ {
+ "start": 1728.35,
+ "duration": 0.0,
+ "text": "And you can see it to some extent in the"
+ },
+ {
+ "start": 1728.36,
+ "duration": 0.0,
+ "text": "And you can see it to some extent in the loss."
+ },
+ {
+ "start": 1729.55,
+ "duration": 0.0,
+ "text": "loss."
+ },
+ {
+ "start": 1729.56,
+ "duration": 0.0,
+ "text": "loss. Um"
+ },
+ {
+ "start": 1730.79,
+ "duration": 0.0,
+ "text": "Um"
+ },
+ {
+ "start": 1730.8,
+ "duration": 0.0,
+ "text": "Um in<00:28:50.960> that"
+ },
+ {
+ "start": 1732.149,
+ "duration": 0.0,
+ "text": "in that"
+ },
+ {
+ "start": 1732.159,
+ "duration": 0.0,
+ "text": "in that in<00:28:52.560> for<00:28:53.120> this<00:28:53.600> low<00:28:54.080> appiplexity<00:28:54.640> data,<00:28:55.000> the"
+ },
+ {
+ "start": 1735.11,
+ "duration": 0.0,
+ "text": "in for this low appiplexity data, the"
+ },
+ {
+ "start": 1735.12,
+ "duration": 0.0,
+ "text": "in for this low appiplexity data, the loss<00:28:55.600> decays<00:28:55.880> very<00:28:56.080> quickly"
+ },
+ {
+ "start": 1737.19,
+ "duration": 0.0,
+ "text": "loss decays very quickly"
+ },
+ {
+ "start": 1737.2,
+ "duration": 0.0,
+ "text": "loss decays very quickly with<00:28:57.919> the<00:28:58.440> the<00:28:58.880> the<00:28:59.000> steps,<00:28:59.640> um<00:28:59.960> and<00:29:00.159> with<00:29:00.280> the"
+ },
+ {
+ "start": 1740.35,
+ "duration": 0.0,
+ "text": "with the the the steps, um and with the"
+ },
+ {
+ "start": 1740.36,
+ "duration": 0.0,
+ "text": "with the the the steps, um and with the compute.<00:29:01.360> And<00:29:01.480> so,<00:29:01.520> spending<00:29:01.840> additional"
+ },
+ {
+ "start": 1742.19,
+ "duration": 0.0,
+ "text": "compute. And so, spending additional"
+ },
+ {
+ "start": 1742.2,
+ "duration": 0.0,
+ "text": "compute. And so, spending additional compute,<00:29:03.120> um<00:29:03.600> making<00:29:04.040> a<00:29:04.120> larger<00:29:04.440> model,<00:29:05.320> is"
+ },
+ {
+ "start": 1745.59,
+ "duration": 0.0,
+ "text": "compute, um making a larger model, is"
+ },
+ {
+ "start": 1745.6,
+ "duration": 0.0,
+ "text": "compute, um making a larger model, is not<00:29:06.000> going<00:29:06.159> to<00:29:06.240> benefit<00:29:06.560> us."
+ },
+ {
+ "start": 1747.35,
+ "duration": 0.0,
+ "text": "not going to benefit us."
+ },
+ {
+ "start": 1747.36,
+ "duration": 0.0,
+ "text": "not going to benefit us. On<00:29:07.440> the<00:29:07.520> other<00:29:07.679> hand,<00:29:08.159> for<00:29:08.679> random<00:29:08.960> noise"
+ },
+ {
+ "start": 1749.19,
+ "duration": 0.0,
+ "text": "On the other hand, for random noise"
+ },
+ {
+ "start": 1749.2,
+ "duration": 0.0,
+ "text": "On the other hand, for random noise data,<00:29:09.679> or<00:29:09.760> for<00:29:09.880> data<00:29:10.080> that<00:29:10.240> is<00:29:10.360> fundamentally"
+ },
+ {
+ "start": 1750.99,
+ "duration": 0.0,
+ "text": "data, or for data that is fundamentally"
+ },
+ {
+ "start": 1751.0,
+ "duration": 0.0,
+ "text": "data, or for data that is fundamentally unpredictable,"
+ },
+ {
+ "start": 1752.47,
+ "duration": 0.0,
+ "text": "unpredictable,"
+ },
+ {
+ "start": 1752.48,
+ "duration": 0.0,
+ "text": "unpredictable, um<00:29:13.159> or<00:29:13.320> at<00:29:13.400> least<00:29:13.640> unpredictable<00:29:14.200> given<00:29:14.400> a"
+ },
+ {
+ "start": 1754.43,
+ "duration": 0.0,
+ "text": "um or at least unpredictable given a"
+ },
+ {
+ "start": 1754.44,
+ "duration": 0.0,
+ "text": "um or at least unpredictable given a certain<00:29:14.640> amount<00:29:14.800> of<00:29:14.840> compute,<00:29:15.400> say,<00:29:16.320> you"
+ },
+ {
+ "start": 1756.39,
+ "duration": 0.0,
+ "text": "certain amount of compute, say, you"
+ },
+ {
+ "start": 1756.4,
+ "duration": 0.0,
+ "text": "certain amount of compute, say, you know,<00:29:17.080> what<00:29:17.600> uh<00:29:18.120> the<00:29:18.200> hash<00:29:18.560> of<00:29:18.679> our<00:29:19.240> uh<00:29:19.679> of<00:29:19.880> our"
+ },
+ {
+ "start": 1760.19,
+ "duration": 0.0,
+ "text": "know, what uh the hash of our uh of our"
+ },
+ {
+ "start": 1760.2,
+ "duration": 0.0,
+ "text": "know, what uh the hash of our uh of our API<00:29:20.600> key<00:29:20.760> is,"
+ },
+ {
+ "start": 1761.71,
+ "duration": 0.0,
+ "text": "API key is,"
+ },
+ {
+ "start": 1761.72,
+ "duration": 0.0,
+ "text": "API key is, that<00:29:22.400> also<00:29:23.520> the<00:29:23.679> optimal<00:29:24.080> model<00:29:24.320> size<00:29:24.720> will<00:29:24.880> be"
+ },
+ {
+ "start": 1764.99,
+ "duration": 0.0,
+ "text": "that also the optimal model size will be"
+ },
+ {
+ "start": 1765.0,
+ "duration": 0.0,
+ "text": "that also the optimal model size will be small.<00:29:25.720> And<00:29:25.840> by<00:29:25.919> the<00:29:26.000> way,<00:29:26.520> feel<00:29:26.720> free<00:29:27.040> to"
+ },
+ {
+ "start": 1767.149,
+ "duration": 0.0,
+ "text": "small. And by the way, feel free to"
+ },
+ {
+ "start": 1767.159,
+ "duration": 0.0,
+ "text": "small. And by the way, feel free to interrupt<00:29:27.560> me<00:29:27.720> with<00:29:27.880> questions.<00:29:29.080> Um<00:29:29.520> that's,"
+ },
+ {
+ "start": 1769.909,
+ "duration": 0.0,
+ "text": "interrupt me with questions. Um that's,"
+ },
+ {
+ "start": 1769.919,
+ "duration": 0.0,
+ "text": "interrupt me with questions. Um that's, you<00:29:30.000> know,"
+ },
+ {
+ "start": 1770.79,
+ "duration": 0.0,
+ "text": "you know,"
+ },
+ {
+ "start": 1770.8,
+ "duration": 0.0,
+ "text": "you know, that's<00:29:31.040> that's<00:29:31.320> a<00:29:31.880> real<00:29:32.040> part<00:29:32.159> of<00:29:32.240> this<00:29:32.320> talk."
+ },
+ {
+ "start": 1772.59,
+ "duration": 0.0,
+ "text": "that's that's a real part of this talk."
+ },
+ {
+ "start": 1772.6,
+ "duration": 0.0,
+ "text": "that's that's a real part of this talk. Happy<00:29:32.840> to<00:29:33.159> uh<00:29:33.520> happy<00:29:33.640> to<00:29:33.720> take<00:29:33.880> them."
+ },
+ {
+ "start": 1774.669,
+ "duration": 0.0,
+ "text": "Happy to uh happy to take them."
+ },
+ {
+ "start": 1774.679,
+ "duration": 0.0,
+ "text": "Happy to uh happy to take them. So,"
+ },
+ {
+ "start": 1775.71,
+ "duration": 0.0,
+ "text": "So,"
+ },
+ {
+ "start": 1775.72,
+ "duration": 0.0,
+ "text": "So, with<00:29:35.960> the<00:29:36.040> random<00:29:36.320> noise,<00:29:37.240> the<00:29:37.320> trouble<00:29:37.679> is<00:29:37.960> we"
+ },
+ {
+ "start": 1778.11,
+ "duration": 0.0,
+ "text": "with the random noise, the trouble is we"
+ },
+ {
+ "start": 1778.12,
+ "duration": 0.0,
+ "text": "with the random noise, the trouble is we can't<00:29:38.480> do<00:29:39.080> much<00:29:39.400> better"
+ },
+ {
+ "start": 1780.47,
+ "duration": 0.0,
+ "text": "can't do much better"
+ },
+ {
+ "start": 1780.48,
+ "duration": 0.0,
+ "text": "can't do much better than<00:29:41.159> well,<00:29:41.440> if<00:29:41.720> it's<00:29:41.840> purely<00:29:42.080> random<00:29:42.280> noise,"
+ },
+ {
+ "start": 1782.47,
+ "duration": 0.0,
+ "text": "than well, if it's purely random noise,"
+ },
+ {
+ "start": 1782.48,
+ "duration": 0.0,
+ "text": "than well, if it's purely random noise, we<00:29:42.560> can't<00:29:42.800> do<00:29:43.080> any<00:29:43.280> better<00:29:43.800> than<00:29:43.919> just<00:29:44.120> random"
+ },
+ {
+ "start": 1784.35,
+ "duration": 0.0,
+ "text": "we can't do any better than just random"
+ },
+ {
+ "start": 1784.36,
+ "duration": 0.0,
+ "text": "we can't do any better than just random predictions."
+ },
+ {
+ "start": 1785.63,
+ "duration": 0.0,
+ "text": "predictions."
+ },
+ {
+ "start": 1785.64,
+ "duration": 0.0,
+ "text": "predictions. And<00:29:45.760> you<00:29:45.840> can<00:29:45.960> make<00:29:46.200> random<00:29:46.480> predictions<00:29:47.240> a"
+ },
+ {
+ "start": 1787.27,
+ "duration": 0.0,
+ "text": "And you can make random predictions a"
+ },
+ {
+ "start": 1787.28,
+ "duration": 0.0,
+ "text": "And you can make random predictions a very<00:29:47.520> tiny<00:29:47.840> model."
+ },
+ {
+ "start": 1789.67,
+ "duration": 0.0,
+ "text": "very tiny model."
+ },
+ {
+ "start": 1789.68,
+ "duration": 0.0,
+ "text": "very tiny model. So<00:29:49.760> again,<00:29:50.040> thinking<00:29:50.320> about<00:29:50.480> this<00:29:50.640> two-part"
+ },
+ {
+ "start": 1791.03,
+ "duration": 0.0,
+ "text": "So again, thinking about this two-part"
+ },
+ {
+ "start": 1791.04,
+ "duration": 0.0,
+ "text": "So again, thinking about this two-part code<00:29:51.280> length,"
+ },
+ {
+ "start": 1792.35,
+ "duration": 0.0,
+ "text": "code length,"
+ },
+ {
+ "start": 1792.36,
+ "duration": 0.0,
+ "text": "code length, then<00:29:52.520> we<00:29:52.640> are<00:29:52.680> incentivized<00:29:53.480> to<00:29:53.640> use<00:29:54.040> a<00:29:54.120> very"
+ },
+ {
+ "start": 1794.31,
+ "duration": 0.0,
+ "text": "then we are incentivized to use a very"
+ },
+ {
+ "start": 1794.32,
+ "duration": 0.0,
+ "text": "then we are incentivized to use a very tiny<00:29:54.560> model."
+ },
+ {
+ "start": 1797.08,
+ "duration": 0.0,
+ "text": "Trying<00:29:57.360> to<00:29:57.480> minimize<00:29:57.960> this<00:29:58.280> this<00:29:58.480> two-part"
+ },
+ {
+ "start": 1798.79,
+ "duration": 0.0,
+ "text": "Trying to minimize this this two-part"
+ },
+ {
+ "start": 1798.8,
+ "duration": 0.0,
+ "text": "Trying to minimize this this two-part code<00:29:59.000> length<00:29:59.520> on<00:29:59.720> this<00:29:59.840> noise<00:30:00.120> data,<00:30:00.400> we<00:30:00.560> will"
+ },
+ {
+ "start": 1800.71,
+ "duration": 0.0,
+ "text": "code length on this noise data, we will"
+ },
+ {
+ "start": 1800.72,
+ "duration": 0.0,
+ "text": "code length on this noise data, we will end<00:30:00.920> up<00:30:01.320> with<00:30:01.720> a<00:30:01.800> tiny<00:30:02.080> model,"
+ },
+ {
+ "start": 1803.03,
+ "duration": 0.0,
+ "text": "end up with a tiny model,"
+ },
+ {
+ "start": 1803.04,
+ "duration": 0.0,
+ "text": "end up with a tiny model, and<00:30:03.160> therefore<00:30:03.680> also<00:30:04.200> a<00:30:04.280> tiny<00:30:04.840> epi-plexity."
+ },
+ {
+ "start": 1806.27,
+ "duration": 0.0,
+ "text": "and therefore also a tiny epi-plexity."
+ },
+ {
+ "start": 1806.28,
+ "duration": 0.0,
+ "text": "and therefore also a tiny epi-plexity. And<00:30:06.400> that's<00:30:06.720> going<00:30:06.880> to<00:30:06.920> be<00:30:07.000> the<00:30:07.080> same<00:30:07.720> even<00:30:08.040> as"
+ },
+ {
+ "start": 1808.23,
+ "duration": 0.0,
+ "text": "And that's going to be the same even as"
+ },
+ {
+ "start": 1808.24,
+ "duration": 0.0,
+ "text": "And that's going to be the same even as we<00:30:08.360> increase<00:30:08.800> the<00:30:08.880> compute<00:30:09.240> bound."
+ },
+ {
+ "start": 1810.31,
+ "duration": 0.0,
+ "text": "we increase the compute bound."
+ },
+ {
+ "start": 1810.32,
+ "duration": 0.0,
+ "text": "we increase the compute bound. Um<00:30:10.600> whereas<00:30:11.120> the<00:30:11.280> time-bounded<00:30:11.720> entropy<00:30:12.240> is"
+ },
+ {
+ "start": 1812.39,
+ "duration": 0.0,
+ "text": "Um whereas the time-bounded entropy is"
+ },
+ {
+ "start": 1812.4,
+ "duration": 0.0,
+ "text": "Um whereas the time-bounded entropy is high."
+ },
+ {
+ "start": 1813.27,
+ "duration": 0.0,
+ "text": "high."
+ },
+ {
+ "start": 1813.28,
+ "duration": 0.0,
+ "text": "high. So<00:30:13.480> that<00:30:13.720> way<00:30:14.080> time-bounded<00:30:14.440> entropy"
+ },
+ {
+ "start": 1814.71,
+ "duration": 0.0,
+ "text": "So that way time-bounded entropy"
+ },
+ {
+ "start": 1814.72,
+ "duration": 0.0,
+ "text": "So that way time-bounded entropy captures<00:30:15.120> the<00:30:15.200> fact<00:30:15.520> that<00:30:16.240> we<00:30:16.360> have<00:30:16.560> this"
+ },
+ {
+ "start": 1816.79,
+ "duration": 0.0,
+ "text": "captures the fact that we have this"
+ },
+ {
+ "start": 1816.8,
+ "duration": 0.0,
+ "text": "captures the fact that we have this random<00:30:17.520> structure<00:30:17.880> this<00:30:18.160> randomness<00:30:18.520> here,"
+ },
+ {
+ "start": 1819.31,
+ "duration": 0.0,
+ "text": "random structure this randomness here,"
+ },
+ {
+ "start": 1819.32,
+ "duration": 0.0,
+ "text": "random structure this randomness here, um"
+ },
+ {
+ "start": 1820.39,
+ "duration": 0.0,
+ "text": "um"
+ },
+ {
+ "start": 1820.4,
+ "duration": 0.0,
+ "text": "um and<00:30:20.600> very<00:30:20.800> little<00:30:21.000> structure.<00:30:21.960> And<00:30:22.080> then<00:30:22.920> more"
+ },
+ {
+ "start": 1823.11,
+ "duration": 0.0,
+ "text": "and very little structure. And then more"
+ },
+ {
+ "start": 1823.12,
+ "duration": 0.0,
+ "text": "and very little structure. And then more interesting<00:30:23.520> data,<00:30:23.960> the<00:30:24.040> kind<00:30:24.560> that<00:30:24.840> we<00:30:25.000> think"
+ },
+ {
+ "start": 1825.47,
+ "duration": 0.0,
+ "text": "interesting data, the kind that we think"
+ },
+ {
+ "start": 1825.48,
+ "duration": 0.0,
+ "text": "interesting data, the kind that we think provides<00:30:26.240> useful<00:30:26.680> signal<00:30:27.080> to<00:30:27.200> train<00:30:27.480> on,"
+ },
+ {
+ "start": 1828.95,
+ "duration": 0.0,
+ "text": "provides useful signal to train on,"
+ },
+ {
+ "start": 1828.96,
+ "duration": 0.0,
+ "text": "provides useful signal to train on, is"
+ },
+ {
+ "start": 1831.27,
+ "duration": 0.0,
+ "text": "is"
+ },
+ {
+ "start": 1831.28,
+ "duration": 0.0,
+ "text": "is uh<00:30:31.880> in"
+ },
+ {
+ "start": 1832.51,
+ "duration": 0.0,
+ "text": "uh in"
+ },
+ {
+ "start": 1832.52,
+ "duration": 0.0,
+ "text": "uh in we<00:30:32.640> find,<00:30:33.200> right,<00:30:33.640> that"
+ },
+ {
+ "start": 1835.07,
+ "duration": 0.0,
+ "text": "we find, right, that"
+ },
+ {
+ "start": 1835.08,
+ "duration": 0.0,
+ "text": "we find, right, that we<00:30:35.280> get<00:30:35.680> large<00:30:36.000> models<00:30:36.800> on<00:30:36.920> this<00:30:37.040> data.<00:30:37.760> Why<00:30:37.880> is"
+ },
+ {
+ "start": 1837.99,
+ "duration": 0.0,
+ "text": "we get large models on this data. Why is"
+ },
+ {
+ "start": 1838.0,
+ "duration": 0.0,
+ "text": "we get large models on this data. Why is it<00:30:38.120> that<00:30:38.680> that<00:30:39.080> uh<00:30:39.440> we<00:30:39.560> have<00:30:39.720> such<00:30:39.960> large"
+ },
+ {
+ "start": 1840.27,
+ "duration": 0.0,
+ "text": "it that that uh we have such large"
+ },
+ {
+ "start": 1840.28,
+ "duration": 0.0,
+ "text": "it that that uh we have such large models"
+ },
+ {
+ "start": 1841.35,
+ "duration": 0.0,
+ "text": "models"
+ },
+ {
+ "start": 1841.36,
+ "duration": 0.0,
+ "text": "models for"
+ },
+ {
+ "start": 1842.83,
+ "duration": 0.0,
+ "text": "for"
+ },
+ {
+ "start": 1842.84,
+ "duration": 0.0,
+ "text": "for uh<00:30:43.400> doing<00:30:43.640> generative<00:30:43.960> modeling<00:30:44.320> of<00:30:44.440> images"
+ },
+ {
+ "start": 1845.23,
+ "duration": 0.0,
+ "text": "uh doing generative modeling of images"
+ },
+ {
+ "start": 1845.24,
+ "duration": 0.0,
+ "text": "uh doing generative modeling of images or<00:30:45.360> for<00:30:45.480> language<00:30:45.800> models<00:30:46.280> on<00:30:46.760> text<00:30:47.280> and<00:30:47.400> code?"
+ },
+ {
+ "start": 1848.35,
+ "duration": 0.0,
+ "text": "or for language models on text and code?"
+ },
+ {
+ "start": 1848.36,
+ "duration": 0.0,
+ "text": "or for language models on text and code? It's<00:30:48.440> because<00:30:48.680> there's<00:30:48.800> a<00:30:48.880> lot<00:30:49.080> to<00:30:49.200> learn.<00:30:50.120> And"
+ },
+ {
+ "start": 1850.19,
+ "duration": 0.0,
+ "text": "It's because there's a lot to learn. And"
+ },
+ {
+ "start": 1850.2,
+ "duration": 0.0,
+ "text": "It's because there's a lot to learn. And actually<00:30:50.680> even<00:30:51.160> from<00:30:51.520> this<00:30:51.720> MDL<00:30:52.000> perspective,"
+ },
+ {
+ "start": 1853.15,
+ "duration": 0.0,
+ "text": "actually even from this MDL perspective,"
+ },
+ {
+ "start": 1853.16,
+ "duration": 0.0,
+ "text": "actually even from this MDL perspective, we<00:30:53.360> are<00:30:53.520> incentivized<00:30:54.160> to<00:30:54.240> learn<00:30:54.400> a<00:30:54.440> lot"
+ },
+ {
+ "start": 1854.67,
+ "duration": 0.0,
+ "text": "we are incentivized to learn a lot"
+ },
+ {
+ "start": 1854.68,
+ "duration": 0.0,
+ "text": "we are incentivized to learn a lot because<00:30:55.000> incorporating<00:30:55.560> the<00:30:55.640> structure<00:30:55.920> into"
+ },
+ {
+ "start": 1856.03,
+ "duration": 0.0,
+ "text": "because incorporating the structure into"
+ },
+ {
+ "start": 1856.04,
+ "duration": 0.0,
+ "text": "because incorporating the structure into the<00:30:56.120> model<00:30:56.360> still<00:30:56.800> leads<00:30:57.200> to<00:30:57.600> reductions<00:30:58.560> in"
+ },
+ {
+ "start": 1859.19,
+ "duration": 0.0,
+ "text": "the model still leads to reductions in"
+ },
+ {
+ "start": 1859.2,
+ "duration": 0.0,
+ "text": "the model still leads to reductions in the<00:30:59.320> total<00:30:59.720> description<00:31:00.200> length."
+ },
+ {
+ "start": 1861.43,
+ "duration": 0.0,
+ "text": "the total description length."
+ },
+ {
+ "start": 1861.44,
+ "duration": 0.0,
+ "text": "the total description length. Right?<00:31:01.920> So<00:31:02.080> with<00:31:02.160> this<00:31:02.320> interesting,<00:31:03.040> you"
+ },
+ {
+ "start": 1863.11,
+ "duration": 0.0,
+ "text": "Right? So with this interesting, you"
+ },
+ {
+ "start": 1863.12,
+ "duration": 0.0,
+ "text": "Right? So with this interesting, you know,<00:31:03.360> complex,<00:31:04.280> partially<00:31:04.680> predictable,"
+ },
+ {
+ "start": 1865.23,
+ "duration": 0.0,
+ "text": "know, complex, partially predictable,"
+ },
+ {
+ "start": 1865.24,
+ "duration": 0.0,
+ "text": "know, complex, partially predictable, partially<00:31:05.560> unpredictable<00:31:06.880> uh<00:31:06.960> code,<00:31:07.760> as<00:31:07.960> we"
+ },
+ {
+ "start": 1868.07,
+ "duration": 0.0,
+ "text": "partially unpredictable uh code, as we"
+ },
+ {
+ "start": 1868.08,
+ "duration": 0.0,
+ "text": "partially unpredictable uh code, as we spend<00:31:08.560> additional<00:31:09.000> computation,<00:31:10.160> our"
+ },
+ {
+ "start": 1870.27,
+ "duration": 0.0,
+ "text": "spend additional computation, our"
+ },
+ {
+ "start": 1870.28,
+ "duration": 0.0,
+ "text": "spend additional computation, our predictions<00:31:10.720> get<00:31:10.880> better,"
+ },
+ {
+ "start": 1871.95,
+ "duration": 0.0,
+ "text": "predictions get better,"
+ },
+ {
+ "start": 1871.96,
+ "duration": 0.0,
+ "text": "predictions get better, and<00:31:12.520> the<00:31:12.640> optimal<00:31:12.920> model<00:31:13.160> size<00:31:13.760> gets<00:31:13.920> bigger."
+ },
+ {
+ "start": 1875.35,
+ "duration": 0.0,
+ "text": "and the optimal model size gets bigger."
+ },
+ {
+ "start": 1875.36,
+ "duration": 0.0,
+ "text": "and the optimal model size gets bigger. This<00:31:15.640> high<00:31:15.800> epi-plexity<00:31:16.880> and<00:31:17.640> yeah."
+ },
+ {
+ "start": 1880.6,
+ "duration": 0.0,
+ "text": "Now,<00:31:21.080> in<00:31:21.200> the<00:31:21.280> paper<00:31:21.600> we<00:31:21.680> have<00:31:21.800> a<00:31:21.840> couple<00:31:22.120> ways"
+ },
+ {
+ "start": 1882.47,
+ "duration": 0.0,
+ "text": "Now, in the paper we have a couple ways"
+ },
+ {
+ "start": 1882.48,
+ "duration": 0.0,
+ "text": "Now, in the paper we have a couple ways of<00:31:22.800> estimating<00:31:23.240> epi-plexity."
+ },
+ {
+ "start": 1885.31,
+ "duration": 0.0,
+ "text": "of estimating epi-plexity."
+ },
+ {
+ "start": 1885.32,
+ "duration": 0.0,
+ "text": "of estimating epi-plexity. The<00:31:25.400> one<00:31:25.600> that<00:31:25.720> we<00:31:25.840> use<00:31:26.320> for<00:31:26.480> most<00:31:26.760> of"
+ },
+ {
+ "start": 1886.83,
+ "duration": 0.0,
+ "text": "The one that we use for most of"
+ },
+ {
+ "start": 1886.84,
+ "duration": 0.0,
+ "text": "The one that we use for most of experiments<00:31:27.720> is<00:31:27.960> with<00:31:28.120> this<00:31:28.360> particular"
+ },
+ {
+ "start": 1888.83,
+ "duration": 0.0,
+ "text": "experiments is with this particular"
+ },
+ {
+ "start": 1888.84,
+ "duration": 0.0,
+ "text": "experiments is with this particular coding<00:31:29.120> scheme."
+ },
+ {
+ "start": 1890.67,
+ "duration": 0.0,
+ "text": "coding scheme."
+ },
+ {
+ "start": 1890.68,
+ "duration": 0.0,
+ "text": "coding scheme. The<00:31:30.760> thought<00:31:31.040> is,<00:31:31.760> okay,<00:31:32.000> we<00:31:32.160> have<00:31:32.360> this"
+ },
+ {
+ "start": 1892.75,
+ "duration": 0.0,
+ "text": "The thought is, okay, we have this"
+ },
+ {
+ "start": 1892.76,
+ "duration": 0.0,
+ "text": "The thought is, okay, we have this general<00:31:33.080> model<00:31:33.320> class,<00:31:34.040> all<00:31:34.240> of<00:31:34.320> these"
+ },
+ {
+ "start": 1894.75,
+ "duration": 0.0,
+ "text": "general model class, all of these"
+ },
+ {
+ "start": 1894.76,
+ "duration": 0.0,
+ "text": "general model class, all of these time-bounded<00:31:35.200> programs<00:31:36.040> that<00:31:36.320> admit"
+ },
+ {
+ "start": 1896.59,
+ "duration": 0.0,
+ "text": "time-bounded programs that admit"
+ },
+ {
+ "start": 1896.6,
+ "duration": 0.0,
+ "text": "time-bounded programs that admit probability<00:31:37.000> distributions,<00:31:38.240> that<00:31:38.320> we're"
+ },
+ {
+ "start": 1898.47,
+ "duration": 0.0,
+ "text": "probability distributions, that we're"
+ },
+ {
+ "start": 1898.48,
+ "duration": 0.0,
+ "text": "probability distributions, that we're going<00:31:38.600> to<00:31:38.720> use<00:31:39.040> but<00:31:39.160> instead<00:31:39.440> we're<00:31:39.520> going<00:31:39.640> to"
+ },
+ {
+ "start": 1899.75,
+ "duration": 0.0,
+ "text": "going to use but instead we're going to"
+ },
+ {
+ "start": 1899.76,
+ "duration": 0.0,
+ "text": "going to use but instead we're going to use<00:31:40.280> um<00:31:40.640> neural<00:31:40.800> networks<00:31:41.160> for<00:31:41.240> this."
+ },
+ {
+ "start": 1902.35,
+ "duration": 0.0,
+ "text": "use um neural networks for this."
+ },
+ {
+ "start": 1902.36,
+ "duration": 0.0,
+ "text": "use um neural networks for this. And<00:31:42.440> in<00:31:42.520> the<00:31:42.600> paper,<00:31:43.200> even<00:31:43.400> more"
+ },
+ {
+ "start": 1903.55,
+ "duration": 0.0,
+ "text": "And in the paper, even more"
+ },
+ {
+ "start": 1903.56,
+ "duration": 0.0,
+ "text": "And in the paper, even more specifically,<00:31:44.800> uh<00:31:45.120> auto-regressive"
+ },
+ {
+ "start": 1905.71,
+ "duration": 0.0,
+ "text": "specifically, uh auto-regressive"
+ },
+ {
+ "start": 1905.72,
+ "duration": 0.0,
+ "text": "specifically, uh auto-regressive transformers."
+ },
+ {
+ "start": 1907.83,
+ "duration": 0.0,
+ "text": "transformers."
+ },
+ {
+ "start": 1907.84,
+ "duration": 0.0,
+ "text": "transformers. So<00:31:47.880> the<00:31:47.960> question<00:31:48.320> then<00:31:48.680> is"
+ },
+ {
+ "start": 1910.47,
+ "duration": 0.0,
+ "text": "So the question then is"
+ },
+ {
+ "start": 1910.48,
+ "duration": 0.0,
+ "text": "So the question then is how<00:31:51.120> do<00:31:51.360> we"
+ },
+ {
+ "start": 1912.47,
+ "duration": 0.0,
+ "text": "how do we"
+ },
+ {
+ "start": 1912.48,
+ "duration": 0.0,
+ "text": "how do we uh<00:31:53.400> create<00:31:53.760> short<00:31:54.040> codes<00:31:54.880> for<00:31:55.120> those<00:31:55.480> models?"
+ },
+ {
+ "start": 1917.15,
+ "duration": 0.0,
+ "text": "uh create short codes for those models?"
+ },
+ {
+ "start": 1917.16,
+ "duration": 0.0,
+ "text": "uh create short codes for those models? And<00:31:58.000> just<00:31:58.760> counting<00:31:59.040> the<00:31:59.120> parameters<00:31:59.840> doesn't"
+ },
+ {
+ "start": 1920.11,
+ "duration": 0.0,
+ "text": "And just counting the parameters doesn't"
+ },
+ {
+ "start": 1920.12,
+ "duration": 0.0,
+ "text": "And just counting the parameters doesn't work<00:32:00.280> very<00:32:00.440> well"
+ },
+ {
+ "start": 1921.43,
+ "duration": 0.0,
+ "text": "work very well"
+ },
+ {
+ "start": 1921.44,
+ "duration": 0.0,
+ "text": "work very well because<00:32:02.200> you<00:32:02.320> can<00:32:02.440> have"
+ },
+ {
+ "start": 1923.71,
+ "duration": 0.0,
+ "text": "because you can have"
+ },
+ {
+ "start": 1923.72,
+ "duration": 0.0,
+ "text": "because you can have let's<00:32:04.000> say<00:32:04.160> we<00:32:04.280> have<00:32:04.440> a<00:32:04.480> massive<00:32:04.960> model"
+ },
+ {
+ "start": 1926.15,
+ "duration": 0.0,
+ "text": "let's say we have a massive model"
+ },
+ {
+ "start": 1926.16,
+ "duration": 0.0,
+ "text": "let's say we have a massive model and<00:32:06.280> we<00:32:06.360> train<00:32:06.640> it<00:32:06.920> on<00:32:07.760> random<00:32:08.000> noise,"
+ },
+ {
+ "start": 1929.23,
+ "duration": 0.0,
+ "text": "and we train it on random noise,"
+ },
+ {
+ "start": 1929.24,
+ "duration": 0.0,
+ "text": "and we train it on random noise, there's<00:32:09.360> very<00:32:09.560> little<00:32:09.760> information<00:32:10.240> in<00:32:10.320> that"
+ },
+ {
+ "start": 1930.43,
+ "duration": 0.0,
+ "text": "there's very little information in that"
+ },
+ {
+ "start": 1930.44,
+ "duration": 0.0,
+ "text": "there's very little information in that model.<00:32:11.000> You<00:32:11.120> could<00:32:11.240> have<00:32:11.320> used<00:32:11.440> a<00:32:11.480> much"
+ },
+ {
+ "start": 1931.63,
+ "duration": 0.0,
+ "text": "model. You could have used a much"
+ },
+ {
+ "start": 1931.64,
+ "duration": 0.0,
+ "text": "model. You could have used a much smaller<00:32:11.840> model."
+ },
+ {
+ "start": 1932.95,
+ "duration": 0.0,
+ "text": "smaller model."
+ },
+ {
+ "start": 1932.96,
+ "duration": 0.0,
+ "text": "smaller model. Um<00:32:13.920> but<00:32:14.360> if<00:32:14.480> you're<00:32:14.560> just<00:32:14.720> counting<00:32:14.960> the"
+ },
+ {
+ "start": 1934.99,
+ "duration": 0.0,
+ "text": "Um but if you're just counting the"
+ },
+ {
+ "start": 1935.0,
+ "duration": 0.0,
+ "text": "Um but if you're just counting the parameters,<00:32:15.640> you<00:32:15.880> would<00:32:16.000> think<00:32:16.240> that<00:32:16.480> you"
+ },
+ {
+ "start": 1936.55,
+ "duration": 0.0,
+ "text": "parameters, you would think that you"
+ },
+ {
+ "start": 1936.56,
+ "duration": 0.0,
+ "text": "parameters, you would think that you have<00:32:16.679> a<00:32:16.720> large<00:32:16.960> number.<00:32:17.440> So<00:32:17.560> we<00:32:17.600> need<00:32:17.800> a<00:32:17.920> uh"
+ },
+ {
+ "start": 1938.15,
+ "duration": 0.0,
+ "text": "have a large number. So we need a uh"
+ },
+ {
+ "start": 1938.16,
+ "duration": 0.0,
+ "text": "have a large number. So we need a uh slightly<00:32:18.520> more"
+ },
+ {
+ "start": 1939.51,
+ "duration": 0.0,
+ "text": "slightly more"
+ },
+ {
+ "start": 1939.52,
+ "duration": 0.0,
+ "text": "slightly more uh<00:32:20.120> sophisticated<00:32:20.679> code."
+ },
+ {
+ "start": 1941.63,
+ "duration": 0.0,
+ "text": "uh sophisticated code."
+ },
+ {
+ "start": 1941.64,
+ "duration": 0.0,
+ "text": "uh sophisticated code. And<00:32:21.720> that's<00:32:22.120> where<00:32:22.400> this<00:32:22.679> re-quential<00:32:23.160> coding"
+ },
+ {
+ "start": 1943.47,
+ "duration": 0.0,
+ "text": "And that's where this re-quential coding"
+ },
+ {
+ "start": 1943.48,
+ "duration": 0.0,
+ "text": "And that's where this re-quential coding comes<00:32:23.720> in.<00:32:24.320> Now,<00:32:24.440> I'm<00:32:24.520> not<00:32:24.640> going<00:32:24.760> to<00:32:24.800> go<00:32:24.960> into"
+ },
+ {
+ "start": 1945.19,
+ "duration": 0.0,
+ "text": "comes in. Now, I'm not going to go into"
+ },
+ {
+ "start": 1945.2,
+ "duration": 0.0,
+ "text": "comes in. Now, I'm not going to go into this<00:32:25.440> in<00:32:25.920> great<00:32:26.160> detail."
+ },
+ {
+ "start": 1947.27,
+ "duration": 0.0,
+ "text": "this in great detail."
+ },
+ {
+ "start": 1947.28,
+ "duration": 0.0,
+ "text": "this in great detail. Definitely<00:32:27.800> uh<00:32:27.960> first<00:32:28.160> to<00:32:28.200> the<00:32:28.280> paper<00:32:28.480> for"
+ },
+ {
+ "start": 1948.55,
+ "duration": 0.0,
+ "text": "Definitely uh first to the paper for"
+ },
+ {
+ "start": 1948.56,
+ "duration": 0.0,
+ "text": "Definitely uh first to the paper for that,<00:32:28.720> but<00:32:28.800> it's<00:32:28.920> a<00:32:28.960> really<00:32:29.120> cool<00:32:29.320> coding"
+ },
+ {
+ "start": 1949.55,
+ "duration": 0.0,
+ "text": "that, but it's a really cool coding"
+ },
+ {
+ "start": 1949.56,
+ "duration": 0.0,
+ "text": "that, but it's a really cool coding technique<00:32:30.080> that<00:32:30.240> we<00:32:30.320> came<00:32:30.520> up<00:32:30.679> with"
+ },
+ {
+ "start": 1951.71,
+ "duration": 0.0,
+ "text": "technique that we came up with"
+ },
+ {
+ "start": 1951.72,
+ "duration": 0.0,
+ "text": "technique that we came up with where<00:32:32.720> um"
+ },
+ {
+ "start": 1953.95,
+ "duration": 0.0,
+ "text": "where um"
+ },
+ {
+ "start": 1953.96,
+ "duration": 0.0,
+ "text": "where um we<00:32:34.080> try<00:32:34.640> to"
+ },
+ {
+ "start": 1955.55,
+ "duration": 0.0,
+ "text": "we try to"
+ },
+ {
+ "start": 1955.56,
+ "duration": 0.0,
+ "text": "we try to make<00:32:35.920> an<00:32:36.000> explicit<00:32:36.600> code<00:32:37.160> that<00:32:37.400> separates<00:32:37.960> out"
+ },
+ {
+ "start": 1959.19,
+ "duration": 0.0,
+ "text": "make an explicit code that separates out"
+ },
+ {
+ "start": 1959.2,
+ "duration": 0.0,
+ "text": "make an explicit code that separates out the<00:32:39.920> this<00:32:40.240> structural<00:32:41.280> the<00:32:41.400> amount<00:32:41.720> that<00:32:41.920> is"
+ },
+ {
+ "start": 1962.03,
+ "duration": 0.0,
+ "text": "the this structural the amount that is"
+ },
+ {
+ "start": 1962.04,
+ "duration": 0.0,
+ "text": "the this structural the amount that is needed<00:32:42.240> to<00:32:42.320> code<00:32:42.760> the"
+ },
+ {
+ "start": 1963.55,
+ "duration": 0.0,
+ "text": "needed to code the"
+ },
+ {
+ "start": 1963.56,
+ "duration": 0.0,
+ "text": "needed to code the you<00:32:43.600> know,<00:32:43.760> the<00:32:44.400> all<00:32:44.520> the<00:32:44.600> structure<00:32:44.960> in<00:32:45.040> the"
+ },
+ {
+ "start": 1965.11,
+ "duration": 0.0,
+ "text": "you know, the all the structure in the"
+ },
+ {
+ "start": 1965.12,
+ "duration": 0.0,
+ "text": "you know, the all the structure in the model<00:32:45.400> that<00:32:45.520> it<00:32:45.640> uses<00:32:45.920> for<00:32:46.040> predictions,"
+ },
+ {
+ "start": 1967.27,
+ "duration": 0.0,
+ "text": "model that it uses for predictions,"
+ },
+ {
+ "start": 1967.28,
+ "duration": 0.0,
+ "text": "model that it uses for predictions, um"
+ },
+ {
+ "start": 1968.55,
+ "duration": 0.0,
+ "text": "um"
+ },
+ {
+ "start": 1968.56,
+ "duration": 0.0,
+ "text": "um uh<00:32:49.120> also<00:32:49.400> not<00:32:49.600> paying<00:32:50.040> the<00:32:50.320> the<00:32:50.400> cost<00:32:50.760> for<00:32:50.960> the"
+ },
+ {
+ "start": 1971.27,
+ "duration": 0.0,
+ "text": "uh also not paying the the cost for the"
+ },
+ {
+ "start": 1971.28,
+ "duration": 0.0,
+ "text": "uh also not paying the the cost for the the<00:32:51.560> the<00:32:51.679> data,<00:32:52.679> um<00:32:53.040> but<00:32:53.560> that<00:32:54.480> is<00:32:54.720> somewhat"
+ },
+ {
+ "start": 1974.99,
+ "duration": 0.0,
+ "text": "the the data, um but that is somewhat"
+ },
+ {
+ "start": 1975.0,
+ "duration": 0.0,
+ "text": "the the data, um but that is somewhat decoupled<00:32:55.520> from<00:32:55.640> the<00:32:55.720> number<00:32:55.920> of<00:32:56.000> parameters."
+ },
+ {
+ "start": 1977.35,
+ "duration": 0.0,
+ "text": "decoupled from the number of parameters."
+ },
+ {
+ "start": 1977.36,
+ "duration": 0.0,
+ "text": "decoupled from the number of parameters. And<00:32:57.440> the<00:32:57.520> way<00:32:57.679> it<00:32:57.800> works<00:32:58.480> is<00:32:58.800> that<00:32:58.960> we<00:32:59.080> have"
+ },
+ {
+ "start": 1979.55,
+ "duration": 0.0,
+ "text": "And the way it works is that we have"
+ },
+ {
+ "start": 1979.56,
+ "duration": 0.0,
+ "text": "And the way it works is that we have really<00:32:59.880> two<00:33:00.120> models."
+ },
+ {
+ "start": 1981.15,
+ "duration": 0.0,
+ "text": "really two models."
+ },
+ {
+ "start": 1981.16,
+ "duration": 0.0,
+ "text": "really two models. We<00:33:01.200> have<00:33:01.320> a<00:33:01.400> student<00:33:01.840> model<00:33:02.280> and<00:33:02.360> a<00:33:02.400> teacher"
+ },
+ {
+ "start": 1982.75,
+ "duration": 0.0,
+ "text": "We have a student model and a teacher"
+ },
+ {
+ "start": 1982.76,
+ "duration": 0.0,
+ "text": "We have a student model and a teacher model."
+ },
+ {
+ "start": 1984.11,
+ "duration": 0.0,
+ "text": "model."
+ },
+ {
+ "start": 1984.12,
+ "duration": 0.0,
+ "text": "model. And<00:33:04.720> we<00:33:04.840> somehow<00:33:05.600> use<00:33:05.960> the<00:33:06.080> teacher<00:33:06.960> to"
+ },
+ {
+ "start": 1988.19,
+ "duration": 0.0,
+ "text": "And we somehow use the teacher to"
+ },
+ {
+ "start": 1988.2,
+ "duration": 0.0,
+ "text": "And we somehow use the teacher to uh<00:33:08.360> we<00:33:08.520> code<00:33:09.720> data"
+ },
+ {
+ "start": 1991.87,
+ "duration": 0.0,
+ "text": "uh we code data"
+ },
+ {
+ "start": 1991.88,
+ "duration": 0.0,
+ "text": "uh we code data from<00:33:12.040> the<00:33:12.160> teacher's<00:33:12.679> distribution"
+ },
+ {
+ "start": 1994.23,
+ "duration": 0.0,
+ "text": "from the teacher's distribution"
+ },
+ {
+ "start": 1994.24,
+ "duration": 0.0,
+ "text": "from the teacher's distribution um<00:33:14.840> using<00:33:15.520> the<00:33:15.640> student"
+ },
+ {
+ "start": 1997.55,
+ "duration": 0.0,
+ "text": "um using the student"
+ },
+ {
+ "start": 1997.56,
+ "duration": 0.0,
+ "text": "um using the student and<00:33:17.679> then<00:33:18.120> train<00:33:18.440> the<00:33:18.520> student<00:33:18.840> on<00:33:18.920> that<00:33:19.080> data"
+ },
+ {
+ "start": 1999.79,
+ "duration": 0.0,
+ "text": "and then train the student on that data"
+ },
+ {
+ "start": 1999.8,
+ "duration": 0.0,
+ "text": "and then train the student on that data and<00:33:19.920> then<00:33:20.080> repeat."
+ },
+ {
+ "start": 2001.87,
+ "duration": 0.0,
+ "text": "and then repeat."
+ },
+ {
+ "start": 2001.88,
+ "duration": 0.0,
+ "text": "and then repeat. And<00:33:22.679> yeah,<00:33:22.840> so<00:33:23.000> it's<00:33:23.160> it's<00:33:23.320> a<00:33:23.360> little<00:33:23.600> bit<00:33:23.720> of<00:33:23.800> a"
+ },
+ {
+ "start": 2003.87,
+ "duration": 0.0,
+ "text": "And yeah, so it's it's a little bit of a"
+ },
+ {
+ "start": 2003.88,
+ "duration": 0.0,
+ "text": "And yeah, so it's it's a little bit of a tricky<00:33:24.160> thing,<00:33:24.560> um<00:33:24.840> but<00:33:25.160> at<00:33:25.240> the<00:33:25.360> end<00:33:25.480> of<00:33:25.560> the"
+ },
+ {
+ "start": 2005.669,
+ "duration": 0.0,
+ "text": "tricky thing, um but at the end of the"
+ },
+ {
+ "start": 2005.679,
+ "duration": 0.0,
+ "text": "tricky thing, um but at the end of the day,<00:33:26.280> what<00:33:26.400> we<00:33:26.560> get<00:33:27.480> is<00:33:27.600> a<00:33:27.679> code<00:33:28.000> length<00:33:28.280> for<00:33:28.400> a"
+ },
+ {
+ "start": 2008.43,
+ "duration": 0.0,
+ "text": "day, what we get is a code length for a"
+ },
+ {
+ "start": 2008.44,
+ "duration": 0.0,
+ "text": "day, what we get is a code length for a model<00:33:29.440> which<00:33:29.640> is<00:33:30.480> essentially<00:33:31.040> the<00:33:31.160> area"
+ },
+ {
+ "start": 2011.51,
+ "duration": 0.0,
+ "text": "model which is essentially the area"
+ },
+ {
+ "start": 2011.52,
+ "duration": 0.0,
+ "text": "model which is essentially the area between<00:33:32.200> these<00:33:32.440> two<00:33:32.600> curves,<00:33:33.240> between<00:33:33.760> the"
+ },
+ {
+ "start": 2013.87,
+ "duration": 0.0,
+ "text": "between these two curves, between the"
+ },
+ {
+ "start": 2013.88,
+ "duration": 0.0,
+ "text": "between these two curves, between the loss<00:33:34.480> of<00:33:34.679> the<00:33:34.800> teacher<00:33:35.120> model"
+ },
+ {
+ "start": 2016.35,
+ "duration": 0.0,
+ "text": "loss of the teacher model"
+ },
+ {
+ "start": 2016.36,
+ "duration": 0.0,
+ "text": "loss of the teacher model in<00:33:36.480> blue,<00:33:36.880> and<00:33:37.000> then<00:33:37.080> the<00:33:37.160> loss<00:33:37.440> of<00:33:37.520> the"
+ },
+ {
+ "start": 2017.59,
+ "duration": 0.0,
+ "text": "in blue, and then the loss of the"
+ },
+ {
+ "start": 2017.6,
+ "duration": 0.0,
+ "text": "in blue, and then the loss of the student<00:33:37.880> model<00:33:38.400> trained<00:33:39.240> on<00:33:39.480> the<00:33:39.560> data"
+ },
+ {
+ "start": 2019.87,
+ "duration": 0.0,
+ "text": "student model trained on the data"
+ },
+ {
+ "start": 2019.88,
+ "duration": 0.0,
+ "text": "student model trained on the data produced<00:33:40.160> by<00:33:40.240> that<00:33:40.440> teacher.<00:33:41.120> The<00:33:41.240> area"
+ },
+ {
+ "start": 2021.47,
+ "duration": 0.0,
+ "text": "produced by that teacher. The area"
+ },
+ {
+ "start": 2021.48,
+ "duration": 0.0,
+ "text": "produced by that teacher. The area between<00:33:41.920> those<00:33:42.120> two<00:33:42.280> curves"
+ },
+ {
+ "start": 2023.55,
+ "duration": 0.0,
+ "text": "between those two curves"
+ },
+ {
+ "start": 2023.56,
+ "duration": 0.0,
+ "text": "between those two curves essentially<00:33:44.360> gives<00:33:44.720> you<00:33:45.240> I<00:33:45.280> mean,<00:33:45.600> we<00:33:45.720> have<00:33:45.880> a"
+ },
+ {
+ "start": 2026.07,
+ "duration": 0.0,
+ "text": "essentially gives you I mean, we have a"
+ },
+ {
+ "start": 2026.08,
+ "duration": 0.0,
+ "text": "essentially gives you I mean, we have a uh<00:33:46.400> a<00:33:46.440> very,<00:33:46.800> you<00:33:46.880> know,<00:33:47.160> um<00:33:47.400> precise<00:33:47.840> code,"
+ },
+ {
+ "start": 2028.47,
+ "duration": 0.0,
+ "text": "uh a very, you know, um precise code,"
+ },
+ {
+ "start": 2028.48,
+ "duration": 0.0,
+ "text": "uh a very, you know, um precise code, but<00:33:48.760> um<00:33:49.160> I'm<00:33:49.320> just<00:33:49.960> uh<00:33:50.080> laying<00:33:50.280> it<00:33:50.360> out<00:33:50.440> in"
+ },
+ {
+ "start": 2030.51,
+ "duration": 0.0,
+ "text": "but um I'm just uh laying it out in"
+ },
+ {
+ "start": 2030.52,
+ "duration": 0.0,
+ "text": "but um I'm just uh laying it out in high-level<00:33:50.840> terms<00:33:51.040> here,<00:33:51.640> um<00:33:51.960> gives<00:33:52.240> you<00:33:52.440> a"
+ },
+ {
+ "start": 2032.51,
+ "duration": 0.0,
+ "text": "high-level terms here, um gives you a"
+ },
+ {
+ "start": 2032.52,
+ "duration": 0.0,
+ "text": "high-level terms here, um gives you a code<00:33:53.240> for<00:33:53.880> this<00:33:54.440> final<00:33:55.120> student<00:33:55.480> model.<00:33:56.240> And"
+ },
+ {
+ "start": 2036.31,
+ "duration": 0.0,
+ "text": "code for this final student model. And"
+ },
+ {
+ "start": 2036.32,
+ "duration": 0.0,
+ "text": "code for this final student model. And this<00:33:56.520> code<00:33:57.600> is<00:33:57.800> going<00:33:58.120> to<00:33:58.560> vary<00:33:59.040> even<00:33:59.280> with<00:33:59.440> a"
+ },
+ {
+ "start": 2039.47,
+ "duration": 0.0,
+ "text": "this code is going to vary even with a"
+ },
+ {
+ "start": 2039.48,
+ "duration": 0.0,
+ "text": "this code is going to vary even with a large<00:33:59.920> this<00:34:00.080> code<00:34:00.320> can<00:34:00.440> be<00:34:00.560> small<00:34:01.040> even<00:34:01.240> with<00:34:01.400> a"
+ },
+ {
+ "start": 2041.43,
+ "duration": 0.0,
+ "text": "large this code can be small even with a"
+ },
+ {
+ "start": 2041.44,
+ "duration": 0.0,
+ "text": "large this code can be small even with a large<00:34:01.720> model<00:34:02.040> with<00:34:02.120> lots<00:34:02.360> of<00:34:02.440> parameters,"
+ },
+ {
+ "start": 2043.47,
+ "duration": 0.0,
+ "text": "large model with lots of parameters,"
+ },
+ {
+ "start": 2043.48,
+ "duration": 0.0,
+ "text": "large model with lots of parameters, um<00:34:04.120> and<00:34:04.400> so<00:34:04.800> we<00:34:04.960> can<00:34:05.080> actually<00:34:05.360> be<00:34:05.679> and<00:34:05.840> and"
+ },
+ {
+ "start": 2045.95,
+ "duration": 0.0,
+ "text": "um and so we can actually be and and"
+ },
+ {
+ "start": 2045.96,
+ "duration": 0.0,
+ "text": "um and so we can actually be and and it's<00:34:06.080> actually<00:34:06.320> quite<00:34:06.520> competitive<00:34:07.280> just"
+ },
+ {
+ "start": 2047.51,
+ "duration": 0.0,
+ "text": "it's actually quite competitive just"
+ },
+ {
+ "start": 2047.52,
+ "duration": 0.0,
+ "text": "it's actually quite competitive just thinking<00:34:07.679> about<00:34:07.880> the<00:34:07.960> best<00:34:08.679> compression<00:34:09.240> that"
+ },
+ {
+ "start": 2049.389,
+ "duration": 0.0,
+ "text": "thinking about the best compression that"
+ },
+ {
+ "start": 2049.399,
+ "duration": 0.0,
+ "text": "thinking about the best compression that you<00:34:09.440> can<00:34:09.640> do<00:34:10.399> for"
+ },
+ {
+ "start": 2051.83,
+ "duration": 0.0,
+ "text": "you can do for"
+ },
+ {
+ "start": 2051.84,
+ "duration": 0.0,
+ "text": "you can do for an<00:34:11.919> auto-regressive<00:34:12.399> transformer."
+ },
+ {
+ "start": 2054.79,
+ "duration": 0.0,
+ "text": "an auto-regressive transformer."
+ },
+ {
+ "start": 2054.8,
+ "duration": 0.0,
+ "text": "an auto-regressive transformer. So<00:34:15.440> then<00:34:15.800> we<00:34:15.919> just<00:34:16.120> train<00:34:16.600> many<00:34:16.840> different"
+ },
+ {
+ "start": 2057.19,
+ "duration": 0.0,
+ "text": "So then we just train many different"
+ },
+ {
+ "start": 2057.2,
+ "duration": 0.0,
+ "text": "So then we just train many different networks<00:34:17.640> with<00:34:17.720> different<00:34:17.919> parameters<00:34:18.280> to"
+ },
+ {
+ "start": 2058.31,
+ "duration": 0.0,
+ "text": "networks with different parameters to"
+ },
+ {
+ "start": 2058.32,
+ "duration": 0.0,
+ "text": "networks with different parameters to compute"
+ },
+ {
+ "start": 2059.349,
+ "duration": 0.0,
+ "text": "compute"
+ },
+ {
+ "start": 2059.359,
+ "duration": 0.0,
+ "text": "compute compute<00:34:19.560> the<00:34:19.640> total<00:34:19.919> code<00:34:20.120> length<00:34:20.960> um"
+ },
+ {
+ "start": 2062.11,
+ "duration": 0.0,
+ "text": "compute the total code length um"
+ },
+ {
+ "start": 2062.12,
+ "duration": 0.0,
+ "text": "compute the total code length um before<00:34:22.640> again<00:34:23.000> taking<00:34:23.399> this<00:34:23.640> code<00:34:24.080> for<00:34:24.240> the"
+ },
+ {
+ "start": 2064.349,
+ "duration": 0.0,
+ "text": "before again taking this code for the"
+ },
+ {
+ "start": 2064.359,
+ "duration": 0.0,
+ "text": "before again taking this code for the neural<00:34:24.520> network<00:34:25.280> and<00:34:25.440> then<00:34:25.600> also<00:34:26.120> taking<00:34:26.399> the"
+ },
+ {
+ "start": 2066.47,
+ "duration": 0.0,
+ "text": "neural network and then also taking the"
+ },
+ {
+ "start": 2066.48,
+ "duration": 0.0,
+ "text": "neural network and then also taking the code<00:34:26.960> for<00:34:27.040> the<00:34:27.159> data<00:34:27.640> given<00:34:27.840> that<00:34:27.960> network.<00:34:28.879> Um"
+ },
+ {
+ "start": 2069.11,
+ "duration": 0.0,
+ "text": "code for the data given that network. Um"
+ },
+ {
+ "start": 2069.12,
+ "duration": 0.0,
+ "text": "code for the data given that network. Um and<00:34:29.240> then<00:34:29.359> we<00:34:29.440> just<00:34:29.640> evaluate"
+ },
+ {
+ "start": 2070.95,
+ "duration": 0.0,
+ "text": "and then we just evaluate"
+ },
+ {
+ "start": 2070.96,
+ "duration": 0.0,
+ "text": "and then we just evaluate among<00:34:31.280> all<00:34:31.399> these<00:34:31.600> different<00:34:32.040> candidates,"
+ },
+ {
+ "start": 2072.95,
+ "duration": 0.0,
+ "text": "among all these different candidates,"
+ },
+ {
+ "start": 2072.96,
+ "duration": 0.0,
+ "text": "among all these different candidates, all<00:34:33.120> the<00:34:33.240> you<00:34:33.320> know,<00:34:33.399> we<00:34:33.560> lay<00:34:33.800> them<00:34:33.960> all<00:34:34.159> out<00:34:34.359> on"
+ },
+ {
+ "start": 2074.43,
+ "duration": 0.0,
+ "text": "all the you know, we lay them all out on"
+ },
+ {
+ "start": 2074.44,
+ "duration": 0.0,
+ "text": "all the you know, we lay them all out on the<00:34:34.520> same<00:34:34.760> curve<00:34:35.480> that<00:34:35.640> has<00:34:35.960> compute<00:34:36.359> on<00:34:36.480> the"
+ },
+ {
+ "start": 2076.55,
+ "duration": 0.0,
+ "text": "the same curve that has compute on the"
+ },
+ {
+ "start": 2076.56,
+ "duration": 0.0,
+ "text": "the same curve that has compute on the x-axis<00:34:37.600> and<00:34:38.080> this<00:34:38.919> total<00:34:39.159> description<00:34:39.560> length"
+ },
+ {
+ "start": 2079.75,
+ "duration": 0.0,
+ "text": "x-axis and this total description length"
+ },
+ {
+ "start": 2079.76,
+ "duration": 0.0,
+ "text": "x-axis and this total description length on<00:34:39.879> the<00:34:39.960> y-axis,"
+ },
+ {
+ "start": 2081.11,
+ "duration": 0.0,
+ "text": "on the y-axis,"
+ },
+ {
+ "start": 2081.12,
+ "duration": 0.0,
+ "text": "on the y-axis, and<00:34:41.240> we<00:34:41.359> just<00:34:41.560> take<00:34:41.760> the<00:34:41.840> ones<00:34:42.280> on<00:34:42.480> this"
+ },
+ {
+ "start": 2082.869,
+ "duration": 0.0,
+ "text": "and we just take the ones on this"
+ },
+ {
+ "start": 2082.879,
+ "duration": 0.0,
+ "text": "and we just take the ones on this frontier"
+ },
+ {
+ "start": 2083.99,
+ "duration": 0.0,
+ "text": "frontier"
+ },
+ {
+ "start": 2084.0,
+ "duration": 0.0,
+ "text": "frontier and<00:34:44.159> take<00:34:44.800> well,<00:34:45.359> take<00:34:45.720> the<00:34:46.080> uh"
+ },
+ {
+ "start": 2087.19,
+ "duration": 0.0,
+ "text": "and take well, take the uh"
+ },
+ {
+ "start": 2087.2,
+ "duration": 0.0,
+ "text": "and take well, take the uh the<00:34:47.640> the<00:34:47.720> code<00:34:47.919> length<00:34:48.240> for<00:34:48.359> the<00:34:48.440> models<00:34:48.760> on"
+ },
+ {
+ "start": 2088.869,
+ "duration": 0.0,
+ "text": "the the code length for the models on"
+ },
+ {
+ "start": 2088.879,
+ "duration": 0.0,
+ "text": "the the code length for the models on that<00:34:49.000> frontier,<00:34:49.480> right?<00:34:49.640> So<00:34:49.760> here<00:34:50.000> is"
+ },
+ {
+ "start": 2090.349,
+ "duration": 0.0,
+ "text": "that frontier, right? So here is"
+ },
+ {
+ "start": 2090.359,
+ "duration": 0.0,
+ "text": "that frontier, right? So here is example,<00:34:51.120> you<00:34:51.200> have<00:34:51.320> many<00:34:51.520> different<00:34:52.320> uh"
+ },
+ {
+ "start": 2092.99,
+ "duration": 0.0,
+ "text": "example, you have many different uh"
+ },
+ {
+ "start": 2093.0,
+ "duration": 0.0,
+ "text": "example, you have many different uh uh<00:34:53.080> models<00:34:53.320> with<00:34:53.399> different<00:34:53.600> number<00:34:53.720> of"
+ },
+ {
+ "start": 2093.79,
+ "duration": 0.0,
+ "text": "uh models with different number of"
+ },
+ {
+ "start": 2093.8,
+ "duration": 0.0,
+ "text": "uh models with different number of parameters,<00:34:54.760> they<00:34:55.280> each<00:34:55.879> have<00:34:56.000> this<00:34:56.200> little"
+ },
+ {
+ "start": 2096.55,
+ "duration": 0.0,
+ "text": "parameters, they each have this little"
+ },
+ {
+ "start": 2096.56,
+ "duration": 0.0,
+ "text": "parameters, they each have this little U-shaped<00:34:56.840> curve,<00:34:57.120> we<00:34:57.240> overlay<00:34:57.640> them,<00:34:58.440> um<00:34:58.760> and"
+ },
+ {
+ "start": 2098.91,
+ "duration": 0.0,
+ "text": "U-shaped curve, we overlay them, um and"
+ },
+ {
+ "start": 2098.92,
+ "duration": 0.0,
+ "text": "U-shaped curve, we overlay them, um and then<00:34:59.080> this"
+ },
+ {
+ "start": 2100.03,
+ "duration": 0.0,
+ "text": "then this"
+ },
+ {
+ "start": 2100.04,
+ "duration": 0.0,
+ "text": "then this time-bounded<00:35:00.440> entropy<00:35:01.000> is<00:35:01.320> is<00:35:01.440> going<00:35:01.680> down<00:35:02.080> as"
+ },
+ {
+ "start": 2102.31,
+ "duration": 0.0,
+ "text": "time-bounded entropy is is going down as"
+ },
+ {
+ "start": 2102.32,
+ "duration": 0.0,
+ "text": "time-bounded entropy is is going down as we<00:35:02.440> increase<00:35:02.800> the<00:35:02.880> amount<00:35:03.040> of<00:35:03.120> compute<00:35:03.359> that"
+ },
+ {
+ "start": 2103.43,
+ "duration": 0.0,
+ "text": "we increase the amount of compute that"
+ },
+ {
+ "start": 2103.44,
+ "duration": 0.0,
+ "text": "we increase the amount of compute that we<00:35:03.520> have<00:35:03.800> by<00:35:04.200> increasing<00:35:04.560> the<00:35:04.640> number<00:35:04.760> of"
+ },
+ {
+ "start": 2104.83,
+ "duration": 0.0,
+ "text": "we have by increasing the number of"
+ },
+ {
+ "start": 2104.84,
+ "duration": 0.0,
+ "text": "we have by increasing the number of parameters,<00:35:05.720> um<00:35:06.359> and<00:35:06.520> also<00:35:06.720> increasing<00:35:07.120> the"
+ },
+ {
+ "start": 2107.19,
+ "duration": 0.0,
+ "text": "parameters, um and also increasing the"
+ },
+ {
+ "start": 2107.2,
+ "duration": 0.0,
+ "text": "parameters, um and also increasing the number<00:35:07.480> of<00:35:07.880> uh"
+ },
+ {
+ "start": 2108.63,
+ "duration": 0.0,
+ "text": "number of uh"
+ },
+ {
+ "start": 2108.64,
+ "duration": 0.0,
+ "text": "number of uh uh<00:35:08.720> data<00:35:08.840> points<00:35:09.040> that<00:35:09.120> we<00:35:09.160> train<00:35:09.359> on,<00:35:10.000> um<00:35:10.320> and"
+ },
+ {
+ "start": 2110.51,
+ "duration": 0.0,
+ "text": "uh data points that we train on, um and"
+ },
+ {
+ "start": 2110.52,
+ "duration": 0.0,
+ "text": "uh data points that we train on, um and then<00:35:11.080> uh"
+ },
+ {
+ "start": 2111.79,
+ "duration": 0.0,
+ "text": "then uh"
+ },
+ {
+ "start": 2111.8,
+ "duration": 0.0,
+ "text": "then uh right,<00:35:12.040> and<00:35:12.120> then<00:35:12.240> here"
+ },
+ {
+ "start": 2115.64,
+ "duration": 0.0,
+ "text": "So"
+ },
+ {
+ "start": 2116.87,
+ "duration": 0.0,
+ "text": "So"
+ },
+ {
+ "start": 2116.88,
+ "duration": 0.0,
+ "text": "So circling<00:35:17.280> back<00:35:17.720> to"
+ },
+ {
+ "start": 2119.43,
+ "duration": 0.0,
+ "text": "circling back to"
+ },
+ {
+ "start": 2119.44,
+ "duration": 0.0,
+ "text": "circling back to Andrew's<00:35:20.640> uh<00:35:20.800> right,<00:35:21.000> I<00:35:21.040> mean,<00:35:21.160> this<00:35:21.320> framing"
+ },
+ {
+ "start": 2121.55,
+ "duration": 0.0,
+ "text": "Andrew's uh right, I mean, this framing"
+ },
+ {
+ "start": 2121.56,
+ "duration": 0.0,
+ "text": "Andrew's uh right, I mean, this framing that<00:35:21.680> we<00:35:21.760> have,<00:35:22.359> um"
+ },
+ {
+ "start": 2123.59,
+ "duration": 0.0,
+ "text": "that we have, um"
+ },
+ {
+ "start": 2123.6,
+ "duration": 0.0,
+ "text": "that we have, um three<00:35:23.760> paradoxes<00:35:24.480> of<00:35:24.600> information,<00:35:25.160> right?"
+ },
+ {
+ "start": 2125.83,
+ "duration": 0.0,
+ "text": "three paradoxes of information, right?"
+ },
+ {
+ "start": 2125.84,
+ "duration": 0.0,
+ "text": "three paradoxes of information, right? Uh<00:35:25.960> or<00:35:26.080> apparent<00:35:26.400> paradoxes.<00:35:27.359> So"
+ },
+ {
+ "start": 2128.43,
+ "duration": 0.0,
+ "text": "Uh or apparent paradoxes. So"
+ },
+ {
+ "start": 2128.44,
+ "duration": 0.0,
+ "text": "Uh or apparent paradoxes. So we'll<00:35:29.120> now<00:35:29.440> go<00:35:29.600> through<00:35:29.800> them<00:35:30.280> and<00:35:30.840> see<00:35:31.440> if<00:35:31.600> we"
+ },
+ {
+ "start": 2131.75,
+ "duration": 0.0,
+ "text": "we'll now go through them and see if we"
+ },
+ {
+ "start": 2131.76,
+ "duration": 0.0,
+ "text": "we'll now go through them and see if we can<00:35:32.600> reinterpret<00:35:33.120> them<00:35:33.640> with<00:35:33.800> the<00:35:33.880> help<00:35:34.320> of"
+ },
+ {
+ "start": 2134.55,
+ "duration": 0.0,
+ "text": "can reinterpret them with the help of"
+ },
+ {
+ "start": 2134.56,
+ "duration": 0.0,
+ "text": "can reinterpret them with the help of these<00:35:34.960> theoretical<00:35:35.320> tools<00:35:36.120> like"
+ },
+ {
+ "start": 2136.27,
+ "duration": 0.0,
+ "text": "these theoretical tools like"
+ },
+ {
+ "start": 2136.28,
+ "duration": 0.0,
+ "text": "these theoretical tools like epi-plexity."
+ },
+ {
+ "start": 2137.51,
+ "duration": 0.0,
+ "text": "epi-plexity."
+ },
+ {
+ "start": 2137.52,
+ "duration": 0.0,
+ "text": "epi-plexity. So<00:35:37.560> the<00:35:37.640> first<00:35:37.840> one,<00:35:38.160> information<00:35:38.600> cannot<00:35:38.800> be"
+ },
+ {
+ "start": 2138.87,
+ "duration": 0.0,
+ "text": "So the first one, information cannot be"
+ },
+ {
+ "start": 2138.88,
+ "duration": 0.0,
+ "text": "So the first one, information cannot be increased<00:35:39.359> by<00:35:39.480> deterministic<00:35:40.000> processes,"
+ },
+ {
+ "start": 2141.11,
+ "duration": 0.0,
+ "text": "increased by deterministic processes,"
+ },
+ {
+ "start": 2141.12,
+ "duration": 0.0,
+ "text": "increased by deterministic processes, right?<00:35:41.680> In<00:35:41.760> fact,<00:35:42.000> we<00:35:42.040> will<00:35:42.160> find<00:35:42.400> that"
+ },
+ {
+ "start": 2142.55,
+ "duration": 0.0,
+ "text": "right? In fact, we will find that"
+ },
+ {
+ "start": 2142.56,
+ "duration": 0.0,
+ "text": "right? In fact, we will find that time-bounded<00:35:43.320> entropy<00:35:43.680> and<00:35:43.800> epi-plexity<00:35:44.680> can"
+ },
+ {
+ "start": 2145.349,
+ "duration": 0.0,
+ "text": "time-bounded entropy and epi-plexity can"
+ },
+ {
+ "start": 2145.359,
+ "duration": 0.0,
+ "text": "time-bounded entropy and epi-plexity can be<00:35:45.720> created<00:35:46.160> through<00:35:46.359> computation."
+ },
+ {
+ "start": 2147.83,
+ "duration": 0.0,
+ "text": "be created through computation."
+ },
+ {
+ "start": 2147.84,
+ "duration": 0.0,
+ "text": "be created through computation. So<00:35:47.920> the<00:35:48.000> first<00:35:48.240> example<00:35:49.000> is<00:35:49.120> the<00:35:49.200> one<00:35:49.359> Andrew"
+ },
+ {
+ "start": 2149.75,
+ "duration": 0.0,
+ "text": "So the first example is the one Andrew"
+ },
+ {
+ "start": 2149.76,
+ "duration": 0.0,
+ "text": "So the first example is the one Andrew mentioned<00:35:50.000> before,<00:35:50.640> which<00:35:50.880> is<00:35:51.240> pseudo-random"
+ },
+ {
+ "start": 2151.95,
+ "duration": 0.0,
+ "text": "mentioned before, which is pseudo-random"
+ },
+ {
+ "start": 2151.96,
+ "duration": 0.0,
+ "text": "mentioned before, which is pseudo-random generators."
+ },
+ {
+ "start": 2153.31,
+ "duration": 0.0,
+ "text": "generators."
+ },
+ {
+ "start": 2153.32,
+ "duration": 0.0,
+ "text": "generators. So<00:35:54.000> um<00:35:54.359> I<00:35:54.400> think<00:35:54.760> uh<00:35:54.880> Andrew<00:35:55.480> uh<00:35:55.840> right,"
+ },
+ {
+ "start": 2156.51,
+ "duration": 0.0,
+ "text": "So um I think uh Andrew uh right,"
+ },
+ {
+ "start": 2156.52,
+ "duration": 0.0,
+ "text": "So um I think uh Andrew uh right, alluded<00:35:57.080> and<00:35:57.400> you<00:35:57.440> know,<00:35:57.560> a<00:35:57.600> definition<00:35:58.080> is<00:35:58.400> or"
+ },
+ {
+ "start": 2158.59,
+ "duration": 0.0,
+ "text": "alluded and you know, a definition is or"
+ },
+ {
+ "start": 2158.6,
+ "duration": 0.0,
+ "text": "alluded and you know, a definition is or yeah,<00:35:59.280> uh<00:35:59.359> let's<00:35:59.560> see.<00:35:59.800> Um<00:36:00.440> right,<00:36:00.640> so<00:36:00.920> just"
+ },
+ {
+ "start": 2161.19,
+ "duration": 0.0,
+ "text": "yeah, uh let's see. Um right, so just"
+ },
+ {
+ "start": 2161.2,
+ "duration": 0.0,
+ "text": "yeah, uh let's see. Um right, so just just<00:36:01.480> reiterating<00:36:02.200> um<00:36:02.880> uh"
+ },
+ {
+ "start": 2163.43,
+ "duration": 0.0,
+ "text": "just reiterating um uh"
+ },
+ {
+ "start": 2163.44,
+ "duration": 0.0,
+ "text": "just reiterating um uh that<00:36:03.760> you<00:36:03.880> can<00:36:04.120> define<00:36:04.960> a<00:36:05.600> pseudo-random<00:36:06.520> a"
+ },
+ {
+ "start": 2166.55,
+ "duration": 0.0,
+ "text": "that you can define a pseudo-random a"
+ },
+ {
+ "start": 2166.56,
+ "duration": 0.0,
+ "text": "that you can define a pseudo-random a generator<00:36:07.520> um<00:36:07.760> in<00:36:07.840> terms<00:36:08.080> of<00:36:08.200> there's<00:36:08.359> no"
+ },
+ {
+ "start": 2168.51,
+ "duration": 0.0,
+ "text": "generator um in terms of there's no"
+ },
+ {
+ "start": 2168.52,
+ "duration": 0.0,
+ "text": "generator um in terms of there's no polynomial<00:36:09.040> size<00:36:09.359> circuit<00:36:10.280> this"
+ },
+ {
+ "start": 2170.43,
+ "duration": 0.0,
+ "text": "polynomial size circuit this"
+ },
+ {
+ "start": 2170.44,
+ "duration": 0.0,
+ "text": "polynomial size circuit this discriminator<00:36:11.000> D<00:36:11.240> that<00:36:11.440> can<00:36:11.560> distinguish<00:36:11.960> the"
+ },
+ {
+ "start": 2172.03,
+ "duration": 0.0,
+ "text": "discriminator D that can distinguish the"
+ },
+ {
+ "start": 2172.04,
+ "duration": 0.0,
+ "text": "discriminator D that can distinguish the output<00:36:12.280> sequence<00:36:12.720> from<00:36:12.880> random"
+ },
+ {
+ "start": 2173.27,
+ "duration": 0.0,
+ "text": "output sequence from random"
+ },
+ {
+ "start": 2173.28,
+ "duration": 0.0,
+ "text": "output sequence from random substantially<00:36:13.800> better<00:36:14.560> than<00:36:15.120> random<00:36:15.440> chance."
+ },
+ {
+ "start": 2176.31,
+ "duration": 0.0,
+ "text": "substantially better than random chance."
+ },
+ {
+ "start": 2176.32,
+ "duration": 0.0,
+ "text": "substantially better than random chance. So<00:36:16.400> here<00:36:16.760> is<00:36:17.000> this<00:36:17.480> D,<00:36:18.080> here<00:36:18.320> is<00:36:18.520> this"
+ },
+ {
+ "start": 2178.71,
+ "duration": 0.0,
+ "text": "So here is this D, here is this"
+ },
+ {
+ "start": 2178.72,
+ "duration": 0.0,
+ "text": "So here is this D, here is this generator<00:36:19.160> G<00:36:19.840> on<00:36:20.120> input<00:36:20.480> seed,<00:36:20.920> and<00:36:21.040> then<00:36:21.160> here"
+ },
+ {
+ "start": 2181.31,
+ "duration": 0.0,
+ "text": "generator G on input seed, and then here"
+ },
+ {
+ "start": 2181.32,
+ "duration": 0.0,
+ "text": "generator G on input seed, and then here is<00:36:21.480> just<00:36:21.920> um<00:36:22.600> uh<00:36:22.800> uniform<00:36:23.280> random.<00:36:24.000> And<00:36:24.120> the"
+ },
+ {
+ "start": 2184.19,
+ "duration": 0.0,
+ "text": "is just um uh uniform random. And the"
+ },
+ {
+ "start": 2184.2,
+ "duration": 0.0,
+ "text": "is just um uh uniform random. And the point<00:36:24.520> is<00:36:24.760> that"
+ },
+ {
+ "start": 2185.83,
+ "duration": 0.0,
+ "text": "point is that"
+ },
+ {
+ "start": 2185.84,
+ "duration": 0.0,
+ "text": "point is that our<00:36:26.160> distinguisher,<00:36:27.280> the<00:36:27.720> uh<00:36:27.880> the<00:36:27.960> difference"
+ },
+ {
+ "start": 2188.31,
+ "duration": 0.0,
+ "text": "our distinguisher, the uh the difference"
+ },
+ {
+ "start": 2188.32,
+ "duration": 0.0,
+ "text": "our distinguisher, the uh the difference in<00:36:28.359> those<00:36:28.520> probabilities,<00:36:29.560> is<00:36:30.440> um<00:36:30.800> is"
+ },
+ {
+ "start": 2190.91,
+ "duration": 0.0,
+ "text": "in those probabilities, is um is"
+ },
+ {
+ "start": 2190.92,
+ "duration": 0.0,
+ "text": "in those probabilities, is um is actually<00:36:31.240> a<00:36:31.280> negligible<00:36:31.800> function,<00:36:32.359> so<00:36:32.480> it"
+ },
+ {
+ "start": 2192.55,
+ "duration": 0.0,
+ "text": "actually a negligible function, so it"
+ },
+ {
+ "start": 2192.56,
+ "duration": 0.0,
+ "text": "actually a negligible function, so it decays<00:36:32.880> faster<00:36:33.320> than<00:36:33.960> uh<00:36:34.080> one<00:36:34.320> over<00:36:34.560> any"
+ },
+ {
+ "start": 2194.91,
+ "duration": 0.0,
+ "text": "decays faster than uh one over any"
+ },
+ {
+ "start": 2194.92,
+ "duration": 0.0,
+ "text": "decays faster than uh one over any polynomial."
+ },
+ {
+ "start": 2196.23,
+ "duration": 0.0,
+ "text": "polynomial."
+ },
+ {
+ "start": 2196.24,
+ "duration": 0.0,
+ "text": "polynomial. This<00:36:36.359> is<00:36:36.440> epsilon."
+ },
+ {
+ "start": 2197.67,
+ "duration": 0.0,
+ "text": "This is epsilon."
+ },
+ {
+ "start": 2197.68,
+ "duration": 0.0,
+ "text": "This is epsilon. Uh<00:36:38.400> and<00:36:39.040> what<00:36:39.200> we<00:36:39.320> can<00:36:39.480> show<00:36:40.120> is<00:36:40.440> that<00:36:40.640> these"
+ },
+ {
+ "start": 2200.95,
+ "duration": 0.0,
+ "text": "Uh and what we can show is that these"
+ },
+ {
+ "start": 2200.96,
+ "duration": 0.0,
+ "text": "Uh and what we can show is that these PRGs"
+ },
+ {
+ "start": 2202.43,
+ "duration": 0.0,
+ "text": "PRGs"
+ },
+ {
+ "start": 2202.44,
+ "duration": 0.0,
+ "text": "PRGs have"
+ },
+ {
+ "start": 2204.27,
+ "duration": 0.0,
+ "text": "have"
+ },
+ {
+ "start": 2204.28,
+ "duration": 0.0,
+ "text": "have large<00:36:45.160> time-bounded<00:36:46.160> entropy"
+ },
+ {
+ "start": 2207.47,
+ "duration": 0.0,
+ "text": "large time-bounded entropy"
+ },
+ {
+ "start": 2207.48,
+ "duration": 0.0,
+ "text": "large time-bounded entropy um<00:36:48.200> and<00:36:48.359> low<00:36:48.520> epi-plexity,<00:36:49.320> but<00:36:49.480> large"
+ },
+ {
+ "start": 2209.95,
+ "duration": 0.0,
+ "text": "um and low epi-plexity, but large"
+ },
+ {
+ "start": 2209.96,
+ "duration": 0.0,
+ "text": "um and low epi-plexity, but large time-bounded<00:36:50.359> entropy<00:36:50.840> in<00:36:50.960> contrast<00:36:51.840> with"
+ },
+ {
+ "start": 2213.27,
+ "duration": 0.0,
+ "text": "time-bounded entropy in contrast with"
+ },
+ {
+ "start": 2213.28,
+ "duration": 0.0,
+ "text": "time-bounded entropy in contrast with Kolmogorov<00:36:53.680> complexity,<00:36:54.480> in<00:36:54.600> contrast<00:36:55.120> with"
+ },
+ {
+ "start": 2215.99,
+ "duration": 0.0,
+ "text": "Kolmogorov complexity, in contrast with"
+ },
+ {
+ "start": 2216.0,
+ "duration": 0.0,
+ "text": "Kolmogorov complexity, in contrast with uh<00:36:56.160> Shannon<00:36:56.440> information,<00:36:56.960> or<00:36:57.080> even"
+ },
+ {
+ "start": 2217.31,
+ "duration": 0.0,
+ "text": "uh Shannon information, or even"
+ },
+ {
+ "start": 2217.32,
+ "duration": 0.0,
+ "text": "uh Shannon information, or even time-bounded<00:36:58.400> Kolmogorov<00:36:58.760> complexity.<00:36:59.760> Um"
+ },
+ {
+ "start": 2219.91,
+ "duration": 0.0,
+ "text": "time-bounded Kolmogorov complexity. Um"
+ },
+ {
+ "start": 2219.92,
+ "duration": 0.0,
+ "text": "time-bounded Kolmogorov complexity. Um where<00:37:00.120> actually<00:37:00.640> that<00:37:01.120> this<00:37:01.720> time-bounded"
+ },
+ {
+ "start": 2222.11,
+ "duration": 0.0,
+ "text": "where actually that this time-bounded"
+ },
+ {
+ "start": 2222.12,
+ "duration": 0.0,
+ "text": "where actually that this time-bounded entropy<00:37:02.480> is<00:37:02.640> nearly<00:37:03.000> maximum."
+ },
+ {
+ "start": 2224.75,
+ "duration": 0.0,
+ "text": "entropy is nearly maximum."
+ },
+ {
+ "start": 2224.76,
+ "duration": 0.0,
+ "text": "entropy is nearly maximum. Um<00:37:05.160> again,<00:37:05.440> with<00:37:05.560> this<00:37:05.720> epsilon<00:37:06.080> related<00:37:06.359> to"
+ },
+ {
+ "start": 2226.43,
+ "duration": 0.0,
+ "text": "Um again, with this epsilon related to"
+ },
+ {
+ "start": 2226.44,
+ "duration": 0.0,
+ "text": "Um again, with this epsilon related to this<00:37:06.640> advantage."
+ },
+ {
+ "start": 2228.349,
+ "duration": 0.0,
+ "text": "this advantage."
+ },
+ {
+ "start": 2228.359,
+ "duration": 0.0,
+ "text": "this advantage. So<00:37:08.480> then<00:37:08.880> also<00:37:09.440> here<00:37:10.080> uh"
+ },
+ {
+ "start": 2230.79,
+ "duration": 0.0,
+ "text": "So then also here uh"
+ },
+ {
+ "start": 2230.8,
+ "duration": 0.0,
+ "text": "So then also here uh we'll<00:37:10.960> go<00:37:11.320> So<00:37:11.480> this<00:37:11.640> is<00:37:11.760> an<00:37:11.840> example<00:37:12.240> where"
+ },
+ {
+ "start": 2233.23,
+ "duration": 0.0,
+ "text": "we'll go So this is an example where"
+ },
+ {
+ "start": 2233.24,
+ "duration": 0.0,
+ "text": "we'll go So this is an example where through<00:37:14.200> computation,<00:37:15.080> we<00:37:15.359> are<00:37:15.560> able<00:37:15.800> to"
+ },
+ {
+ "start": 2235.87,
+ "duration": 0.0,
+ "text": "through computation, we are able to"
+ },
+ {
+ "start": 2235.88,
+ "duration": 0.0,
+ "text": "through computation, we are able to produce<00:37:16.200> time-bounded<00:37:16.720> entropy,<00:37:17.440> right?"
+ },
+ {
+ "start": 2237.67,
+ "duration": 0.0,
+ "text": "produce time-bounded entropy, right?"
+ },
+ {
+ "start": 2237.68,
+ "duration": 0.0,
+ "text": "produce time-bounded entropy, right? Taking<00:37:18.000> the<00:37:18.080> initial<00:37:18.520> what<00:37:18.640> we<00:37:18.760> had,<00:37:19.200> this<00:37:19.400> K"
+ },
+ {
+ "start": 2239.95,
+ "duration": 0.0,
+ "text": "Taking the initial what we had, this K"
+ },
+ {
+ "start": 2239.96,
+ "duration": 0.0,
+ "text": "Taking the initial what we had, this K from<00:37:20.200> just<00:37:20.400> the<00:37:20.480> size<00:37:20.760> of<00:37:20.800> the<00:37:20.880> seed,<00:37:21.720> and"
+ },
+ {
+ "start": 2241.83,
+ "duration": 0.0,
+ "text": "from just the size of the seed, and"
+ },
+ {
+ "start": 2241.84,
+ "duration": 0.0,
+ "text": "from just the size of the seed, and turning<00:37:22.120> it<00:37:22.240> into<00:37:22.800> something<00:37:23.120> very<00:37:23.320> close<00:37:23.520> to"
+ },
+ {
+ "start": 2243.63,
+ "duration": 0.0,
+ "text": "turning it into something very close to"
+ },
+ {
+ "start": 2243.64,
+ "duration": 0.0,
+ "text": "turning it into something very close to N."
+ },
+ {
+ "start": 2245.23,
+ "duration": 0.0,
+ "text": "N."
+ },
+ {
+ "start": 2245.24,
+ "duration": 0.0,
+ "text": "N. But"
+ },
+ {
+ "start": 2246.19,
+ "duration": 0.0,
+ "text": "But"
+ },
+ {
+ "start": 2246.2,
+ "duration": 0.0,
+ "text": "But what<00:37:26.359> we<00:37:26.480> would<00:37:26.600> really<00:37:26.840> like<00:37:27.800> is<00:37:28.560> something"
+ },
+ {
+ "start": 2249.07,
+ "duration": 0.0,
+ "text": "what we would really like is something"
+ },
+ {
+ "start": 2249.08,
+ "duration": 0.0,
+ "text": "what we would really like is something that<00:37:29.280> can<00:37:29.400> create<00:37:30.120> structured<00:37:31.320> information,"
+ },
+ {
+ "start": 2251.87,
+ "duration": 0.0,
+ "text": "that can create structured information,"
+ },
+ {
+ "start": 2251.88,
+ "duration": 0.0,
+ "text": "that can create structured information, something<00:37:32.160> that<00:37:32.280> can<00:37:32.400> create<00:37:32.680> epi-plexity."
+ },
+ {
+ "start": 2253.79,
+ "duration": 0.0,
+ "text": "something that can create epi-plexity."
+ },
+ {
+ "start": 2253.8,
+ "duration": 0.0,
+ "text": "something that can create epi-plexity. That's<00:37:34.000> a<00:37:34.280> a<00:37:34.320> harder<00:37:34.560> beast,<00:37:34.880> but<00:37:35.440> we<00:37:35.600> can<00:37:35.840> at"
+ },
+ {
+ "start": 2255.95,
+ "duration": 0.0,
+ "text": "That's a a harder beast, but we can at"
+ },
+ {
+ "start": 2255.96,
+ "duration": 0.0,
+ "text": "That's a a harder beast, but we can at least<00:37:36.880> um"
+ },
+ {
+ "start": 2257.67,
+ "duration": 0.0,
+ "text": "least um"
+ },
+ {
+ "start": 2257.68,
+ "duration": 0.0,
+ "text": "least um turn<00:37:38.080> to<00:37:39.040> uh<00:37:39.240> some<00:37:40.160> uh<00:37:40.320> already<00:37:40.600> studied"
+ },
+ {
+ "start": 2260.91,
+ "duration": 0.0,
+ "text": "turn to uh some uh already studied"
+ },
+ {
+ "start": 2260.92,
+ "duration": 0.0,
+ "text": "turn to uh some uh already studied examples<00:37:41.520> like<00:37:42.120> cellular<00:37:42.440> automaton."
+ },
+ {
+ "start": 2263.87,
+ "duration": 0.0,
+ "text": "examples like cellular automaton."
+ },
+ {
+ "start": 2263.88,
+ "duration": 0.0,
+ "text": "examples like cellular automaton. So<00:37:44.080> here<00:37:44.480> are<00:37:44.600> these<00:37:45.280> rule<00:37:45.840> 15,<00:37:46.359> rule<00:37:46.520> 30,<00:37:46.880> and"
+ },
+ {
+ "start": 2267.03,
+ "duration": 0.0,
+ "text": "So here are these rule 15, rule 30, and"
+ },
+ {
+ "start": 2267.04,
+ "duration": 0.0,
+ "text": "So here are these rule 15, rule 30, and rule<00:37:47.200> 54"
+ },
+ {
+ "start": 2268.39,
+ "duration": 0.0,
+ "text": "rule 54"
+ },
+ {
+ "start": 2268.4,
+ "duration": 0.0,
+ "text": "rule 54 um<00:37:48.640> cellular<00:37:48.920> automaton<00:37:49.920> from<00:37:50.280> random"
+ },
+ {
+ "start": 2270.55,
+ "duration": 0.0,
+ "text": "um cellular automaton from random"
+ },
+ {
+ "start": 2270.56,
+ "duration": 0.0,
+ "text": "um cellular automaton from random initial<00:37:50.840> conditions<00:37:51.280> with<00:37:51.400> a<00:37:51.440> fixed<00:37:51.760> width"
+ },
+ {
+ "start": 2273.349,
+ "duration": 0.0,
+ "text": "initial conditions with a fixed width"
+ },
+ {
+ "start": 2273.359,
+ "duration": 0.0,
+ "text": "initial conditions with a fixed width with<00:37:53.560> time<00:37:53.800> going<00:37:54.040> down.<00:37:54.800> Uh<00:37:54.880> of<00:37:55.000> course,<00:37:55.240> the"
+ },
+ {
+ "start": 2275.31,
+ "duration": 0.0,
+ "text": "with time going down. Uh of course, the"
+ },
+ {
+ "start": 2275.32,
+ "duration": 0.0,
+ "text": "with time going down. Uh of course, the rule<00:37:55.520> 15,<00:37:56.080> as<00:37:56.200> Andrew<00:37:56.359> mentioned,<00:37:56.680> right,<00:37:56.840> is"
+ },
+ {
+ "start": 2276.95,
+ "duration": 0.0,
+ "text": "rule 15, as Andrew mentioned, right, is"
+ },
+ {
+ "start": 2276.96,
+ "duration": 0.0,
+ "text": "rule 15, as Andrew mentioned, right, is this<00:37:57.160> is<00:37:57.400> very<00:37:57.920> um<00:37:58.520> very<00:37:58.720> very<00:37:58.960> boring<00:37:59.400> and<00:37:59.680> and"
+ },
+ {
+ "start": 2279.79,
+ "duration": 0.0,
+ "text": "this is very um very very boring and and"
+ },
+ {
+ "start": 2279.8,
+ "duration": 0.0,
+ "text": "this is very um very very boring and and just<00:38:00.280> uh<00:38:00.320> predictable.<00:38:01.000> Um<00:38:01.440> rule<00:38:01.640> 30<00:38:02.040> is"
+ },
+ {
+ "start": 2282.51,
+ "duration": 0.0,
+ "text": "just uh predictable. Um rule 30 is"
+ },
+ {
+ "start": 2282.52,
+ "duration": 0.0,
+ "text": "just uh predictable. Um rule 30 is essentially<00:38:03.440> uh<00:38:03.560> is<00:38:03.760> very<00:38:04.040> hard<00:38:04.280> to<00:38:04.359> predict"
+ },
+ {
+ "start": 2285.03,
+ "duration": 0.0,
+ "text": "essentially uh is very hard to predict"
+ },
+ {
+ "start": 2285.04,
+ "duration": 0.0,
+ "text": "essentially uh is very hard to predict um<00:38:05.280> the<00:38:05.480> the<00:38:05.640> output<00:38:05.920> state,<00:38:06.280> right?<00:38:06.440> It's"
+ },
+ {
+ "start": 2286.55,
+ "duration": 0.0,
+ "text": "um the the output state, right? It's"
+ },
+ {
+ "start": 2286.56,
+ "duration": 0.0,
+ "text": "um the the output state, right? It's seemingly<00:38:06.960> random.<00:38:07.520> And<00:38:07.680> rule<00:38:07.800> 54<00:38:08.440> is<00:38:08.560> instead"
+ },
+ {
+ "start": 2289.11,
+ "duration": 0.0,
+ "text": "seemingly random. And rule 54 is instead"
+ },
+ {
+ "start": 2289.12,
+ "duration": 0.0,
+ "text": "seemingly random. And rule 54 is instead some<00:38:09.800> interesting<00:38:10.560> situation<00:38:11.000> in<00:38:11.080> between"
+ },
+ {
+ "start": 2291.59,
+ "duration": 0.0,
+ "text": "some interesting situation in between"
+ },
+ {
+ "start": 2291.6,
+ "duration": 0.0,
+ "text": "some interesting situation in between where<00:38:11.720> there's<00:38:11.920> all<00:38:12.040> this<00:38:12.760> both<00:38:12.960> structure"
+ },
+ {
+ "start": 2293.349,
+ "duration": 0.0,
+ "text": "where there's all this both structure"
+ },
+ {
+ "start": 2293.359,
+ "duration": 0.0,
+ "text": "where there's all this both structure and<00:38:13.520> randomness."
+ },
+ {
+ "start": 2295.27,
+ "duration": 0.0,
+ "text": "and randomness."
+ },
+ {
+ "start": 2295.28,
+ "duration": 0.0,
+ "text": "and randomness. So<00:38:15.400> applying<00:38:15.800> this<00:38:16.000> setup<00:38:16.920> to<00:38:18.040> um<00:38:18.560> what<00:38:18.720> we"
+ },
+ {
+ "start": 2298.83,
+ "duration": 0.0,
+ "text": "So applying this setup to um what we"
+ },
+ {
+ "start": 2298.84,
+ "duration": 0.0,
+ "text": "So applying this setup to um what we have<00:38:19.680> uh<00:38:20.240> with<00:38:20.359> these<00:38:20.520> cellular<00:38:20.720> automaton"
+ },
+ {
+ "start": 2301.43,
+ "duration": 0.0,
+ "text": "have uh with these cellular automaton"
+ },
+ {
+ "start": 2301.44,
+ "duration": 0.0,
+ "text": "have uh with these cellular automaton where<00:38:21.760> we<00:38:21.920> are<00:38:22.040> trying<00:38:22.359> to<00:38:22.480> predict<00:38:23.120> the<00:38:23.240> final"
+ },
+ {
+ "start": 2303.63,
+ "duration": 0.0,
+ "text": "where we are trying to predict the final"
+ },
+ {
+ "start": 2303.64,
+ "duration": 0.0,
+ "text": "where we are trying to predict the final row<00:38:24.120> from<00:38:24.320> the<00:38:24.400> initial<00:38:24.760> row,"
+ },
+ {
+ "start": 2305.75,
+ "duration": 0.0,
+ "text": "row from the initial row,"
+ },
+ {
+ "start": 2305.76,
+ "duration": 0.0,
+ "text": "row from the initial row, what<00:38:25.800> we<00:38:25.960> find<00:38:27.160> is<00:38:28.000> So<00:38:28.160> first<00:38:28.440> of<00:38:28.520> all,<00:38:28.640> here<00:38:28.840> is"
+ },
+ {
+ "start": 2308.95,
+ "duration": 0.0,
+ "text": "what we find is So first of all, here is"
+ },
+ {
+ "start": 2308.96,
+ "duration": 0.0,
+ "text": "what we find is So first of all, here is this<00:38:29.120> curve<00:38:29.920> on<00:38:30.040> the<00:38:30.120> left<00:38:30.840> with<00:38:31.000> this<00:38:31.160> total"
+ },
+ {
+ "start": 2311.39,
+ "duration": 0.0,
+ "text": "this curve on the left with this total"
+ },
+ {
+ "start": 2311.4,
+ "duration": 0.0,
+ "text": "this curve on the left with this total description<00:38:31.800> length<00:38:32.240> as<00:38:32.359> a<00:38:32.440> function<00:38:32.760> of"
+ },
+ {
+ "start": 2312.83,
+ "duration": 0.0,
+ "text": "description length as a function of"
+ },
+ {
+ "start": 2312.84,
+ "duration": 0.0,
+ "text": "description length as a function of compute."
+ },
+ {
+ "start": 2314.03,
+ "duration": 0.0,
+ "text": "compute."
+ },
+ {
+ "start": 2314.04,
+ "duration": 0.0,
+ "text": "compute. For<00:38:34.160> rule<00:38:34.359> 30,<00:38:34.800> we<00:38:34.960> make<00:38:35.160> no<00:38:35.280> progress."
+ },
+ {
+ "start": 2316.71,
+ "duration": 0.0,
+ "text": "For rule 30, we make no progress."
+ },
+ {
+ "start": 2316.72,
+ "duration": 0.0,
+ "text": "For rule 30, we make no progress. We<00:38:37.320> are<00:38:37.440> not<00:38:37.720> able<00:38:37.960> to<00:38:38.080> do<00:38:38.280> predictions<00:38:39.160> better"
+ },
+ {
+ "start": 2319.59,
+ "duration": 0.0,
+ "text": "We are not able to do predictions better"
+ },
+ {
+ "start": 2319.6,
+ "duration": 0.0,
+ "text": "We are not able to do predictions better than<00:38:39.760> random<00:38:40.000> chance."
+ },
+ {
+ "start": 2321.03,
+ "duration": 0.0,
+ "text": "than random chance."
+ },
+ {
+ "start": 2321.04,
+ "duration": 0.0,
+ "text": "than random chance. So<00:38:41.359> as<00:38:41.520> the<00:38:41.600> total<00:38:41.800> description<00:38:42.160> length<00:38:42.440> is"
+ },
+ {
+ "start": 2322.63,
+ "duration": 0.0,
+ "text": "So as the total description length is"
+ },
+ {
+ "start": 2322.64,
+ "duration": 0.0,
+ "text": "So as the total description length is just<00:38:43.040> um<00:38:43.440> right,<00:38:44.080> uh<00:38:44.480> the<00:38:45.160> the<00:38:45.280> the<00:38:45.480> total"
+ },
+ {
+ "start": 2325.75,
+ "duration": 0.0,
+ "text": "just um right, uh the the the total"
+ },
+ {
+ "start": 2325.76,
+ "duration": 0.0,
+ "text": "just um right, uh the the the total number<00:38:46.000> of<00:38:46.359> um"
+ },
+ {
+ "start": 2326.99,
+ "duration": 0.0,
+ "text": "number of um"
+ },
+ {
+ "start": 2327.0,
+ "duration": 0.0,
+ "text": "number of um uh<00:38:47.320> bits<00:38:47.520> that<00:38:47.600> we<00:38:47.680> need<00:38:47.800> to<00:38:48.000> output."
+ },
+ {
+ "start": 2328.91,
+ "duration": 0.0,
+ "text": "uh bits that we need to output."
+ },
+ {
+ "start": 2328.92,
+ "duration": 0.0,
+ "text": "uh bits that we need to output. Uh<00:38:49.280> and"
+ },
+ {
+ "start": 2331.19,
+ "duration": 0.0,
+ "text": "Uh and"
+ },
+ {
+ "start": 2331.2,
+ "duration": 0.0,
+ "text": "Uh and for<00:38:51.400> rule<00:38:51.760> 15,<00:38:52.240> we<00:38:52.359> very<00:38:52.560> quickly<00:38:52.840> make"
+ },
+ {
+ "start": 2332.99,
+ "duration": 0.0,
+ "text": "for rule 15, we very quickly make"
+ },
+ {
+ "start": 2333.0,
+ "duration": 0.0,
+ "text": "for rule 15, we very quickly make progress,"
+ },
+ {
+ "start": 2334.07,
+ "duration": 0.0,
+ "text": "progress,"
+ },
+ {
+ "start": 2334.08,
+ "duration": 0.0,
+ "text": "progress, but<00:38:54.800> now<00:38:55.280> we<00:38:55.400> have<00:38:55.520> perfect<00:38:55.840> predictions."
+ },
+ {
+ "start": 2336.71,
+ "duration": 0.0,
+ "text": "but now we have perfect predictions."
+ },
+ {
+ "start": 2336.72,
+ "duration": 0.0,
+ "text": "but now we have perfect predictions. There's<00:38:56.840> no<00:38:56.960> more<00:38:57.080> learning<00:38:57.320> to<00:38:57.440> do.<00:38:58.160> Whereas"
+ },
+ {
+ "start": 2338.39,
+ "duration": 0.0,
+ "text": "There's no more learning to do. Whereas"
+ },
+ {
+ "start": 2338.4,
+ "duration": 0.0,
+ "text": "There's no more learning to do. Whereas for<00:38:58.480> rule<00:38:58.640> 54,<00:38:59.080> we<00:38:59.200> continue<00:38:59.840> to<00:38:59.960> make"
+ },
+ {
+ "start": 2340.19,
+ "duration": 0.0,
+ "text": "for rule 54, we continue to make"
+ },
+ {
+ "start": 2340.2,
+ "duration": 0.0,
+ "text": "for rule 54, we continue to make progress<00:39:00.920> proving<00:39:01.240> predictions<00:39:01.840> as<00:39:01.960> we<00:39:02.080> spend"
+ },
+ {
+ "start": 2342.47,
+ "duration": 0.0,
+ "text": "progress proving predictions as we spend"
+ },
+ {
+ "start": 2342.48,
+ "duration": 0.0,
+ "text": "progress proving predictions as we spend additional<00:39:02.840> compute."
+ },
+ {
+ "start": 2344.59,
+ "duration": 0.0,
+ "text": "additional compute."
+ },
+ {
+ "start": 2344.6,
+ "duration": 0.0,
+ "text": "additional compute. And<00:39:04.680> so<00:39:05.080> in<00:39:05.200> terms<00:39:05.440> of<00:39:05.560> epi-plexity<00:39:06.240> and"
+ },
+ {
+ "start": 2346.47,
+ "duration": 0.0,
+ "text": "And so in terms of epi-plexity and"
+ },
+ {
+ "start": 2346.48,
+ "duration": 0.0,
+ "text": "And so in terms of epi-plexity and time-bounded<00:39:06.880> entropy,<00:39:07.280> we<00:39:07.440> see<00:39:07.560> that<00:39:07.760> in"
+ },
+ {
+ "start": 2347.83,
+ "duration": 0.0,
+ "text": "time-bounded entropy, we see that in"
+ },
+ {
+ "start": 2347.84,
+ "duration": 0.0,
+ "text": "time-bounded entropy, we see that in these<00:39:07.960> two<00:39:08.080> curves."
+ },
+ {
+ "start": 2349.15,
+ "duration": 0.0,
+ "text": "these two curves."
+ },
+ {
+ "start": 2349.16,
+ "duration": 0.0,
+ "text": "these two curves. The<00:39:09.280> time<00:39:09.640> the<00:39:09.840> epi-plexity<00:39:11.000> continues<00:39:11.400> to"
+ },
+ {
+ "start": 2351.47,
+ "duration": 0.0,
+ "text": "The time the epi-plexity continues to"
+ },
+ {
+ "start": 2351.48,
+ "duration": 0.0,
+ "text": "The time the epi-plexity continues to increase<00:39:12.440> as<00:39:12.600> we<00:39:12.720> spend<00:39:13.320> additional<00:39:13.720> compute"
+ },
+ {
+ "start": 2354.349,
+ "duration": 0.0,
+ "text": "increase as we spend additional compute"
+ },
+ {
+ "start": 2354.359,
+ "duration": 0.0,
+ "text": "increase as we spend additional compute on<00:39:14.480> this<00:39:14.600> learning<00:39:14.840> task,"
+ },
+ {
+ "start": 2355.95,
+ "duration": 0.0,
+ "text": "on this learning task,"
+ },
+ {
+ "start": 2355.96,
+ "duration": 0.0,
+ "text": "on this learning task, um<00:39:16.520> the<00:39:16.680> conditional<00:39:17.240> one,<00:39:17.520> you<00:39:17.600> know,<00:39:17.680> Y"
+ },
+ {
+ "start": 2357.87,
+ "duration": 0.0,
+ "text": "um the conditional one, you know, Y"
+ },
+ {
+ "start": 2357.88,
+ "duration": 0.0,
+ "text": "um the conditional one, you know, Y given<00:39:18.120> X,<00:39:18.640> the<00:39:18.680> final<00:39:18.920> row<00:39:19.080> given<00:39:19.280> the<00:39:19.320> initial"
+ },
+ {
+ "start": 2359.63,
+ "duration": 0.0,
+ "text": "given X, the final row given the initial"
+ },
+ {
+ "start": 2359.64,
+ "duration": 0.0,
+ "text": "given X, the final row given the initial row,"
+ },
+ {
+ "start": 2360.47,
+ "duration": 0.0,
+ "text": "row,"
+ },
+ {
+ "start": 2360.48,
+ "duration": 0.0,
+ "text": "row, and<00:39:20.640> then<00:39:20.760> the<00:39:20.840> time-bounded<00:39:21.320> entropy"
+ },
+ {
+ "start": 2361.79,
+ "duration": 0.0,
+ "text": "and then the time-bounded entropy"
+ },
+ {
+ "start": 2361.8,
+ "duration": 0.0,
+ "text": "and then the time-bounded entropy decreases."
+ },
+ {
+ "start": 2363.43,
+ "duration": 0.0,
+ "text": "decreases."
+ },
+ {
+ "start": 2363.44,
+ "duration": 0.0,
+ "text": "decreases. But<00:39:23.640> again,"
+ },
+ {
+ "start": 2364.67,
+ "duration": 0.0,
+ "text": "But again,"
+ },
+ {
+ "start": 2364.68,
+ "duration": 0.0,
+ "text": "But again, for<00:39:25.040> rule<00:39:25.240> 30<00:39:25.600> and<00:39:25.720> rule<00:39:25.840> 15,<00:39:26.680> we<00:39:26.760> do<00:39:26.880> not<00:39:27.120> see"
+ },
+ {
+ "start": 2367.27,
+ "duration": 0.0,
+ "text": "for rule 30 and rule 15, we do not see"
+ },
+ {
+ "start": 2367.28,
+ "duration": 0.0,
+ "text": "for rule 30 and rule 15, we do not see this<00:39:27.440> increase<00:39:28.120> in<00:39:28.680> epi-plexity.<00:39:29.920> And<00:39:30.080> so"
+ },
+ {
+ "start": 2370.47,
+ "duration": 0.0,
+ "text": "this increase in epi-plexity. And so"
+ },
+ {
+ "start": 2370.48,
+ "duration": 0.0,
+ "text": "this increase in epi-plexity. And so this<00:39:30.680> is,<00:39:31.440> you<00:39:31.480> know,<00:39:32.000> nicely<00:39:32.720> separating<00:39:33.960> uh"
+ },
+ {
+ "start": 2374.39,
+ "duration": 0.0,
+ "text": "this is, you know, nicely separating uh"
+ },
+ {
+ "start": 2374.4,
+ "duration": 0.0,
+ "text": "this is, you know, nicely separating uh these<00:39:35.280> uh<00:39:35.560> these<00:39:35.800> these<00:39:36.480> different"
+ },
+ {
+ "start": 2376.75,
+ "duration": 0.0,
+ "text": "these uh these these different"
+ },
+ {
+ "start": 2376.76,
+ "duration": 0.0,
+ "text": "these uh these these different classifications<00:39:37.600> of<00:39:37.840> these<00:39:38.480> cellular"
+ },
+ {
+ "start": 2378.67,
+ "duration": 0.0,
+ "text": "classifications of these cellular"
+ },
+ {
+ "start": 2378.68,
+ "duration": 0.0,
+ "text": "classifications of these cellular automaton<00:39:39.440> with<00:39:39.640> rule<00:39:39.760> 54<00:39:40.280> being<00:39:40.480> in<00:39:40.560> its<00:39:40.840> its"
+ },
+ {
+ "start": 2381.03,
+ "duration": 0.0,
+ "text": "automaton with rule 54 being in its its"
+ },
+ {
+ "start": 2381.04,
+ "duration": 0.0,
+ "text": "automaton with rule 54 being in its its own<00:39:41.160> category,<00:39:41.600> rule<00:39:41.760> 30<00:39:42.000> being<00:39:42.160> in<00:39:42.200> a"
+ },
+ {
+ "start": 2382.27,
+ "duration": 0.0,
+ "text": "own category, rule 30 being in a"
+ },
+ {
+ "start": 2382.28,
+ "duration": 0.0,
+ "text": "own category, rule 30 being in a different<00:39:42.520> category.<00:39:42.880> We're<00:39:43.080> able<00:39:43.240> to<00:39:43.320> nicely"
+ },
+ {
+ "start": 2383.59,
+ "duration": 0.0,
+ "text": "different category. We're able to nicely"
+ },
+ {
+ "start": 2383.6,
+ "duration": 0.0,
+ "text": "different category. We're able to nicely separate<00:39:43.960> these<00:39:44.560> with<00:39:45.200> looking<00:39:45.640> at"
+ },
+ {
+ "start": 2385.87,
+ "duration": 0.0,
+ "text": "separate these with looking at"
+ },
+ {
+ "start": 2385.88,
+ "duration": 0.0,
+ "text": "separate these with looking at perplexity"
+ },
+ {
+ "start": 2387.15,
+ "duration": 0.0,
+ "text": "perplexity"
+ },
+ {
+ "start": 2387.16,
+ "duration": 0.0,
+ "text": "perplexity and<00:39:47.320> seeing<00:39:47.560> how"
+ },
+ {
+ "start": 2388.47,
+ "duration": 0.0,
+ "text": "and seeing how"
+ },
+ {
+ "start": 2388.48,
+ "duration": 0.0,
+ "text": "and seeing how as<00:39:48.600> we<00:39:48.680> spend<00:39:48.880> additional<00:39:49.200> compute,<00:39:50.040> um"
+ },
+ {
+ "start": 2390.67,
+ "duration": 0.0,
+ "text": "as we spend additional compute, um"
+ },
+ {
+ "start": 2390.68,
+ "duration": 0.0,
+ "text": "as we spend additional compute, um the<00:39:50.800> perplexity<00:39:51.440> increases."
+ },
+ {
+ "start": 2392.67,
+ "duration": 0.0,
+ "text": "the perplexity increases."
+ },
+ {
+ "start": 2392.68,
+ "duration": 0.0,
+ "text": "the perplexity increases. Right.<00:39:53.000> And<00:39:53.120> it's<00:39:53.240> interesting<00:39:53.720> here<00:39:53.880> where"
+ },
+ {
+ "start": 2394.03,
+ "duration": 0.0,
+ "text": "Right. And it's interesting here where"
+ },
+ {
+ "start": 2394.04,
+ "duration": 0.0,
+ "text": "Right. And it's interesting here where it's<00:39:54.720> it's<00:39:54.840> essentially<00:39:55.240> the<00:39:55.400> same"
+ },
+ {
+ "start": 2395.95,
+ "duration": 0.0,
+ "text": "it's it's essentially the same"
+ },
+ {
+ "start": 2395.96,
+ "duration": 0.0,
+ "text": "it's it's essentially the same computation<00:39:56.640> but<00:39:56.760> just<00:39:56.960> these<00:39:57.080> tiny<00:39:57.440> tweaks"
+ },
+ {
+ "start": 2398.03,
+ "duration": 0.0,
+ "text": "computation but just these tiny tweaks"
+ },
+ {
+ "start": 2398.04,
+ "duration": 0.0,
+ "text": "computation but just these tiny tweaks to"
+ },
+ {
+ "start": 2399.27,
+ "duration": 0.0,
+ "text": "to"
+ },
+ {
+ "start": 2399.28,
+ "duration": 0.0,
+ "text": "to what<00:39:59.360> exactly<00:39:59.680> the<00:39:59.760> rule<00:40:00.080> is<00:40:00.200> being"
+ },
+ {
+ "start": 2400.35,
+ "duration": 0.0,
+ "text": "what exactly the rule is being"
+ },
+ {
+ "start": 2400.36,
+ "duration": 0.0,
+ "text": "what exactly the rule is being implemented,<00:40:01.040> and<00:40:01.120> we're<00:40:01.200> going<00:40:01.320> to<00:40:01.360> have"
+ },
+ {
+ "start": 2401.43,
+ "duration": 0.0,
+ "text": "implemented, and we're going to have"
+ },
+ {
+ "start": 2401.44,
+ "duration": 0.0,
+ "text": "implemented, and we're going to have three<00:40:01.680> very<00:40:01.920> different<00:40:02.240> outcomes,<00:40:02.720> right?<00:40:02.880> We"
+ },
+ {
+ "start": 2402.99,
+ "duration": 0.0,
+ "text": "three very different outcomes, right? We"
+ },
+ {
+ "start": 2403.0,
+ "duration": 0.0,
+ "text": "three very different outcomes, right? We can<00:40:03.120> essentially<00:40:03.520> if<00:40:03.640> we're<00:40:03.800> thinking<00:40:04.000> about"
+ },
+ {
+ "start": 2404.15,
+ "duration": 0.0,
+ "text": "can essentially if we're thinking about"
+ },
+ {
+ "start": 2404.16,
+ "duration": 0.0,
+ "text": "can essentially if we're thinking about this<00:40:04.360> in<00:40:04.480> terms<00:40:04.720> of<00:40:04.800> making<00:40:04.960> useful<00:40:05.200> data,<00:40:06.120> one"
+ },
+ {
+ "start": 2406.31,
+ "duration": 0.0,
+ "text": "this in terms of making useful data, one"
+ },
+ {
+ "start": 2406.32,
+ "duration": 0.0,
+ "text": "this in terms of making useful data, one outcome<00:40:06.640> is<00:40:06.800> that<00:40:06.880> we<00:40:07.000> make"
+ },
+ {
+ "start": 2407.99,
+ "duration": 0.0,
+ "text": "outcome is that we make"
+ },
+ {
+ "start": 2408.0,
+ "duration": 0.0,
+ "text": "outcome is that we make this<00:40:08.280> boring"
+ },
+ {
+ "start": 2409.43,
+ "duration": 0.0,
+ "text": "this boring"
+ },
+ {
+ "start": 2409.44,
+ "duration": 0.0,
+ "text": "this boring super<00:40:09.840> predictable<00:40:10.240> data.<00:40:10.640> Another<00:40:11.000> is<00:40:11.120> that"
+ },
+ {
+ "start": 2411.19,
+ "duration": 0.0,
+ "text": "super predictable data. Another is that"
+ },
+ {
+ "start": 2411.2,
+ "duration": 0.0,
+ "text": "super predictable data. Another is that we<00:40:11.320> make<00:40:12.040> kind<00:40:12.200> of<00:40:12.280> chaotic"
+ },
+ {
+ "start": 2413.59,
+ "duration": 0.0,
+ "text": "we make kind of chaotic"
+ },
+ {
+ "start": 2413.6,
+ "duration": 0.0,
+ "text": "we make kind of chaotic completely<00:40:14.000> unpredictable<00:40:14.520> data<00:40:14.800> that's"
+ },
+ {
+ "start": 2414.99,
+ "duration": 0.0,
+ "text": "completely unpredictable data that's"
+ },
+ {
+ "start": 2415.0,
+ "duration": 0.0,
+ "text": "completely unpredictable data that's also<00:40:15.560> not<00:40:15.720> useful<00:40:15.960> to<00:40:16.080> us."
+ },
+ {
+ "start": 2416.91,
+ "duration": 0.0,
+ "text": "also not useful to us."
+ },
+ {
+ "start": 2416.92,
+ "duration": 0.0,
+ "text": "also not useful to us. But<00:40:17.160> with<00:40:17.280> the<00:40:17.360> same<00:40:17.520> computation,<00:40:18.080> we<00:40:18.160> can"
+ },
+ {
+ "start": 2418.27,
+ "duration": 0.0,
+ "text": "But with the same computation, we can"
+ },
+ {
+ "start": 2418.28,
+ "duration": 0.0,
+ "text": "But with the same computation, we can also<00:40:18.520> make<00:40:18.800> data<00:40:19.040> that<00:40:19.240> is<00:40:19.640> is<00:40:20.080> interesting<00:40:20.520> to"
+ },
+ {
+ "start": 2420.55,
+ "duration": 0.0,
+ "text": "also make data that is is interesting to"
+ },
+ {
+ "start": 2420.56,
+ "duration": 0.0,
+ "text": "also make data that is is interesting to predict.<00:40:20.960> That<00:40:21.080> is<00:40:21.200> we<00:40:21.320> spend<00:40:21.640> more"
+ },
+ {
+ "start": 2421.79,
+ "duration": 0.0,
+ "text": "predict. That is we spend more"
+ },
+ {
+ "start": 2421.8,
+ "duration": 0.0,
+ "text": "predict. That is we spend more computation,<00:40:22.480> we<00:40:22.520> make<00:40:22.680> better<00:40:22.880> predictions."
+ },
+ {
+ "start": 2424.99,
+ "duration": 0.0,
+ "text": "computation, we make better predictions."
+ },
+ {
+ "start": 2425.0,
+ "duration": 0.0,
+ "text": "computation, we make better predictions. So<00:40:25.120> then<00:40:25.320> going<00:40:25.600> to<00:40:25.720> paradox<00:40:26.160> two,"
+ },
+ {
+ "start": 2428.11,
+ "duration": 0.0,
+ "text": "So then going to paradox two,"
+ },
+ {
+ "start": 2428.12,
+ "duration": 0.0,
+ "text": "So then going to paradox two, information<00:40:28.840> is<00:40:29.000> independent<00:40:29.600> factorization"
+ },
+ {
+ "start": 2430.19,
+ "duration": 0.0,
+ "text": "information is independent factorization"
+ },
+ {
+ "start": 2430.2,
+ "duration": 0.0,
+ "text": "information is independent factorization order."
+ },
+ {
+ "start": 2431.59,
+ "duration": 0.0,
+ "text": "order."
+ },
+ {
+ "start": 2431.6,
+ "duration": 0.0,
+ "text": "order. Well,<00:40:32.280> we're<00:40:32.800> we'll<00:40:32.960> show<00:40:33.200> that<00:40:33.360> actually"
+ },
+ {
+ "start": 2433.79,
+ "duration": 0.0,
+ "text": "Well, we're we'll show that actually"
+ },
+ {
+ "start": 2433.8,
+ "duration": 0.0,
+ "text": "Well, we're we'll show that actually time-bounded<00:40:34.240> entropy<00:40:34.680> and<00:40:34.800> perplexity"
+ },
+ {
+ "start": 2435.67,
+ "duration": 0.0,
+ "text": "time-bounded entropy and perplexity"
+ },
+ {
+ "start": 2435.68,
+ "duration": 0.0,
+ "text": "time-bounded entropy and perplexity depend<00:40:36.200> on<00:40:36.320> the<00:40:36.400> data<00:40:36.640> ordering."
+ },
+ {
+ "start": 2439.24,
+ "duration": 0.0,
+ "text": "So,"
+ },
+ {
+ "start": 2440.39,
+ "duration": 0.0,
+ "text": "So,"
+ },
+ {
+ "start": 2440.4,
+ "duration": 0.0,
+ "text": "So, um<00:40:41.280> right.<00:40:41.720> We<00:40:41.840> have<00:40:42.000> one-way<00:40:42.200> functions,"
+ },
+ {
+ "start": 2442.67,
+ "duration": 0.0,
+ "text": "um right. We have one-way functions,"
+ },
+ {
+ "start": 2442.68,
+ "duration": 0.0,
+ "text": "um right. We have one-way functions, which<00:40:43.000> Andrew<00:40:43.720> uh<00:40:43.920> briefly<00:40:44.160> mentioned,<00:40:45.160> um"
+ },
+ {
+ "start": 2445.71,
+ "duration": 0.0,
+ "text": "which Andrew uh briefly mentioned, um"
+ },
+ {
+ "start": 2445.72,
+ "duration": 0.0,
+ "text": "which Andrew uh briefly mentioned, um where<00:40:46.640> the<00:40:47.360> we<00:40:47.520> have"
+ },
+ {
+ "start": 2448.47,
+ "duration": 0.0,
+ "text": "where the we have"
+ },
+ {
+ "start": 2448.48,
+ "duration": 0.0,
+ "text": "where the we have a<00:40:48.840> function<00:40:49.600> that<00:40:50.640> uh"
+ },
+ {
+ "start": 2451.59,
+ "duration": 0.0,
+ "text": "a function that uh"
+ },
+ {
+ "start": 2451.6,
+ "duration": 0.0,
+ "text": "a function that uh is<00:40:51.760> very<00:40:51.960> difficult<00:40:52.600> to<00:40:52.720> find<00:40:53.080> elements<00:40:53.920> in<00:40:54.520> in"
+ },
+ {
+ "start": 2454.63,
+ "duration": 0.0,
+ "text": "is very difficult to find elements in in"
+ },
+ {
+ "start": 2454.64,
+ "duration": 0.0,
+ "text": "is very difficult to find elements in in its<00:40:54.760> inverse,<00:40:55.520> right?<00:40:55.680> The<00:40:55.760> inverse<00:40:56.120> asset."
+ },
+ {
+ "start": 2457.03,
+ "duration": 0.0,
+ "text": "its inverse, right? The inverse asset."
+ },
+ {
+ "start": 2457.04,
+ "duration": 0.0,
+ "text": "its inverse, right? The inverse asset. Um<00:40:57.480> where<00:40:57.680> the<00:40:57.800> probability<00:40:58.680> of<00:40:59.520> outputting"
+ },
+ {
+ "start": 2460.19,
+ "duration": 0.0,
+ "text": "Um where the probability of outputting"
+ },
+ {
+ "start": 2460.2,
+ "duration": 0.0,
+ "text": "Um where the probability of outputting an<00:41:00.320> element<00:41:00.640> in<00:41:00.680> the<00:41:00.800> inverse<00:41:01.520> can<00:41:01.720> be<00:41:01.920> again"
+ },
+ {
+ "start": 2462.23,
+ "duration": 0.0,
+ "text": "an element in the inverse can be again"
+ },
+ {
+ "start": 2462.24,
+ "duration": 0.0,
+ "text": "an element in the inverse can be again bounded<00:41:02.760> by<00:41:02.920> a<00:41:03.000> negligible<00:41:03.920> function,<00:41:04.600> in"
+ },
+ {
+ "start": 2464.67,
+ "duration": 0.0,
+ "text": "bounded by a negligible function, in"
+ },
+ {
+ "start": 2464.68,
+ "duration": 0.0,
+ "text": "bounded by a negligible function, in this<00:41:04.840> case<00:41:05.280> of<00:41:05.360> the<00:41:05.480> size<00:41:06.040> of<00:41:06.720> this<00:41:07.240> um"
+ },
+ {
+ "start": 2467.99,
+ "duration": 0.0,
+ "text": "this case of the size of this um"
+ },
+ {
+ "start": 2468.0,
+ "duration": 0.0,
+ "text": "this case of the size of this um state."
+ },
+ {
+ "start": 2469.99,
+ "duration": 0.0,
+ "text": "state."
+ },
+ {
+ "start": 2470.0,
+ "duration": 0.0,
+ "text": "state. So,<00:41:10.640> and<00:41:10.800> of<00:41:10.880> course<00:41:11.120> this<00:41:11.280> is<00:41:11.440> used"
+ },
+ {
+ "start": 2472.59,
+ "duration": 0.0,
+ "text": "So, and of course this is used"
+ },
+ {
+ "start": 2472.6,
+ "duration": 0.0,
+ "text": "So, and of course this is used that<00:41:12.800> is<00:41:13.080> the<00:41:13.200> foundation<00:41:13.800> for<00:41:13.960> cryptography."
+ },
+ {
+ "start": 2476.35,
+ "duration": 0.0,
+ "text": "that is the foundation for cryptography."
+ },
+ {
+ "start": 2476.36,
+ "duration": 0.0,
+ "text": "that is the foundation for cryptography. And<00:41:16.520> we<00:41:16.640> can<00:41:16.760> show<00:41:17.400> that"
+ },
+ {
+ "start": 2478.47,
+ "duration": 0.0,
+ "text": "And we can show that"
+ },
+ {
+ "start": 2478.48,
+ "duration": 0.0,
+ "text": "And we can show that um"
+ },
+ {
+ "start": 2479.99,
+ "duration": 0.0,
+ "text": "um"
+ },
+ {
+ "start": 2480.0,
+ "duration": 0.0,
+ "text": "um taking<00:41:20.280> the<00:41:20.360> input<00:41:20.640> and<00:41:20.720> output<00:41:20.960> pairs<00:41:21.440> of<00:41:21.560> a"
+ },
+ {
+ "start": 2481.79,
+ "duration": 0.0,
+ "text": "taking the input and output pairs of a"
+ },
+ {
+ "start": 2481.8,
+ "duration": 0.0,
+ "text": "taking the input and output pairs of a of<00:41:21.880> a<00:41:21.920> one-way<00:41:22.200> function,"
+ },
+ {
+ "start": 2483.23,
+ "duration": 0.0,
+ "text": "of a one-way function,"
+ },
+ {
+ "start": 2483.24,
+ "duration": 0.0,
+ "text": "of a one-way function, that<00:41:23.960> they<00:41:24.080> have<00:41:24.240> this<00:41:24.560> asymmetry<00:41:25.160> with"
+ },
+ {
+ "start": 2485.31,
+ "duration": 0.0,
+ "text": "that they have this asymmetry with"
+ },
+ {
+ "start": 2485.32,
+ "duration": 0.0,
+ "text": "that they have this asymmetry with respect<00:41:25.840> to<00:41:26.040> the<00:41:26.160> time-bounded<00:41:26.600> entropy.<00:41:27.440> So,"
+ },
+ {
+ "start": 2488.03,
+ "duration": 0.0,
+ "text": "respect to the time-bounded entropy. So,"
+ },
+ {
+ "start": 2488.04,
+ "duration": 0.0,
+ "text": "respect to the time-bounded entropy. So, in<00:41:28.200> one<00:41:28.400> direction<00:41:28.920> it'll<00:41:29.120> appear<00:41:29.360> random<00:41:29.880> and"
+ },
+ {
+ "start": 2489.99,
+ "duration": 0.0,
+ "text": "in one direction it'll appear random and"
+ },
+ {
+ "start": 2490.0,
+ "duration": 0.0,
+ "text": "in one direction it'll appear random and the<00:41:30.080> other<00:41:30.560> not."
+ },
+ {
+ "start": 2491.71,
+ "duration": 0.0,
+ "text": "the other not."
+ },
+ {
+ "start": 2491.72,
+ "duration": 0.0,
+ "text": "the other not. So,<00:41:31.880> we<00:41:32.000> have<00:41:32.160> a<00:41:32.200> theorem<00:41:32.560> here.<00:41:32.960> Um<00:41:33.200> so,<00:41:33.400> for<00:41:33.640> a"
+ },
+ {
+ "start": 2493.83,
+ "duration": 0.0,
+ "text": "So, we have a theorem here. Um so, for a"
+ },
+ {
+ "start": 2493.84,
+ "duration": 0.0,
+ "text": "So, we have a theorem here. Um so, for a one-way<00:41:34.320> permutation,<00:41:35.160> so<00:41:36.000> we<00:41:36.040> also<00:41:36.200> want<00:41:36.320> it"
+ },
+ {
+ "start": 2496.39,
+ "duration": 0.0,
+ "text": "one-way permutation, so we also want it"
+ },
+ {
+ "start": 2496.4,
+ "duration": 0.0,
+ "text": "one-way permutation, so we also want it to<00:41:36.440> be<00:41:36.520> a<00:41:36.560> bijection,<00:41:37.720> um<00:41:38.360> we<00:41:38.480> can<00:41:38.640> show<00:41:38.880> that"
+ },
+ {
+ "start": 2499.55,
+ "duration": 0.0,
+ "text": "to be a bijection, um we can show that"
+ },
+ {
+ "start": 2499.56,
+ "duration": 0.0,
+ "text": "to be a bijection, um we can show that this<00:41:40.320> uh"
+ },
+ {
+ "start": 2501.35,
+ "duration": 0.0,
+ "text": "this uh"
+ },
+ {
+ "start": 2501.36,
+ "duration": 0.0,
+ "text": "this uh time-bounded<00:41:41.800> entropy<00:41:42.320> with<00:41:42.800> polynomial"
+ },
+ {
+ "start": 2503.55,
+ "duration": 0.0,
+ "text": "time-bounded entropy with polynomial"
+ },
+ {
+ "start": 2503.56,
+ "duration": 0.0,
+ "text": "time-bounded entropy with polynomial time<00:41:43.800> bound"
+ },
+ {
+ "start": 2504.79,
+ "duration": 0.0,
+ "text": "time bound"
+ },
+ {
+ "start": 2504.8,
+ "duration": 0.0,
+ "text": "time bound um<00:41:45.680> for<00:41:45.920> X<00:41:46.080> given<00:41:46.280> Y<00:41:46.480> plus<00:41:46.960> uh<00:41:47.240> time-bounded"
+ },
+ {
+ "start": 2507.63,
+ "duration": 0.0,
+ "text": "um for X given Y plus uh time-bounded"
+ },
+ {
+ "start": 2507.64,
+ "duration": 0.0,
+ "text": "um for X given Y plus uh time-bounded entropy<00:41:47.840> of<00:41:47.920> Y<00:41:48.200> is<00:41:48.400> greater<00:41:48.720> than<00:41:48.960> Y<00:41:49.120> given<00:41:49.360> X"
+ },
+ {
+ "start": 2510.19,
+ "duration": 0.0,
+ "text": "entropy of Y is greater than Y given X"
+ },
+ {
+ "start": 2510.2,
+ "duration": 0.0,
+ "text": "entropy of Y is greater than Y given X uh<00:41:50.400> plus<00:41:50.640> H<00:41:50.840> of<00:41:50.920> X<00:41:51.560> plus<00:41:52.600> um"
+ },
+ {
+ "start": 2513.75,
+ "duration": 0.0,
+ "text": "uh plus H of X plus um"
+ },
+ {
+ "start": 2513.76,
+ "duration": 0.0,
+ "text": "uh plus H of X plus um omega<00:41:54.160> of<00:41:54.280> log<00:41:54.480> n.<00:41:54.760> So,<00:41:54.920> there's<00:41:55.120> a<00:41:55.200> separation"
+ },
+ {
+ "start": 2516.11,
+ "duration": 0.0,
+ "text": "omega of log n. So, there's a separation"
+ },
+ {
+ "start": 2516.12,
+ "duration": 0.0,
+ "text": "omega of log n. So, there's a separation that<00:41:56.240> scales"
+ },
+ {
+ "start": 2517.87,
+ "duration": 0.0,
+ "text": "that scales"
+ },
+ {
+ "start": 2517.88,
+ "duration": 0.0,
+ "text": "that scales uh<00:41:58.440> faster<00:41:59.120> than<00:41:59.360> log<00:41:59.600> n."
+ },
+ {
+ "start": 2521.83,
+ "duration": 0.0,
+ "text": "uh faster than log n."
+ },
+ {
+ "start": 2521.84,
+ "duration": 0.0,
+ "text": "uh faster than log n. And<00:42:02.320> we<00:42:02.440> also<00:42:02.640> have<00:42:03.000> an<00:42:03.120> empirical<00:42:03.480> experiment"
+ },
+ {
+ "start": 2524.51,
+ "duration": 0.0,
+ "text": "And we also have an empirical experiment"
+ },
+ {
+ "start": 2524.52,
+ "duration": 0.0,
+ "text": "And we also have an empirical experiment um<00:42:04.640> demonstrating<00:42:05.760> uh<00:42:06.080> something<00:42:06.520> to<00:42:06.920> this"
+ },
+ {
+ "start": 2527.19,
+ "duration": 0.0,
+ "text": "um demonstrating uh something to this"
+ },
+ {
+ "start": 2527.2,
+ "duration": 0.0,
+ "text": "um demonstrating uh something to this effect.<00:42:07.840> So,<00:42:08.080> here<00:42:08.480> the<00:42:08.600> difficulty<00:42:09.120> is<00:42:09.320> that"
+ },
+ {
+ "start": 2529.51,
+ "duration": 0.0,
+ "text": "effect. So, here the difficulty is that"
+ },
+ {
+ "start": 2529.52,
+ "duration": 0.0,
+ "text": "effect. So, here the difficulty is that you<00:42:10.120> need<00:42:10.320> to<00:42:10.400> find<00:42:10.680> a<00:42:10.720> function<00:42:11.440> where<00:42:12.080> your"
+ },
+ {
+ "start": 2532.99,
+ "duration": 0.0,
+ "text": "you need to find a function where your"
+ },
+ {
+ "start": 2533.0,
+ "duration": 0.0,
+ "text": "you need to find a function where your uh<00:42:13.080> model<00:42:13.320> class<00:42:13.640> that<00:42:13.800> you're<00:42:13.920> searching<00:42:14.240> in"
+ },
+ {
+ "start": 2534.63,
+ "duration": 0.0,
+ "text": "uh model class that you're searching in"
+ },
+ {
+ "start": 2534.64,
+ "duration": 0.0,
+ "text": "uh model class that you're searching in can<00:42:14.800> actually<00:42:15.040> fit<00:42:15.240> the<00:42:15.320> forward<00:42:15.520> direction."
+ },
+ {
+ "start": 2536.59,
+ "duration": 0.0,
+ "text": "can actually fit the forward direction."
+ },
+ {
+ "start": 2536.6,
+ "duration": 0.0,
+ "text": "can actually fit the forward direction. That<00:42:16.720> is<00:42:16.880> also<00:42:17.640> a<00:42:17.720> conjectured<00:42:18.200> one-way"
+ },
+ {
+ "start": 2538.39,
+ "duration": 0.0,
+ "text": "That is also a conjectured one-way"
+ },
+ {
+ "start": 2538.4,
+ "duration": 0.0,
+ "text": "That is also a conjectured one-way function."
+ },
+ {
+ "start": 2539.47,
+ "duration": 0.0,
+ "text": "function."
+ },
+ {
+ "start": 2539.48,
+ "duration": 0.0,
+ "text": "function. So,<00:42:19.560> here<00:42:20.080> we<00:42:20.240> use<00:42:21.040> um"
+ },
+ {
+ "start": 2541.79,
+ "duration": 0.0,
+ "text": "So, here we use um"
+ },
+ {
+ "start": 2541.8,
+ "duration": 0.0,
+ "text": "So, here we use um we<00:42:21.920> actually<00:42:22.240> use<00:42:22.480> again<00:42:23.280> uh<00:42:23.400> well,<00:42:23.600> okay."
+ },
+ {
+ "start": 2543.79,
+ "duration": 0.0,
+ "text": "we actually use again uh well, okay."
+ },
+ {
+ "start": 2543.8,
+ "duration": 0.0,
+ "text": "we actually use again uh well, okay. Yes,<00:42:24.040> so<00:42:24.200> so<00:42:24.320> we<00:42:24.480> we<00:42:24.680> again<00:42:24.960> use<00:42:25.400> um"
+ },
+ {
+ "start": 2546.55,
+ "duration": 0.0,
+ "text": "Yes, so so we we again use um"
+ },
+ {
+ "start": 2546.56,
+ "duration": 0.0,
+ "text": "Yes, so so we we again use um uh"
+ },
+ {
+ "start": 2547.27,
+ "duration": 0.0,
+ "text": "uh"
+ },
+ {
+ "start": 2547.28,
+ "duration": 0.0,
+ "text": "uh uh"
+ },
+ {
+ "start": 2547.99,
+ "duration": 0.0,
+ "text": "uh"
+ },
+ {
+ "start": 2548.0,
+ "duration": 0.0,
+ "text": "uh uh<00:42:28.120> cellular<00:42:28.440> automata<00:42:28.760> here,<00:42:29.000> but<00:42:29.480> uh<00:42:29.760> using"
+ },
+ {
+ "start": 2550.03,
+ "duration": 0.0,
+ "text": "uh cellular automata here, but uh using"
+ },
+ {
+ "start": 2550.04,
+ "duration": 0.0,
+ "text": "uh cellular automata here, but uh using the<00:42:30.160> conjectured<00:42:30.600> one-way<00:42:31.200> uh<00:42:31.400> properties<00:42:31.920> of"
+ },
+ {
+ "start": 2552.59,
+ "duration": 0.0,
+ "text": "the conjectured one-way uh properties of"
+ },
+ {
+ "start": 2552.6,
+ "duration": 0.0,
+ "text": "the conjectured one-way uh properties of uh<00:42:32.880> of<00:42:32.960> rule<00:42:33.080> 30<00:42:33.480> and<00:42:33.600> then<00:42:33.720> look<00:42:33.920> at<00:42:34.040> the"
+ },
+ {
+ "start": 2554.11,
+ "duration": 0.0,
+ "text": "uh of rule 30 and then look at the"
+ },
+ {
+ "start": 2554.12,
+ "duration": 0.0,
+ "text": "uh of rule 30 and then look at the forward<00:42:34.400> prediction<00:42:34.720> versus<00:42:34.960> the<00:42:35.040> reverse"
+ },
+ {
+ "start": 2555.31,
+ "duration": 0.0,
+ "text": "forward prediction versus the reverse"
+ },
+ {
+ "start": 2555.32,
+ "duration": 0.0,
+ "text": "forward prediction versus the reverse prediction.<00:42:36.200> In<00:42:36.320> the<00:42:36.440> forward<00:42:36.720> direction,"
+ },
+ {
+ "start": 2557.87,
+ "duration": 0.0,
+ "text": "prediction. In the forward direction,"
+ },
+ {
+ "start": 2557.88,
+ "duration": 0.0,
+ "text": "prediction. In the forward direction, um<00:42:38.000> you<00:42:38.160> line<00:42:38.400> up<00:42:38.520> right<00:42:38.640> with<00:42:38.760> the<00:42:38.840> entropy<00:42:39.800> so"
+ },
+ {
+ "start": 2559.91,
+ "duration": 0.0,
+ "text": "um you line up right with the entropy so"
+ },
+ {
+ "start": 2559.92,
+ "duration": 0.0,
+ "text": "um you line up right with the entropy so you<00:42:40.000> have<00:42:40.080> random<00:42:40.360> initial<00:42:40.560> conditions<00:42:41.160> in"
+ },
+ {
+ "start": 2561.23,
+ "duration": 0.0,
+ "text": "you have random initial conditions in"
+ },
+ {
+ "start": 2561.24,
+ "duration": 0.0,
+ "text": "you have random initial conditions in forward.<00:42:41.800> And<00:42:41.960> then<00:42:42.120> the<00:42:42.200> reverse<00:42:42.480> direction,"
+ },
+ {
+ "start": 2562.91,
+ "duration": 0.0,
+ "text": "forward. And then the reverse direction,"
+ },
+ {
+ "start": 2562.92,
+ "duration": 0.0,
+ "text": "forward. And then the reverse direction, you<00:42:43.200> have<00:42:43.400> this<00:42:43.560> gap.<00:42:44.440> Um<00:42:45.040> and<00:42:45.680> yeah,<00:42:45.840> I<00:42:45.880> guess"
+ },
+ {
+ "start": 2566.07,
+ "duration": 0.0,
+ "text": "you have this gap. Um and yeah, I guess"
+ },
+ {
+ "start": 2566.08,
+ "duration": 0.0,
+ "text": "you have this gap. Um and yeah, I guess it<00:42:46.120> would<00:42:46.200> be<00:42:46.320> good<00:42:46.480> to<00:42:46.760> to<00:42:46.880> see<00:42:47.080> like<00:42:47.280> yeah,"
+ },
+ {
+ "start": 2567.43,
+ "duration": 0.0,
+ "text": "it would be good to to see like yeah,"
+ },
+ {
+ "start": 2567.44,
+ "duration": 0.0,
+ "text": "it would be good to to see like yeah, does<00:42:47.600> this<00:42:47.800> this<00:42:47.960> gap<00:42:48.200> actually<00:42:49.040> grow<00:42:49.320> with"
+ },
+ {
+ "start": 2569.51,
+ "duration": 0.0,
+ "text": "does this this gap actually grow with"
+ },
+ {
+ "start": 2569.52,
+ "duration": 0.0,
+ "text": "does this this gap actually grow with log<00:42:49.720> n?<00:42:49.920> We<00:42:50.040> don't<00:42:50.400> quite<00:42:50.600> have<00:42:50.720> the"
+ },
+ {
+ "start": 2570.79,
+ "duration": 0.0,
+ "text": "log n? We don't quite have the"
+ },
+ {
+ "start": 2570.8,
+ "duration": 0.0,
+ "text": "log n? We don't quite have the resolution<00:42:51.200> here<00:42:51.600> to<00:42:51.720> see<00:42:51.840> that.<00:42:52.520> Um<00:42:52.800> but"
+ },
+ {
+ "start": 2573.51,
+ "duration": 0.0,
+ "text": "resolution here to see that. Um but"
+ },
+ {
+ "start": 2573.52,
+ "duration": 0.0,
+ "text": "resolution here to see that. Um but right,<00:42:53.760> we're<00:42:53.880> able<00:42:54.000> to<00:42:54.080> see<00:42:54.160> it"
+ },
+ {
+ "start": 2574.39,
+ "duration": 0.0,
+ "text": "right, we're able to see it"
+ },
+ {
+ "start": 2574.4,
+ "duration": 0.0,
+ "text": "right, we're able to see it theoretically<00:42:54.800> and<00:42:54.880> empirically."
+ },
+ {
+ "start": 2576.43,
+ "duration": 0.0,
+ "text": "theoretically and empirically."
+ },
+ {
+ "start": 2576.44,
+ "duration": 0.0,
+ "text": "theoretically and empirically. Another<00:42:56.760> example,<00:42:57.640> or<00:42:57.760> practical<00:42:58.040> example,"
+ },
+ {
+ "start": 2578.47,
+ "duration": 0.0,
+ "text": "Another example, or practical example,"
+ },
+ {
+ "start": 2578.48,
+ "duration": 0.0,
+ "text": "Another example, or practical example, um<00:42:59.200> right<00:42:59.520> uh<00:42:59.560> so<00:42:59.720> so<00:42:59.920> we<00:43:00.360> uh<00:43:00.440> looked<00:43:00.640> at<00:43:00.800> say<00:43:01.040> at"
+ },
+ {
+ "start": 2581.71,
+ "duration": 0.0,
+ "text": "um right uh so so we uh looked at say at"
+ },
+ {
+ "start": 2581.72,
+ "duration": 0.0,
+ "text": "um right uh so so we uh looked at say at some<00:43:02.240> real<00:43:02.440> data<00:43:02.760> like<00:43:03.240> well,<00:43:03.360> okay.<00:43:03.600> So<00:43:03.760> so"
+ },
+ {
+ "start": 2584.47,
+ "duration": 0.0,
+ "text": "some real data like well, okay. So so"
+ },
+ {
+ "start": 2584.48,
+ "duration": 0.0,
+ "text": "some real data like well, okay. So so synthetic<00:43:04.800> data,<00:43:05.080> but<00:43:05.520> uh<00:43:06.000> data<00:43:06.400> of<00:43:06.880> mapping"
+ },
+ {
+ "start": 2587.75,
+ "duration": 0.0,
+ "text": "synthetic data, but uh data of mapping"
+ },
+ {
+ "start": 2587.76,
+ "duration": 0.0,
+ "text": "synthetic data, but uh data of mapping chess<00:43:08.040> moves<00:43:08.480> to<00:43:08.960> a<00:43:09.040> chessboard<00:43:10.080> versus<00:43:11.000> um<00:43:11.600> so"
+ },
+ {
+ "start": 2591.71,
+ "duration": 0.0,
+ "text": "chess moves to a chessboard versus um so"
+ },
+ {
+ "start": 2591.72,
+ "duration": 0.0,
+ "text": "chess moves to a chessboard versus um so a<00:43:11.800> sequence<00:43:12.160> of<00:43:12.240> chess<00:43:12.440> moves<00:43:12.920> to<00:43:13.280> the<00:43:13.400> final"
+ },
+ {
+ "start": 2593.79,
+ "duration": 0.0,
+ "text": "a sequence of chess moves to the final"
+ },
+ {
+ "start": 2593.8,
+ "duration": 0.0,
+ "text": "a sequence of chess moves to the final chessboard<00:43:14.720> versus<00:43:15.120> taking<00:43:15.320> the<00:43:15.400> final"
+ },
+ {
+ "start": 2595.75,
+ "duration": 0.0,
+ "text": "chessboard versus taking the final"
+ },
+ {
+ "start": 2595.76,
+ "duration": 0.0,
+ "text": "chessboard versus taking the final chessboard<00:43:16.400> and<00:43:16.520> then<00:43:16.640> mapping<00:43:16.920> that<00:43:17.200> to<00:43:17.440> the"
+ },
+ {
+ "start": 2597.51,
+ "duration": 0.0,
+ "text": "chessboard and then mapping that to the"
+ },
+ {
+ "start": 2597.52,
+ "duration": 0.0,
+ "text": "chessboard and then mapping that to the sequence<00:43:17.880> of<00:43:17.960> chess<00:43:18.160> moves<00:43:18.360> that<00:43:18.480> got<00:43:18.680> there."
+ },
+ {
+ "start": 2599.15,
+ "duration": 0.0,
+ "text": "sequence of chess moves that got there."
+ },
+ {
+ "start": 2599.16,
+ "duration": 0.0,
+ "text": "sequence of chess moves that got there. In<00:43:19.320> one<00:43:19.440> direction,<00:43:19.920> all<00:43:20.080> you<00:43:20.160> need<00:43:20.320> to<00:43:20.400> do<00:43:20.680> is"
+ },
+ {
+ "start": 2601.39,
+ "duration": 0.0,
+ "text": "In one direction, all you need to do is"
+ },
+ {
+ "start": 2601.4,
+ "duration": 0.0,
+ "text": "In one direction, all you need to do is um<00:43:21.520> keep<00:43:21.760> track<00:43:22.040> of<00:43:22.120> the<00:43:22.240> state.<00:43:23.000> You<00:43:23.120> need<00:43:23.320> to"
+ },
+ {
+ "start": 2603.47,
+ "duration": 0.0,
+ "text": "um keep track of the state. You need to"
+ },
+ {
+ "start": 2603.48,
+ "duration": 0.0,
+ "text": "um keep track of the state. You need to basically<00:43:24.080> run<00:43:24.440> this,<00:43:25.080> you<00:43:25.160> know,<00:43:25.480> um<00:43:25.960> where"
+ },
+ {
+ "start": 2606.19,
+ "duration": 0.0,
+ "text": "basically run this, you know, um where"
+ },
+ {
+ "start": 2606.2,
+ "duration": 0.0,
+ "text": "basically run this, you know, um where does<00:43:26.360> this<00:43:26.520> move<00:43:26.720> bring<00:43:26.920> you?<00:43:27.080> Where<00:43:27.200> does"
+ },
+ {
+ "start": 2607.27,
+ "duration": 0.0,
+ "text": "does this move bring you? Where does"
+ },
+ {
+ "start": 2607.28,
+ "duration": 0.0,
+ "text": "does this move bring you? Where does this<00:43:27.440> move<00:43:27.600> bring<00:43:27.800> you<00:43:28.280> on<00:43:28.360> the<00:43:28.440> board?<00:43:29.080> In<00:43:29.200> the"
+ },
+ {
+ "start": 2609.27,
+ "duration": 0.0,
+ "text": "this move bring you on the board? In the"
+ },
+ {
+ "start": 2609.28,
+ "duration": 0.0,
+ "text": "this move bring you on the board? In the other<00:43:29.440> direction,<00:43:29.880> you<00:43:29.960> have<00:43:30.080> to<00:43:30.160> do<00:43:30.280> some"
+ },
+ {
+ "start": 2610.43,
+ "duration": 0.0,
+ "text": "other direction, you have to do some"
+ },
+ {
+ "start": 2610.44,
+ "duration": 0.0,
+ "text": "other direction, you have to do some kind<00:43:30.560> of<00:43:30.640> inference.<00:43:31.120> You<00:43:31.200> have<00:43:31.320> to<00:43:31.440> do<00:43:31.520> some"
+ },
+ {
+ "start": 2611.67,
+ "duration": 0.0,
+ "text": "kind of inference. You have to do some"
+ },
+ {
+ "start": 2611.68,
+ "duration": 0.0,
+ "text": "kind of inference. You have to do some kind<00:43:31.800> of<00:43:31.880> induction<00:43:32.400> of<00:43:32.600> like,<00:43:32.800> \"Hmm,<00:43:33.240> how<00:43:33.360> did"
+ },
+ {
+ "start": 2613.47,
+ "duration": 0.0,
+ "text": "kind of induction of like, \"Hmm, how did"
+ },
+ {
+ "start": 2613.48,
+ "duration": 0.0,
+ "text": "kind of induction of like, \"Hmm, how did we<00:43:33.600> get<00:43:33.720> here?<00:43:33.960> Maybe<00:43:34.160> there<00:43:34.280> are<00:43:34.320> multiple"
+ },
+ {
+ "start": 2614.59,
+ "duration": 0.0,
+ "text": "we get here? Maybe there are multiple"
+ },
+ {
+ "start": 2614.6,
+ "duration": 0.0,
+ "text": "we get here? Maybe there are multiple ways<00:43:34.800> to<00:43:34.880> get<00:43:35.040> there.\"<00:43:35.360> Have<00:43:35.520> to<00:43:35.600> do<00:43:35.720> some"
+ },
+ {
+ "start": 2616.51,
+ "duration": 0.0,
+ "text": "ways to get there.\" Have to do some"
+ },
+ {
+ "start": 2616.52,
+ "duration": 0.0,
+ "text": "ways to get there.\" Have to do some And<00:43:36.720> what<00:43:36.840> we<00:43:36.920> find<00:43:37.240> is<00:43:37.360> that<00:43:37.880> of<00:43:38.000> course<00:43:38.320> in"
+ },
+ {
+ "start": 2618.51,
+ "duration": 0.0,
+ "text": "And what we find is that of course in"
+ },
+ {
+ "start": 2618.52,
+ "duration": 0.0,
+ "text": "And what we find is that of course in the<00:43:38.800> more<00:43:39.080> straightforward<00:43:39.560> direction,<00:43:40.040> the"
+ },
+ {
+ "start": 2620.15,
+ "duration": 0.0,
+ "text": "the more straightforward direction, the"
+ },
+ {
+ "start": 2620.16,
+ "duration": 0.0,
+ "text": "the more straightforward direction, the the<00:43:40.200> time-bounded<00:43:40.640> entropy<00:43:40.800> is<00:43:40.880> lower,<00:43:41.680> um"
+ },
+ {
+ "start": 2622.31,
+ "duration": 0.0,
+ "text": "the time-bounded entropy is lower, um"
+ },
+ {
+ "start": 2622.32,
+ "duration": 0.0,
+ "text": "the time-bounded entropy is lower, um but<00:43:43.000> that<00:43:43.280> actually<00:43:44.120> uh"
+ },
+ {
+ "start": 2624.75,
+ "duration": 0.0,
+ "text": "but that actually uh"
+ },
+ {
+ "start": 2624.76,
+ "duration": 0.0,
+ "text": "but that actually uh the"
+ },
+ {
+ "start": 2625.87,
+ "duration": 0.0,
+ "text": "the"
+ },
+ {
+ "start": 2625.88,
+ "duration": 0.0,
+ "text": "the perplexity<00:43:46.600> is<00:43:47.200> also<00:43:47.760> lower.<00:43:48.440> So,<00:43:48.680> yeah,<00:43:48.840> it's"
+ },
+ {
+ "start": 2628.91,
+ "duration": 0.0,
+ "text": "perplexity is also lower. So, yeah, it's"
+ },
+ {
+ "start": 2628.92,
+ "duration": 0.0,
+ "text": "perplexity is also lower. So, yeah, it's also<00:43:49.160> lower."
+ },
+ {
+ "start": 2630.47,
+ "duration": 0.0,
+ "text": "also lower."
+ },
+ {
+ "start": 2630.48,
+ "duration": 0.0,
+ "text": "also lower. Um<00:43:51.040> right.<00:43:51.280> And<00:43:51.400> so,<00:43:51.520> we<00:43:51.640> can<00:43:51.760> actually<00:43:52.160> find"
+ },
+ {
+ "start": 2632.43,
+ "duration": 0.0,
+ "text": "Um right. And so, we can actually find"
+ },
+ {
+ "start": 2632.44,
+ "duration": 0.0,
+ "text": "Um right. And so, we can actually find ways<00:43:52.720> of<00:43:52.840> tweaking<00:43:53.200> the<00:43:53.320> data<00:43:53.640> to<00:43:53.760> make<00:43:53.920> it"
+ },
+ {
+ "start": 2634.07,
+ "duration": 0.0,
+ "text": "ways of tweaking the data to make it"
+ },
+ {
+ "start": 2634.08,
+ "duration": 0.0,
+ "text": "ways of tweaking the data to make it harder,<00:43:54.520> but<00:43:54.760> harder<00:43:55.080> in<00:43:55.240> an<00:43:55.320> interesting"
+ },
+ {
+ "start": 2635.75,
+ "duration": 0.0,
+ "text": "harder, but harder in an interesting"
+ },
+ {
+ "start": 2635.76,
+ "duration": 0.0,
+ "text": "harder, but harder in an interesting way.<00:43:56.200> And<00:43:56.320> then<00:43:56.440> also<00:43:56.640> you<00:43:56.760> have<00:43:56.880> data,<00:43:57.200> you"
+ },
+ {
+ "start": 2637.39,
+ "duration": 0.0,
+ "text": "way. And then also you have data, you"
+ },
+ {
+ "start": 2637.4,
+ "duration": 0.0,
+ "text": "way. And then also you have data, you know,<00:43:57.480> evidence<00:43:57.800> from<00:43:57.960> arrow<00:43:58.160> of<00:43:58.240> time<00:43:58.520> and"
+ },
+ {
+ "start": 2638.63,
+ "duration": 0.0,
+ "text": "know, evidence from arrow of time and"
+ },
+ {
+ "start": 2638.64,
+ "duration": 0.0,
+ "text": "know, evidence from arrow of time and LLMs,<00:43:59.240> like<00:43:59.359> I<00:43:59.400> had<00:43:59.480> mentioned.<00:44:00.359> Um<00:44:01.160> and<00:44:01.640> so"
+ },
+ {
+ "start": 2642.47,
+ "duration": 0.0,
+ "text": "LLMs, like I had mentioned. Um and so"
+ },
+ {
+ "start": 2642.48,
+ "duration": 0.0,
+ "text": "LLMs, like I had mentioned. Um and so I'll<00:44:02.600> now<00:44:02.720> move<00:44:02.960> on<00:44:03.120> to<00:44:03.359> paradox<00:44:03.760> three,<00:44:04.440> um"
+ },
+ {
+ "start": 2644.91,
+ "duration": 0.0,
+ "text": "I'll now move on to paradox three, um"
+ },
+ {
+ "start": 2644.92,
+ "duration": 0.0,
+ "text": "I'll now move on to paradox three, um likelihood<00:44:05.400> modeling<00:44:05.800> is<00:44:05.960> merely"
+ },
+ {
+ "start": 2646.23,
+ "duration": 0.0,
+ "text": "likelihood modeling is merely"
+ },
+ {
+ "start": 2646.24,
+ "duration": 0.0,
+ "text": "likelihood modeling is merely distribution<00:44:06.680> matching."
+ },
+ {
+ "start": 2648.31,
+ "duration": 0.0,
+ "text": "distribution matching."
+ },
+ {
+ "start": 2648.32,
+ "duration": 0.0,
+ "text": "distribution matching. So,"
+ },
+ {
+ "start": 2649.83,
+ "duration": 0.0,
+ "text": "So,"
+ },
+ {
+ "start": 2649.84,
+ "duration": 0.0,
+ "text": "So, uh<00:44:10.160> it<00:44:10.280> is<00:44:10.440> our<00:44:10.640> contention<00:44:11.120> that<00:44:11.640> uh"
+ },
+ {
+ "start": 2652.349,
+ "duration": 0.0,
+ "text": "uh it is our contention that uh"
+ },
+ {
+ "start": 2652.359,
+ "duration": 0.0,
+ "text": "uh it is our contention that uh All<00:44:12.480> right.<00:44:12.680> So<00:44:12.800> so<00:44:12.960> yeah,<00:44:13.160> so<00:44:13.400> but<00:44:14.160> actually"
+ },
+ {
+ "start": 2654.75,
+ "duration": 0.0,
+ "text": "All right. So so yeah, so but actually"
+ },
+ {
+ "start": 2654.76,
+ "duration": 0.0,
+ "text": "All right. So so yeah, so but actually uh<00:44:15.240> where<00:44:15.440> do<00:44:15.560> you<00:44:15.640> know<00:44:16.080> um<00:44:16.640> that<00:44:17.240> uh<00:44:17.560> again"
+ },
+ {
+ "start": 2658.47,
+ "duration": 0.0,
+ "text": "uh where do you know um that uh again"
+ },
+ {
+ "start": 2658.48,
+ "duration": 0.0,
+ "text": "uh where do you know um that uh again that<00:44:18.840> that<00:44:19.040> actually<00:44:19.280> time-bounded"
+ },
+ {
+ "start": 2659.75,
+ "duration": 0.0,
+ "text": "that that actually time-bounded"
+ },
+ {
+ "start": 2659.76,
+ "duration": 0.0,
+ "text": "that that actually time-bounded perplexity<00:44:20.280> can<00:44:20.400> be<00:44:20.480> greater<00:44:20.800> than<00:44:20.960> the<00:44:21.000> size"
+ },
+ {
+ "start": 2661.23,
+ "duration": 0.0,
+ "text": "perplexity can be greater than the size"
+ },
+ {
+ "start": 2661.24,
+ "duration": 0.0,
+ "text": "perplexity can be greater than the size of<00:44:21.320> the<00:44:21.400> generating<00:44:21.720> program<00:44:22.200> with<00:44:22.359> a<00:44:22.400> couple"
+ },
+ {
+ "start": 2662.63,
+ "duration": 0.0,
+ "text": "of the generating program with a couple"
+ },
+ {
+ "start": 2662.64,
+ "duration": 0.0,
+ "text": "of the generating program with a couple of<00:44:22.720> examples."
+ },
+ {
+ "start": 2664.59,
+ "duration": 0.0,
+ "text": "of examples."
+ },
+ {
+ "start": 2664.6,
+ "duration": 0.0,
+ "text": "of examples. So,<00:44:25.040> um<00:44:25.680> let<00:44:25.800> me<00:44:25.840> just<00:44:26.040> quickly<00:44:26.280> go<00:44:26.359> through"
+ },
+ {
+ "start": 2666.51,
+ "duration": 0.0,
+ "text": "So, um let me just quickly go through"
+ },
+ {
+ "start": 2666.52,
+ "duration": 0.0,
+ "text": "So, um let me just quickly go through this.<00:44:27.120> Uh<00:44:27.280> right.<00:44:27.480> So<00:44:27.600> so"
+ },
+ {
+ "start": 2668.43,
+ "duration": 0.0,
+ "text": "this. Uh right. So so"
+ },
+ {
+ "start": 2668.44,
+ "duration": 0.0,
+ "text": "this. Uh right. So so where<00:44:28.680> this<00:44:28.880> intuition<00:44:29.240> is<00:44:29.320> coming<00:44:29.560> from,"
+ },
+ {
+ "start": 2669.99,
+ "duration": 0.0,
+ "text": "where this intuition is coming from,"
+ },
+ {
+ "start": 2670.0,
+ "duration": 0.0,
+ "text": "where this intuition is coming from, right?<00:44:30.280> This<00:44:30.480> is<00:44:30.640> this<00:44:31.400> uh<00:44:31.920> thing<00:44:32.080> that<00:44:32.200> people"
+ },
+ {
+ "start": 2672.39,
+ "duration": 0.0,
+ "text": "right? This is this uh thing that people"
+ },
+ {
+ "start": 2672.4,
+ "duration": 0.0,
+ "text": "right? This is this uh thing that people have<00:44:32.640> expressed<00:44:33.440> of<00:44:34.200> uh"
+ },
+ {
+ "start": 2675.83,
+ "duration": 0.0,
+ "text": "have expressed of uh"
+ },
+ {
+ "start": 2675.84,
+ "duration": 0.0,
+ "text": "have expressed of uh that<00:44:36.280> somehow<00:44:36.600> if<00:44:36.720> we<00:44:36.800> train<00:44:37.000> on<00:44:37.080> human<00:44:37.280> data,"
+ },
+ {
+ "start": 2677.75,
+ "duration": 0.0,
+ "text": "that somehow if we train on human data,"
+ },
+ {
+ "start": 2677.76,
+ "duration": 0.0,
+ "text": "that somehow if we train on human data, we<00:44:37.840> can<00:44:37.960> never<00:44:38.280> exceed<00:44:38.720> human<00:44:38.960> capabilities,"
+ },
+ {
+ "start": 2679.79,
+ "duration": 0.0,
+ "text": "we can never exceed human capabilities,"
+ },
+ {
+ "start": 2679.8,
+ "duration": 0.0,
+ "text": "we can never exceed human capabilities, right?<00:44:40.440> We<00:44:41.400> uh<00:44:41.760> or<00:44:42.200> that<00:44:42.760> um<00:44:43.040> okay,<00:44:43.680> uh<00:44:44.040> the"
+ },
+ {
+ "start": 2684.11,
+ "duration": 0.0,
+ "text": "right? We uh or that um okay, uh the"
+ },
+ {
+ "start": 2684.12,
+ "duration": 0.0,
+ "text": "right? We uh or that um okay, uh the model<00:44:44.400> that<00:44:44.520> minimizes<00:44:45.000> the<00:44:45.040> cross-entropy"
+ },
+ {
+ "start": 2685.51,
+ "duration": 0.0,
+ "text": "model that minimizes the cross-entropy"
+ },
+ {
+ "start": 2685.52,
+ "duration": 0.0,
+ "text": "model that minimizes the cross-entropy loss<00:44:46.200> is<00:44:46.440> just<00:44:47.080> the<00:44:47.880> uh"
+ },
+ {
+ "start": 2688.51,
+ "duration": 0.0,
+ "text": "loss is just the uh"
+ },
+ {
+ "start": 2688.52,
+ "duration": 0.0,
+ "text": "loss is just the uh the<00:44:48.920> distribution<00:44:49.400> that<00:44:49.520> generated<00:44:49.840> the"
+ },
+ {
+ "start": 2689.87,
+ "duration": 0.0,
+ "text": "the distribution that generated the"
+ },
+ {
+ "start": 2689.88,
+ "duration": 0.0,
+ "text": "the distribution that generated the data.<00:44:50.480> So<00:44:50.600> then<00:44:50.960> as<00:44:51.240> we<00:44:51.359> minimize<00:44:51.760> our"
+ },
+ {
+ "start": 2691.87,
+ "duration": 0.0,
+ "text": "data. So then as we minimize our"
+ },
+ {
+ "start": 2691.88,
+ "duration": 0.0,
+ "text": "data. So then as we minimize our cross-entropy<00:44:52.359> loss,<00:44:52.600> we<00:44:52.720> should<00:44:52.880> expect"
+ },
+ {
+ "start": 2693.23,
+ "duration": 0.0,
+ "text": "cross-entropy loss, we should expect"
+ },
+ {
+ "start": 2693.24,
+ "duration": 0.0,
+ "text": "cross-entropy loss, we should expect just<00:44:53.400> to<00:44:53.480> approach<00:44:53.760> that<00:44:54.000> and<00:44:54.080> not<00:44:54.240> be<00:44:54.320> able<00:44:54.440> to"
+ },
+ {
+ "start": 2694.51,
+ "duration": 0.0,
+ "text": "just to approach that and not be able to"
+ },
+ {
+ "start": 2694.52,
+ "duration": 0.0,
+ "text": "just to approach that and not be able to do<00:44:54.560> anything<00:44:54.760> better."
+ },
+ {
+ "start": 2695.59,
+ "duration": 0.0,
+ "text": "do anything better."
+ },
+ {
+ "start": 2695.6,
+ "duration": 0.0,
+ "text": "do anything better. But<00:44:56.000> uh<00:44:56.520> there's<00:44:56.600> a<00:44:56.640> great<00:44:56.840> quote<00:44:57.080> from<00:44:57.359> Ilya"
+ },
+ {
+ "start": 2697.55,
+ "duration": 0.0,
+ "text": "But uh there's a great quote from Ilya"
+ },
+ {
+ "start": 2697.56,
+ "duration": 0.0,
+ "text": "But uh there's a great quote from Ilya Sutskever.<00:44:58.520> Um<00:44:59.280> so,<00:44:59.440> you're<00:44:59.560> reading<00:44:59.800> a"
+ },
+ {
+ "start": 2699.83,
+ "duration": 0.0,
+ "text": "Sutskever. Um so, you're reading a"
+ },
+ {
+ "start": 2699.84,
+ "duration": 0.0,
+ "text": "Sutskever. Um so, you're reading a murder<00:45:00.080> mystery<00:45:00.520> and<00:45:00.600> at<00:45:00.680> some<00:45:00.840> point<00:45:01.040> the"
+ },
+ {
+ "start": 2701.11,
+ "duration": 0.0,
+ "text": "murder mystery and at some point the"
+ },
+ {
+ "start": 2701.12,
+ "duration": 0.0,
+ "text": "murder mystery and at some point the text<00:45:01.359> reveals<00:45:01.680> the<00:45:01.720> identity<00:45:02.200> of<00:45:02.320> the"
+ },
+ {
+ "start": 2702.39,
+ "duration": 0.0,
+ "text": "text reveals the identity of the"
+ },
+ {
+ "start": 2702.4,
+ "duration": 0.0,
+ "text": "text reveals the identity of the criminal.<00:45:03.120> The<00:45:03.240> model<00:45:03.480> can<00:45:03.640> predict<00:45:04.240> the<00:45:04.320> name"
+ },
+ {
+ "start": 2704.87,
+ "duration": 0.0,
+ "text": "criminal. The model can predict the name"
+ },
+ {
+ "start": 2704.88,
+ "duration": 0.0,
+ "text": "criminal. The model can predict the name of<00:45:04.920> that<00:45:05.080> criminal,<00:45:05.440> then<00:45:05.600> it<00:45:05.680> must<00:45:05.840> have"
+ },
+ {
+ "start": 2705.99,
+ "duration": 0.0,
+ "text": "of that criminal, then it must have"
+ },
+ {
+ "start": 2706.0,
+ "duration": 0.0,
+ "text": "of that criminal, then it must have figured<00:45:06.280> out<00:45:06.440> who<00:45:06.600> perpetrated<00:45:07.080> the<00:45:07.160> murder"
+ },
+ {
+ "start": 2707.39,
+ "duration": 0.0,
+ "text": "figured out who perpetrated the murder"
+ },
+ {
+ "start": 2707.4,
+ "duration": 0.0,
+ "text": "figured out who perpetrated the murder from<00:45:07.560> the<00:45:07.640> evidence<00:45:07.920> provided.<00:45:08.680> And<00:45:08.800> the<00:45:08.880> key"
+ },
+ {
+ "start": 2709.15,
+ "duration": 0.0,
+ "text": "from the evidence provided. And the key"
+ },
+ {
+ "start": 2709.16,
+ "duration": 0.0,
+ "text": "from the evidence provided. And the key point<00:45:09.480> here<00:45:10.080> is<00:45:10.320> that<00:45:10.640> the<00:45:10.880> author<00:45:11.359> of<00:45:11.480> the"
+ },
+ {
+ "start": 2711.59,
+ "duration": 0.0,
+ "text": "point here is that the author of the"
+ },
+ {
+ "start": 2711.6,
+ "duration": 0.0,
+ "text": "point here is that the author of the book<00:45:12.400> may<00:45:12.560> not<00:45:13.080> have<00:45:13.440> needed<00:45:13.840> to<00:45:13.960> make<00:45:14.120> that"
+ },
+ {
+ "start": 2714.31,
+ "duration": 0.0,
+ "text": "book may not have needed to make that"
+ },
+ {
+ "start": 2714.32,
+ "duration": 0.0,
+ "text": "book may not have needed to make that same<00:45:14.560> induction.<00:45:15.520> Instead,<00:45:15.880> they<00:45:15.960> may<00:45:16.080> have"
+ },
+ {
+ "start": 2716.19,
+ "duration": 0.0,
+ "text": "same induction. Instead, they may have"
+ },
+ {
+ "start": 2716.2,
+ "duration": 0.0,
+ "text": "same induction. Instead, they may have decided<00:45:16.640> ahead<00:45:16.840> of<00:45:16.920> time<00:45:17.720> how<00:45:17.840> they're<00:45:17.960> going"
+ },
+ {
+ "start": 2718.07,
+ "duration": 0.0,
+ "text": "decided ahead of time how they're going"
+ },
+ {
+ "start": 2718.08,
+ "duration": 0.0,
+ "text": "decided ahead of time how they're going to<00:45:18.120> craft<00:45:18.320> the<00:45:18.400> story<00:45:18.920> in<00:45:19.000> terms<00:45:19.280> of<00:45:19.359> the"
+ },
+ {
+ "start": 2719.43,
+ "duration": 0.0,
+ "text": "to craft the story in terms of the"
+ },
+ {
+ "start": 2719.44,
+ "duration": 0.0,
+ "text": "to craft the story in terms of the murderer."
+ },
+ {
+ "start": 2720.47,
+ "duration": 0.0,
+ "text": "murderer."
+ },
+ {
+ "start": 2720.48,
+ "duration": 0.0,
+ "text": "murderer. Um<00:45:21.120> but<00:45:21.280> then<00:45:21.359> the<00:45:21.480> person<00:45:21.840> reading<00:45:22.160> the<00:45:22.240> book"
+ },
+ {
+ "start": 2722.67,
+ "duration": 0.0,
+ "text": "Um but then the person reading the book"
+ },
+ {
+ "start": 2722.68,
+ "duration": 0.0,
+ "text": "Um but then the person reading the book and<00:45:22.760> making<00:45:23.040> predictions<00:45:23.560> token<00:45:23.840> by<00:45:23.960> token"
+ },
+ {
+ "start": 2724.47,
+ "duration": 0.0,
+ "text": "and making predictions token by token"
+ },
+ {
+ "start": 2724.48,
+ "duration": 0.0,
+ "text": "and making predictions token by token does<00:45:24.720> have<00:45:24.880> to<00:45:24.960> do<00:45:25.080> this<00:45:25.200> induction.<00:45:25.640> So,"
+ },
+ {
+ "start": 2725.79,
+ "duration": 0.0,
+ "text": "does have to do this induction. So,"
+ },
+ {
+ "start": 2725.8,
+ "duration": 0.0,
+ "text": "does have to do this induction. So, there's<00:45:25.960> an<00:45:26.120> asymmetry<00:45:26.680> here<00:45:26.880> between<00:45:27.160> the"
+ },
+ {
+ "start": 2727.27,
+ "duration": 0.0,
+ "text": "there's an asymmetry here between the"
+ },
+ {
+ "start": 2727.28,
+ "duration": 0.0,
+ "text": "there's an asymmetry here between the two<00:45:27.440> tasks<00:45:27.960> required<00:45:28.400> by<00:45:28.480> the<00:45:28.600> person<00:45:28.840> who"
+ },
+ {
+ "start": 2728.95,
+ "duration": 0.0,
+ "text": "two tasks required by the person who"
+ },
+ {
+ "start": 2728.96,
+ "duration": 0.0,
+ "text": "two tasks required by the person who generated<00:45:29.359> the<00:45:29.440> data<00:45:30.040> and<00:45:30.120> the<00:45:30.200> person<00:45:30.520> who<00:45:30.680> is"
+ },
+ {
+ "start": 2730.79,
+ "duration": 0.0,
+ "text": "generated the data and the person who is"
+ },
+ {
+ "start": 2730.8,
+ "duration": 0.0,
+ "text": "generated the data and the person who is making<00:45:31.080> the<00:45:31.160> predictions<00:45:31.600> on<00:45:31.680> the<00:45:31.720> data.<00:45:32.480> And"
+ },
+ {
+ "start": 2732.59,
+ "duration": 0.0,
+ "text": "making the predictions on the data. And"
+ },
+ {
+ "start": 2732.6,
+ "duration": 0.0,
+ "text": "making the predictions on the data. And we<00:45:32.720> have<00:45:32.920> a<00:45:33.000> toy<00:45:33.240> attack<00:45:33.600> where<00:45:33.760> we<00:45:33.880> have<00:45:34.080> a"
+ },
+ {
+ "start": 2734.27,
+ "duration": 0.0,
+ "text": "we have a toy attack where we have a"
+ },
+ {
+ "start": 2734.28,
+ "duration": 0.0,
+ "text": "we have a toy attack where we have a experimental<00:45:34.760> analog<00:45:35.160> of<00:45:35.240> this<00:45:35.480> where<00:45:35.680> we<00:45:36.240> we"
+ },
+ {
+ "start": 2736.349,
+ "duration": 0.0,
+ "text": "experimental analog of this where we we"
+ },
+ {
+ "start": 2736.359,
+ "duration": 0.0,
+ "text": "experimental analog of this where we we have<00:45:36.520> some<00:45:36.680> state<00:45:37.000> n,<00:45:37.680> we<00:45:37.800> apply<00:45:38.120> it<00:45:38.240> through"
+ },
+ {
+ "start": 2738.39,
+ "duration": 0.0,
+ "text": "have some state n, we apply it through"
+ },
+ {
+ "start": 2738.4,
+ "duration": 0.0,
+ "text": "have some state n, we apply it through some<00:45:38.560> function<00:45:38.920> f,<00:45:39.560> and<00:45:39.720> then<00:45:39.880> also<00:45:40.240> we"
+ },
+ {
+ "start": 2740.349,
+ "duration": 0.0,
+ "text": "some function f, and then also we"
+ },
+ {
+ "start": 2740.359,
+ "duration": 0.0,
+ "text": "some function f, and then also we consider<00:45:40.840> a<00:45:40.920> version<00:45:41.320> where<00:45:41.520> we<00:45:41.680> remove<00:45:42.160> some"
+ },
+ {
+ "start": 2742.31,
+ "duration": 0.0,
+ "text": "consider a version where we remove some"
+ },
+ {
+ "start": 2742.32,
+ "duration": 0.0,
+ "text": "consider a version where we remove some of<00:45:42.400> the<00:45:42.480> information<00:45:43.040> from<00:45:43.320> the<00:45:43.440> original"
+ },
+ {
+ "start": 2743.75,
+ "duration": 0.0,
+ "text": "of the information from the original"
+ },
+ {
+ "start": 2743.76,
+ "duration": 0.0,
+ "text": "of the information from the original state.<00:45:44.320> And<00:45:44.440> then<00:45:44.560> we<00:45:44.680> make<00:45:44.840> predictions<00:45:45.600> with"
+ },
+ {
+ "start": 2745.75,
+ "duration": 0.0,
+ "text": "state. And then we make predictions with"
+ },
+ {
+ "start": 2745.76,
+ "duration": 0.0,
+ "text": "state. And then we make predictions with this"
+ },
+ {
+ "start": 2746.59,
+ "duration": 0.0,
+ "text": "this"
+ },
+ {
+ "start": 2746.6,
+ "duration": 0.0,
+ "text": "this uh<00:45:46.680> ablated<00:45:47.280> input<00:45:47.760> and<00:45:47.960> then<00:45:48.320> with<00:45:48.480> this"
+ },
+ {
+ "start": 2748.63,
+ "duration": 0.0,
+ "text": "uh ablated input and then with this"
+ },
+ {
+ "start": 2748.64,
+ "duration": 0.0,
+ "text": "uh ablated input and then with this output<00:45:48.880> of<00:45:48.960> this<00:45:49.120> function."
+ },
+ {
+ "start": 2750.99,
+ "duration": 0.0,
+ "text": "output of this function."
+ },
+ {
+ "start": 2751.0,
+ "duration": 0.0,
+ "text": "output of this function. Um<00:45:51.480> the<00:45:51.600> key<00:45:51.760> point<00:45:51.960> here<00:45:52.120> is<00:45:52.200> that<00:45:52.320> this"
+ },
+ {
+ "start": 2752.47,
+ "duration": 0.0,
+ "text": "Um the key point here is that this"
+ },
+ {
+ "start": 2752.48,
+ "duration": 0.0,
+ "text": "Um the key point here is that this function<00:45:52.800> f<00:45:53.000> is<00:45:53.120> not<00:45:53.320> so<00:45:53.440> hard<00:45:53.640> to<00:45:53.720> compute.<00:45:54.560> Um"
+ },
+ {
+ "start": 2755.23,
+ "duration": 0.0,
+ "text": "function f is not so hard to compute. Um"
+ },
+ {
+ "start": 2755.24,
+ "duration": 0.0,
+ "text": "function f is not so hard to compute. Um however,<00:45:55.960> uh<00:45:56.359> we<00:45:56.520> can<00:45:56.680> consider<00:45:57.080> what<00:45:57.240> happens"
+ },
+ {
+ "start": 2757.67,
+ "duration": 0.0,
+ "text": "however, uh we can consider what happens"
+ },
+ {
+ "start": 2757.68,
+ "duration": 0.0,
+ "text": "however, uh we can consider what happens as<00:45:58.040> the<00:45:58.480> f<00:45:58.760> inverse<00:45:59.640> is<00:46:00.080> hard<00:46:00.400> or<00:46:00.520> easy<00:46:00.680> to"
+ },
+ {
+ "start": 2760.75,
+ "duration": 0.0,
+ "text": "as the f inverse is hard or easy to"
+ },
+ {
+ "start": 2760.76,
+ "duration": 0.0,
+ "text": "as the f inverse is hard or easy to compute.<00:46:01.120> So,<00:46:01.280> here<00:46:01.480> we<00:46:01.600> have<00:46:01.680> an<00:46:01.760> example"
+ },
+ {
+ "start": 2762.11,
+ "duration": 0.0,
+ "text": "compute. So, here we have an example"
+ },
+ {
+ "start": 2762.12,
+ "duration": 0.0,
+ "text": "compute. So, here we have an example where<00:46:02.240> it's<00:46:02.400> hard<00:46:02.640> to<00:46:02.720> compute."
+ },
+ {
+ "start": 2764.43,
+ "duration": 0.0,
+ "text": "where it's hard to compute."
+ },
+ {
+ "start": 2764.44,
+ "duration": 0.0,
+ "text": "where it's hard to compute. And<00:46:04.560> what<00:46:04.680> we<00:46:04.800> see<00:46:05.040> is<00:46:05.200> that<00:46:05.400> actually<00:46:05.640> by"
+ },
+ {
+ "start": 2765.75,
+ "duration": 0.0,
+ "text": "And what we see is that actually by"
+ },
+ {
+ "start": 2765.76,
+ "duration": 0.0,
+ "text": "And what we see is that actually by removing<00:46:06.680> elements<00:46:07.240> of<00:46:07.320> the<00:46:07.440> input,"
+ },
+ {
+ "start": 2769.15,
+ "duration": 0.0,
+ "text": "removing elements of the input,"
+ },
+ {
+ "start": 2769.16,
+ "duration": 0.0,
+ "text": "removing elements of the input, now<00:46:09.720> the<00:46:09.840> model<00:46:10.240> has<00:46:10.480> to<00:46:10.600> do<00:46:10.800> this<00:46:10.960> induction"
+ },
+ {
+ "start": 2771.51,
+ "duration": 0.0,
+ "text": "now the model has to do this induction"
+ },
+ {
+ "start": 2771.52,
+ "duration": 0.0,
+ "text": "now the model has to do this induction over<00:46:11.800> what<00:46:12.040> was<00:46:12.320> the<00:46:12.440> input<00:46:12.760> that<00:46:12.880> is"
+ },
+ {
+ "start": 2772.95,
+ "duration": 0.0,
+ "text": "over what was the input that is"
+ },
+ {
+ "start": 2772.96,
+ "duration": 0.0,
+ "text": "over what was the input that is consistent<00:46:13.560> with<00:46:13.640> the<00:46:13.760> output<00:46:14.040> that<00:46:14.120> it's"
+ },
+ {
+ "start": 2774.23,
+ "duration": 0.0,
+ "text": "consistent with the output that it's"
+ },
+ {
+ "start": 2774.24,
+ "duration": 0.0,
+ "text": "consistent with the output that it's seen<00:46:14.600> so<00:46:14.760> far."
+ },
+ {
+ "start": 2775.67,
+ "duration": 0.0,
+ "text": "seen so far."
+ },
+ {
+ "start": 2775.68,
+ "duration": 0.0,
+ "text": "seen so far. And<00:46:15.880> this<00:46:16.560> um<00:46:16.800> leads<00:46:17.520> to<00:46:18.400> a<00:46:18.480> greater"
+ },
+ {
+ "start": 2778.95,
+ "duration": 0.0,
+ "text": "And this um leads to a greater"
+ },
+ {
+ "start": 2778.96,
+ "duration": 0.0,
+ "text": "And this um leads to a greater perplexity<00:46:20.080> in<00:46:20.200> the<00:46:20.280> model.<00:46:20.560> We<00:46:20.680> also<00:46:20.880> see"
+ },
+ {
+ "start": 2780.99,
+ "duration": 0.0,
+ "text": "perplexity in the model. We also see"
+ },
+ {
+ "start": 2781.0,
+ "duration": 0.0,
+ "text": "perplexity in the model. We also see some<00:46:21.200> other<00:46:21.400> interesting<00:46:21.720> behavior<00:46:22.120> of<00:46:22.480> uh"
+ },
+ {
+ "start": 2782.51,
+ "duration": 0.0,
+ "text": "some other interesting behavior of uh"
+ },
+ {
+ "start": 2782.52,
+ "duration": 0.0,
+ "text": "some other interesting behavior of uh basically<00:46:22.960> where<00:46:23.359> the<00:46:23.840> uh<00:46:24.240> the<00:46:24.359> learning<00:46:24.880> is"
+ },
+ {
+ "start": 2785.19,
+ "duration": 0.0,
+ "text": "basically where the uh the learning is"
+ },
+ {
+ "start": 2785.2,
+ "duration": 0.0,
+ "text": "basically where the uh the learning is pushed<00:46:25.520> out<00:46:25.960> exponentially<00:46:26.680> in<00:46:26.800> the<00:46:26.880> number"
+ },
+ {
+ "start": 2787.11,
+ "duration": 0.0,
+ "text": "pushed out exponentially in the number"
+ },
+ {
+ "start": 2787.12,
+ "duration": 0.0,
+ "text": "pushed out exponentially in the number of<00:46:27.200> bits<00:46:27.560> because<00:46:28.320> what<00:46:28.440> the<00:46:28.560> model<00:46:28.840> has<00:46:29.000> to<00:46:29.080> do"
+ },
+ {
+ "start": 2789.31,
+ "duration": 0.0,
+ "text": "of bits because what the model has to do"
+ },
+ {
+ "start": 2789.32,
+ "duration": 0.0,
+ "text": "of bits because what the model has to do is<00:46:29.560> is<00:46:29.760> really<00:46:30.040> just<00:46:30.320> a<00:46:30.560> a<00:46:30.640> brute<00:46:30.920> force<00:46:31.240> search"
+ },
+ {
+ "start": 2791.75,
+ "duration": 0.0,
+ "text": "is is really just a a brute force search"
+ },
+ {
+ "start": 2791.76,
+ "duration": 0.0,
+ "text": "is is really just a a brute force search over<00:46:32.280> what<00:46:32.480> are<00:46:32.680> the<00:46:32.760> missing<00:46:33.080> bits<00:46:33.400> in<00:46:33.520> the"
+ },
+ {
+ "start": 2793.59,
+ "duration": 0.0,
+ "text": "over what are the missing bits in the"
+ },
+ {
+ "start": 2793.6,
+ "duration": 0.0,
+ "text": "over what are the missing bits in the input."
+ },
+ {
+ "start": 2794.79,
+ "duration": 0.0,
+ "text": "input."
+ },
+ {
+ "start": 2794.8,
+ "duration": 0.0,
+ "text": "input. Um<00:46:34.960> but<00:46:35.080> again,<00:46:35.320> you<00:46:35.920> you<00:46:36.040> have<00:46:36.160> this"
+ },
+ {
+ "start": 2796.31,
+ "duration": 0.0,
+ "text": "Um but again, you you have this"
+ },
+ {
+ "start": 2796.32,
+ "duration": 0.0,
+ "text": "Um but again, you you have this asymmetry<00:46:36.760> where<00:46:37.120> this<00:46:37.280> masking<00:46:37.680> function<00:46:38.000> is"
+ },
+ {
+ "start": 2798.11,
+ "duration": 0.0,
+ "text": "asymmetry where this masking function is"
+ },
+ {
+ "start": 2798.12,
+ "duration": 0.0,
+ "text": "asymmetry where this masking function is a<00:46:38.160> very<00:46:38.320> simple<00:46:38.560> function.<00:46:38.920> This<00:46:39.120> f<00:46:39.280> is<00:46:39.400> a<00:46:39.440> very"
+ },
+ {
+ "start": 2799.59,
+ "duration": 0.0,
+ "text": "a very simple function. This f is a very"
+ },
+ {
+ "start": 2799.6,
+ "duration": 0.0,
+ "text": "a very simple function. This f is a very simple<00:46:39.840> function.<00:46:40.480> But<00:46:40.640> somehow<00:46:41.400> what<00:46:41.520> the"
+ },
+ {
+ "start": 2801.63,
+ "duration": 0.0,
+ "text": "simple function. But somehow what the"
+ },
+ {
+ "start": 2801.64,
+ "duration": 0.0,
+ "text": "simple function. But somehow what the model<00:46:42.000> with<00:46:42.280> where<00:46:43.160> it's<00:46:43.400> training<00:46:43.640> on<00:46:43.720> this"
+ },
+ {
+ "start": 2803.83,
+ "duration": 0.0,
+ "text": "model with where it's training on this"
+ },
+ {
+ "start": 2803.84,
+ "duration": 0.0,
+ "text": "model with where it's training on this data,<00:46:44.120> it<00:46:44.280> has<00:46:44.400> to<00:46:44.480> learn<00:46:44.640> something<00:46:44.920> more"
+ },
+ {
+ "start": 2805.07,
+ "duration": 0.0,
+ "text": "data, it has to learn something more"
+ },
+ {
+ "start": 2805.08,
+ "duration": 0.0,
+ "text": "data, it has to learn something more complex."
+ },
+ {
+ "start": 2806.59,
+ "duration": 0.0,
+ "text": "complex."
+ },
+ {
+ "start": 2806.6,
+ "duration": 0.0,
+ "text": "complex. And<00:46:46.720> same<00:46:46.920> with<00:46:47.040> this<00:46:47.160> example<00:46:47.480> here,"
+ },
+ {
+ "start": 2808.39,
+ "duration": 0.0,
+ "text": "And same with this example here,"
+ },
+ {
+ "start": 2808.4,
+ "duration": 0.0,
+ "text": "And same with this example here, um<00:46:48.640> although<00:46:48.840> this<00:46:49.040> example<00:46:49.400> is<00:46:49.520> one<00:46:49.680> where"
+ },
+ {
+ "start": 2809.83,
+ "duration": 0.0,
+ "text": "um although this example is one where"
+ },
+ {
+ "start": 2809.84,
+ "duration": 0.0,
+ "text": "um although this example is one where we've<00:46:50.000> made<00:46:50.440> the<00:46:50.520> induction<00:46:50.880> problem<00:46:51.160> much"
+ },
+ {
+ "start": 2811.39,
+ "duration": 0.0,
+ "text": "we've made the induction problem much"
+ },
+ {
+ "start": 2811.4,
+ "duration": 0.0,
+ "text": "we've made the induction problem much easier,<00:46:52.080> there's<00:46:52.280> still<00:46:52.560> an<00:46:52.680> asymmetry<00:46:53.120> which"
+ },
+ {
+ "start": 2813.27,
+ "duration": 0.0,
+ "text": "easier, there's still an asymmetry which"
+ },
+ {
+ "start": 2813.28,
+ "duration": 0.0,
+ "text": "easier, there's still an asymmetry which I<00:46:53.320> mean<00:46:53.440> there's<00:46:53.600> still,<00:46:53.960> you<00:46:54.040> know,<00:46:54.520> a"
+ },
+ {
+ "start": 2814.95,
+ "duration": 0.0,
+ "text": "I mean there's still, you know, a"
+ },
+ {
+ "start": 2814.96,
+ "duration": 0.0,
+ "text": "I mean there's still, you know, a interesting<00:46:55.400> inverse<00:46:55.720> to<00:46:55.840> learn,<00:46:56.359> but<00:46:56.520> it's"
+ },
+ {
+ "start": 2816.71,
+ "duration": 0.0,
+ "text": "interesting inverse to learn, but it's"
+ },
+ {
+ "start": 2816.72,
+ "duration": 0.0,
+ "text": "interesting inverse to learn, but it's no<00:46:56.880> longer<00:46:57.320> pushing<00:46:57.680> out<00:46:58.000> the<00:46:58.560> where<00:46:58.720> that"
+ },
+ {
+ "start": 2818.87,
+ "duration": 0.0,
+ "text": "no longer pushing out the where that"
+ },
+ {
+ "start": 2818.88,
+ "duration": 0.0,
+ "text": "no longer pushing out the where that learning<00:46:59.120> happens<00:46:59.520> exponentially."
+ },
+ {
+ "start": 2820.71,
+ "duration": 0.0,
+ "text": "learning happens exponentially."
+ },
+ {
+ "start": 2820.72,
+ "duration": 0.0,
+ "text": "learning happens exponentially. Um<00:47:01.080> and<00:47:01.240> instead<00:47:01.560> again,<00:47:01.800> we<00:47:01.920> find<00:47:02.160> this"
+ },
+ {
+ "start": 2822.63,
+ "duration": 0.0,
+ "text": "Um and instead again, we find this"
+ },
+ {
+ "start": 2822.64,
+ "duration": 0.0,
+ "text": "Um and instead again, we find this increase<00:47:03.000> in<00:47:03.080> perplexity<00:47:03.720> as<00:47:03.960> we"
+ },
+ {
+ "start": 2825.03,
+ "duration": 0.0,
+ "text": "increase in perplexity as we"
+ },
+ {
+ "start": 2825.04,
+ "duration": 0.0,
+ "text": "increase in perplexity as we as<00:47:05.200> we<00:47:05.280> actually<00:47:05.560> remove<00:47:06.080> information<00:47:06.520> from"
+ },
+ {
+ "start": 2826.63,
+ "duration": 0.0,
+ "text": "as we actually remove information from"
+ },
+ {
+ "start": 2826.64,
+ "duration": 0.0,
+ "text": "as we actually remove information from the<00:47:06.720> input."
+ },
+ {
+ "start": 2828.39,
+ "duration": 0.0,
+ "text": "the input."
+ },
+ {
+ "start": 2828.4,
+ "duration": 0.0,
+ "text": "the input. And<00:47:08.560> then<00:47:08.760> another<00:47:09.120> really<00:47:09.400> interesting"
+ },
+ {
+ "start": 2829.75,
+ "duration": 0.0,
+ "text": "And then another really interesting"
+ },
+ {
+ "start": 2829.76,
+ "duration": 0.0,
+ "text": "And then another really interesting example,<00:47:10.440> um"
+ },
+ {
+ "start": 2831.75,
+ "duration": 0.0,
+ "text": "example, um"
+ },
+ {
+ "start": 2831.76,
+ "duration": 0.0,
+ "text": "example, um uh<00:47:11.960> going<00:47:12.240> back<00:47:12.520> to<00:47:12.640> the<00:47:12.720> cellular<00:47:12.920> automaton"
+ },
+ {
+ "start": 2833.87,
+ "duration": 0.0,
+ "text": "uh going back to the cellular automaton"
+ },
+ {
+ "start": 2833.88,
+ "duration": 0.0,
+ "text": "uh going back to the cellular automaton is<00:47:14.520> um"
+ },
+ {
+ "start": 2835.47,
+ "duration": 0.0,
+ "text": "is um"
+ },
+ {
+ "start": 2835.48,
+ "duration": 0.0,
+ "text": "is um uh<00:47:15.600> right,<00:47:15.840> is<00:47:16.240> is<00:47:16.560> is<00:47:16.680> thinking<00:47:16.920> about"
+ },
+ {
+ "start": 2837.11,
+ "duration": 0.0,
+ "text": "uh right, is is is thinking about"
+ },
+ {
+ "start": 2837.12,
+ "duration": 0.0,
+ "text": "uh right, is is is thinking about emergent<00:47:17.440> phenomena."
+ },
+ {
+ "start": 2839.43,
+ "duration": 0.0,
+ "text": "emergent phenomena."
+ },
+ {
+ "start": 2839.44,
+ "duration": 0.0,
+ "text": "emergent phenomena. So,<00:47:20.200> um<00:47:20.600> you<00:47:20.680> know,<00:47:20.760> there's<00:47:20.880> a<00:47:20.920> lot<00:47:21.080> to<00:47:21.160> say"
+ },
+ {
+ "start": 2841.31,
+ "duration": 0.0,
+ "text": "So, um you know, there's a lot to say"
+ },
+ {
+ "start": 2841.32,
+ "duration": 0.0,
+ "text": "So, um you know, there's a lot to say here<00:47:21.800> and<00:47:22.520> I<00:47:22.560> probably<00:47:22.720> won't<00:47:22.880> have<00:47:23.000> time<00:47:23.160> to"
+ },
+ {
+ "start": 2843.23,
+ "duration": 0.0,
+ "text": "here and I probably won't have time to"
+ },
+ {
+ "start": 2843.24,
+ "duration": 0.0,
+ "text": "here and I probably won't have time to say<00:47:23.359> all<00:47:23.560> of<00:47:23.640> it,<00:47:23.920> um<00:47:24.320> but<00:47:25.240> I<00:47:25.320> think<00:47:25.840> it<00:47:26.000> is"
+ },
+ {
+ "start": 2846.23,
+ "duration": 0.0,
+ "text": "say all of it, um but I think it is"
+ },
+ {
+ "start": 2846.24,
+ "duration": 0.0,
+ "text": "say all of it, um but I think it is interesting<00:47:26.840> reflecting<00:47:27.359> on<00:47:27.440> the<00:47:27.520> fact<00:47:27.840> that"
+ },
+ {
+ "start": 2848.55,
+ "duration": 0.0,
+ "text": "interesting reflecting on the fact that"
+ },
+ {
+ "start": 2848.56,
+ "duration": 0.0,
+ "text": "interesting reflecting on the fact that uh"
+ },
+ {
+ "start": 2850.07,
+ "duration": 0.0,
+ "text": "uh"
+ },
+ {
+ "start": 2850.08,
+ "duration": 0.0,
+ "text": "uh we"
+ },
+ {
+ "start": 2851.27,
+ "duration": 0.0,
+ "text": "we"
+ },
+ {
+ "start": 2851.28,
+ "duration": 0.0,
+ "text": "we uh<00:47:31.359> right,<00:47:31.520> with<00:47:31.640> a<00:47:31.680> game<00:47:31.880> like<00:47:32.400> uh<00:47:32.480> game<00:47:32.640> of"
+ },
+ {
+ "start": 2852.75,
+ "duration": 0.0,
+ "text": "uh right, with a game like uh game of"
+ },
+ {
+ "start": 2852.76,
+ "duration": 0.0,
+ "text": "uh right, with a game like uh game of life,<00:47:33.320> right?<00:47:33.520> We<00:47:33.640> have"
+ },
+ {
+ "start": 2854.75,
+ "duration": 0.0,
+ "text": "life, right? We have"
+ },
+ {
+ "start": 2854.76,
+ "duration": 0.0,
+ "text": "life, right? We have uh<00:47:34.920> we<00:47:35.040> can<00:47:35.160> observe<00:47:35.440> all<00:47:35.560> these<00:47:35.720> different"
+ },
+ {
+ "start": 2856.59,
+ "duration": 0.0,
+ "text": "uh we can observe all these different"
+ },
+ {
+ "start": 2856.6,
+ "duration": 0.0,
+ "text": "uh we can observe all these different patterns<00:47:36.960> and<00:47:37.240> and<00:47:37.400> persistent<00:47:37.800> structures"
+ },
+ {
+ "start": 2858.349,
+ "duration": 0.0,
+ "text": "patterns and and persistent structures"
+ },
+ {
+ "start": 2858.359,
+ "duration": 0.0,
+ "text": "patterns and and persistent structures like,<00:47:38.560> you<00:47:38.640> know,<00:47:38.720> these<00:47:38.800> still<00:47:39.000> lives<00:47:39.280> and"
+ },
+ {
+ "start": 2859.39,
+ "duration": 0.0,
+ "text": "like, you know, these still lives and"
+ },
+ {
+ "start": 2859.4,
+ "duration": 0.0,
+ "text": "like, you know, these still lives and oscillators<00:47:40.000> and<00:47:40.080> spaceships."
+ },
+ {
+ "start": 2862.07,
+ "duration": 0.0,
+ "text": "oscillators and spaceships."
+ },
+ {
+ "start": 2862.08,
+ "duration": 0.0,
+ "text": "oscillators and spaceships. And"
+ },
+ {
+ "start": 2863.43,
+ "duration": 0.0,
+ "text": "And"
+ },
+ {
+ "start": 2863.44,
+ "duration": 0.0,
+ "text": "And with<00:47:43.680> large<00:47:44.040> compute,<00:47:44.880> we<00:47:45.120> can<00:47:45.600> if<00:47:45.720> we're"
+ },
+ {
+ "start": 2865.83,
+ "duration": 0.0,
+ "text": "with large compute, we can if we're"
+ },
+ {
+ "start": 2865.84,
+ "duration": 0.0,
+ "text": "with large compute, we can if we're imagining<00:47:46.640> predicting<00:47:47.320> the<00:47:47.480> final<00:47:47.840> state"
+ },
+ {
+ "start": 2868.19,
+ "duration": 0.0,
+ "text": "imagining predicting the final state"
+ },
+ {
+ "start": 2868.2,
+ "duration": 0.0,
+ "text": "imagining predicting the final state from<00:47:48.400> the<00:47:48.440> initial<00:47:48.760> state<00:47:49.320> um<00:47:49.640> after<00:47:50.160> the"
+ },
+ {
+ "start": 2870.27,
+ "duration": 0.0,
+ "text": "from the initial state um after the"
+ },
+ {
+ "start": 2870.28,
+ "duration": 0.0,
+ "text": "from the initial state um after the final<00:47:50.480> state<00:47:50.640> after<00:47:50.800> many<00:47:51.080> steps<00:47:51.520> after<00:47:51.720> the"
+ },
+ {
+ "start": 2871.75,
+ "duration": 0.0,
+ "text": "final state after many steps after the"
+ },
+ {
+ "start": 2871.76,
+ "duration": 0.0,
+ "text": "final state after many steps after the initial<00:47:52.000> state.<00:47:52.520> With<00:47:52.720> large<00:47:53.040> compute,<00:47:53.400> we"
+ },
+ {
+ "start": 2873.51,
+ "duration": 0.0,
+ "text": "initial state. With large compute, we"
+ },
+ {
+ "start": 2873.52,
+ "duration": 0.0,
+ "text": "initial state. With large compute, we can<00:47:53.720> run<00:47:54.359> the<00:47:55.000> the<00:47:55.160> rule<00:47:55.480> directly,<00:47:56.160> right?<00:47:56.400> We"
+ },
+ {
+ "start": 2876.55,
+ "duration": 0.0,
+ "text": "can run the the rule directly, right? We"
+ },
+ {
+ "start": 2876.56,
+ "duration": 0.0,
+ "text": "can run the the rule directly, right? We can<00:47:56.760> expect<00:47:57.160> our<00:47:57.560> our<00:47:58.080> language<00:47:58.440> model<00:47:58.680> to"
+ },
+ {
+ "start": 2878.79,
+ "duration": 0.0,
+ "text": "can expect our our language model to"
+ },
+ {
+ "start": 2878.8,
+ "duration": 0.0,
+ "text": "can expect our our language model to implement<00:47:59.200> it<00:47:59.440> and<00:47:59.680> run<00:47:59.840> it."
+ },
+ {
+ "start": 2881.07,
+ "duration": 0.0,
+ "text": "implement it and run it."
+ },
+ {
+ "start": 2881.08,
+ "duration": 0.0,
+ "text": "implement it and run it. And<00:48:01.240> then<00:48:01.520> we<00:48:01.600> don't<00:48:01.920> need<00:48:02.320> to<00:48:02.440> have<00:48:02.600> a<00:48:02.680> complex"
+ },
+ {
+ "start": 2883.15,
+ "duration": 0.0,
+ "text": "And then we don't need to have a complex"
+ },
+ {
+ "start": 2883.16,
+ "duration": 0.0,
+ "text": "And then we don't need to have a complex model<00:48:03.560> to<00:48:03.840> perfectly<00:48:04.400> fit<00:48:04.720> the<00:48:04.840> predictions."
+ },
+ {
+ "start": 2886.03,
+ "duration": 0.0,
+ "text": "model to perfectly fit the predictions."
+ },
+ {
+ "start": 2886.04,
+ "duration": 0.0,
+ "text": "model to perfectly fit the predictions. But<00:48:06.160> with<00:48:06.280> limited<00:48:06.640> compute,<00:48:07.760> you<00:48:08.240> with"
+ },
+ {
+ "start": 2888.43,
+ "duration": 0.0,
+ "text": "But with limited compute, you with"
+ },
+ {
+ "start": 2888.44,
+ "duration": 0.0,
+ "text": "But with limited compute, you with compute<00:48:08.760> that<00:48:08.880> is<00:48:08.960> not<00:48:09.240> enough<00:48:09.440> to<00:48:09.600> run<00:48:09.800> it,"
+ },
+ {
+ "start": 2890.03,
+ "duration": 0.0,
+ "text": "compute that is not enough to run it,"
+ },
+ {
+ "start": 2890.04,
+ "duration": 0.0,
+ "text": "compute that is not enough to run it, then<00:48:10.240> you<00:48:10.320> have<00:48:10.440> to<00:48:10.520> do<00:48:10.640> something"
+ },
+ {
+ "start": 2890.87,
+ "duration": 0.0,
+ "text": "then you have to do something"
+ },
+ {
+ "start": 2890.88,
+ "duration": 0.0,
+ "text": "then you have to do something interesting,<00:48:11.720> right?<00:48:12.200> And<00:48:12.640> you<00:48:12.720> can<00:48:12.840> have"
+ },
+ {
+ "start": 2892.95,
+ "duration": 0.0,
+ "text": "interesting, right? And you can have"
+ },
+ {
+ "start": 2892.96,
+ "duration": 0.0,
+ "text": "interesting, right? And you can have very<00:48:13.160> much<00:48:13.400> you<00:48:13.480> can<00:48:13.600> imagine<00:48:14.160> how<00:48:14.760> a<00:48:14.800> model"
+ },
+ {
+ "start": 2895.15,
+ "duration": 0.0,
+ "text": "very much you can imagine how a model"
+ },
+ {
+ "start": 2895.16,
+ "duration": 0.0,
+ "text": "very much you can imagine how a model here<00:48:15.480> is<00:48:16.080> um"
+ },
+ {
+ "start": 2897.23,
+ "duration": 0.0,
+ "text": "here is um"
+ },
+ {
+ "start": 2897.24,
+ "duration": 0.0,
+ "text": "here is um basically<00:48:17.680> looking<00:48:18.040> at<00:48:18.240> what<00:48:19.000> structures<00:48:19.560> are"
+ },
+ {
+ "start": 2899.83,
+ "duration": 0.0,
+ "text": "basically looking at what structures are"
+ },
+ {
+ "start": 2899.84,
+ "duration": 0.0,
+ "text": "basically looking at what structures are in<00:48:20.000> the<00:48:20.080> input,"
+ },
+ {
+ "start": 2901.47,
+ "duration": 0.0,
+ "text": "in the input,"
+ },
+ {
+ "start": 2901.48,
+ "duration": 0.0,
+ "text": "in the input, trying<00:48:22.080> to"
+ },
+ {
+ "start": 2903.15,
+ "duration": 0.0,
+ "text": "trying to"
+ },
+ {
+ "start": 2903.16,
+ "duration": 0.0,
+ "text": "trying to uh"
+ },
+ {
+ "start": 2903.79,
+ "duration": 0.0,
+ "text": "uh"
+ },
+ {
+ "start": 2903.8,
+ "duration": 0.0,
+ "text": "uh relate<00:48:24.160> that<00:48:24.400> to<00:48:24.520> a<00:48:24.560> bank<00:48:25.120> of<00:48:25.320> these<00:48:25.480> different"
+ },
+ {
+ "start": 2905.71,
+ "duration": 0.0,
+ "text": "relate that to a bank of these different"
+ },
+ {
+ "start": 2905.72,
+ "duration": 0.0,
+ "text": "relate that to a bank of these different persistent<00:48:26.160> structures<00:48:26.680> that<00:48:26.800> each<00:48:26.960> have"
+ },
+ {
+ "start": 2907.07,
+ "duration": 0.0,
+ "text": "persistent structures that each have"
+ },
+ {
+ "start": 2907.08,
+ "duration": 0.0,
+ "text": "persistent structures that each have their<00:48:27.200> own<00:48:27.280> properties.<00:48:27.720> Some<00:48:27.880> of<00:48:27.960> them"
+ },
+ {
+ "start": 2908.11,
+ "duration": 0.0,
+ "text": "their own properties. Some of them"
+ },
+ {
+ "start": 2908.12,
+ "duration": 0.0,
+ "text": "their own properties. Some of them generate<00:48:29.040> other<00:48:29.320> structures,<00:48:30.160> some<00:48:30.320> of<00:48:30.400> them"
+ },
+ {
+ "start": 2910.51,
+ "duration": 0.0,
+ "text": "generate other structures, some of them"
+ },
+ {
+ "start": 2910.52,
+ "duration": 0.0,
+ "text": "generate other structures, some of them move<00:48:30.760> in<00:48:30.840> a<00:48:30.880> certain<00:48:31.080> direction,<00:48:31.640> right?<00:48:32.080> And"
+ },
+ {
+ "start": 2912.19,
+ "duration": 0.0,
+ "text": "move in a certain direction, right? And"
+ },
+ {
+ "start": 2912.2,
+ "duration": 0.0,
+ "text": "move in a certain direction, right? And then<00:48:32.400> trying<00:48:32.640> to<00:48:32.960> think<00:48:33.200> about,<00:48:33.440> \"Okay,<00:48:33.680> well,"
+ },
+ {
+ "start": 2914.39,
+ "duration": 0.0,
+ "text": "then trying to think about, \"Okay, well,"
+ },
+ {
+ "start": 2914.4,
+ "duration": 0.0,
+ "text": "then trying to think about, \"Okay, well, we<00:48:34.520> have<00:48:34.640> this<00:48:34.800> one<00:48:35.000> which<00:48:35.160> goes<00:48:35.320> in<00:48:35.359> this<00:48:35.720> this"
+ },
+ {
+ "start": 2915.87,
+ "duration": 0.0,
+ "text": "we have this one which goes in this this"
+ },
+ {
+ "start": 2915.88,
+ "duration": 0.0,
+ "text": "we have this one which goes in this this direction.<00:48:36.400> We<00:48:36.440> have<00:48:36.520> this<00:48:36.680> one<00:48:36.840> which<00:48:36.960> stays"
+ },
+ {
+ "start": 2917.15,
+ "duration": 0.0,
+ "text": "direction. We have this one which stays"
+ },
+ {
+ "start": 2917.16,
+ "duration": 0.0,
+ "text": "direction. We have this one which stays still,<00:48:37.640> right?\"<00:48:38.440> Hmm,<00:48:38.720> there's<00:48:38.880> going<00:48:39.000> to<00:48:39.080> be"
+ },
+ {
+ "start": 2919.11,
+ "duration": 0.0,
+ "text": "still, right?\" Hmm, there's going to be"
+ },
+ {
+ "start": 2919.12,
+ "duration": 0.0,
+ "text": "still, right?\" Hmm, there's going to be a<00:48:39.200> collision<00:48:39.640> between<00:48:39.920> these<00:48:40.080> two.<00:48:40.520> This<00:48:40.800> kind"
+ },
+ {
+ "start": 2921.03,
+ "duration": 0.0,
+ "text": "a collision between these two. This kind"
+ },
+ {
+ "start": 2921.04,
+ "duration": 0.0,
+ "text": "a collision between these two. This kind of<00:48:41.120> prediction<00:48:41.800> can<00:48:41.960> be<00:48:42.120> done"
+ },
+ {
+ "start": 2923.43,
+ "duration": 0.0,
+ "text": "of prediction can be done"
+ },
+ {
+ "start": 2923.44,
+ "duration": 0.0,
+ "text": "of prediction can be done with<00:48:43.720> much<00:48:43.960> less<00:48:44.200> compute<00:48:44.880> than<00:48:45.040> running<00:48:45.400> the"
+ },
+ {
+ "start": 2925.51,
+ "duration": 0.0,
+ "text": "with much less compute than running the"
+ },
+ {
+ "start": 2925.52,
+ "duration": 0.0,
+ "text": "with much less compute than running the full<00:48:45.720> grid."
+ },
+ {
+ "start": 2927.79,
+ "duration": 0.0,
+ "text": "full grid."
+ },
+ {
+ "start": 2927.8,
+ "duration": 0.0,
+ "text": "full grid. Um"
+ },
+ {
+ "start": 2929.87,
+ "duration": 0.0,
+ "text": "Um"
+ },
+ {
+ "start": 2929.88,
+ "duration": 0.0,
+ "text": "Um and<00:48:50.920> it's<00:48:51.280> not<00:48:51.600> going<00:48:51.720> to<00:48:51.800> be<00:48:52.200> you're<00:48:52.280> not"
+ },
+ {
+ "start": 2932.39,
+ "duration": 0.0,
+ "text": "and it's not going to be you're not"
+ },
+ {
+ "start": 2932.4,
+ "duration": 0.0,
+ "text": "and it's not going to be you're not going<00:48:52.520> to<00:48:52.560> be<00:48:52.640> able<00:48:52.760> to<00:48:52.800> make<00:48:52.880> perfect"
+ },
+ {
+ "start": 2933.19,
+ "duration": 0.0,
+ "text": "going to be able to make perfect"
+ },
+ {
+ "start": 2933.2,
+ "duration": 0.0,
+ "text": "going to be able to make perfect predictions<00:48:53.640> this<00:48:53.840> way,<00:48:54.640> but<00:48:55.680> what<00:48:55.840> you<00:48:56.000> are"
+ },
+ {
+ "start": 2936.31,
+ "duration": 0.0,
+ "text": "predictions this way, but what you are"
+ },
+ {
+ "start": 2936.32,
+ "duration": 0.0,
+ "text": "predictions this way, but what you are going<00:48:56.480> to<00:48:56.560> have<00:48:57.120> is"
+ },
+ {
+ "start": 2938.27,
+ "duration": 0.0,
+ "text": "going to have is"
+ },
+ {
+ "start": 2938.28,
+ "duration": 0.0,
+ "text": "going to have is a<00:48:58.359> lots<00:48:58.840> of<00:48:58.960> interesting<00:48:59.440> structures<00:48:59.960> within"
+ },
+ {
+ "start": 2940.15,
+ "duration": 0.0,
+ "text": "a lots of interesting structures within"
+ },
+ {
+ "start": 2940.16,
+ "duration": 0.0,
+ "text": "a lots of interesting structures within this<00:49:00.320> model.<00:49:01.040> So,<00:49:01.160> what<00:49:01.280> we<00:49:01.359> should<00:49:01.480> expect<00:49:01.880> is"
+ },
+ {
+ "start": 2941.95,
+ "duration": 0.0,
+ "text": "this model. So, what we should expect is"
+ },
+ {
+ "start": 2941.96,
+ "duration": 0.0,
+ "text": "this model. So, what we should expect is actually<00:49:02.480> with<00:49:02.640> limited<00:49:03.000> compute,<00:49:03.520> we<00:49:03.600> should"
+ },
+ {
+ "start": 2943.75,
+ "duration": 0.0,
+ "text": "actually with limited compute, we should"
+ },
+ {
+ "start": 2943.76,
+ "duration": 0.0,
+ "text": "actually with limited compute, we should have<00:49:03.880> a<00:49:04.000> higher<00:49:04.680> perplexity<00:49:05.560> for<00:49:05.640> this<00:49:05.760> data"
+ },
+ {
+ "start": 2946.27,
+ "duration": 0.0,
+ "text": "have a higher perplexity for this data"
+ },
+ {
+ "start": 2946.28,
+ "duration": 0.0,
+ "text": "have a higher perplexity for this data than<00:49:06.560> with<00:49:06.720> very<00:49:06.880> large<00:49:07.120> compute."
+ },
+ {
+ "start": 2948.91,
+ "duration": 0.0,
+ "text": "than with very large compute."
+ },
+ {
+ "start": 2948.92,
+ "duration": 0.0,
+ "text": "than with very large compute. So,<00:49:09.040> we<00:49:09.160> set<00:49:09.320> out<00:49:09.480> to<00:49:10.040> um<00:49:10.120> to<00:49:10.240> try<00:49:10.560> to"
+ },
+ {
+ "start": 2950.75,
+ "duration": 0.0,
+ "text": "So, we set out to um to try to"
+ },
+ {
+ "start": 2950.76,
+ "duration": 0.0,
+ "text": "So, we set out to um to try to experimentally<00:49:11.320> measure<00:49:11.560> this.<00:49:12.359> Um<00:49:12.840> we<00:49:13.000> have"
+ },
+ {
+ "start": 2953.11,
+ "duration": 0.0,
+ "text": "experimentally measure this. Um we have"
+ },
+ {
+ "start": 2953.12,
+ "duration": 0.0,
+ "text": "experimentally measure this. Um we have a<00:49:13.160> very<00:49:13.359> toy<00:49:13.520> set<00:49:13.680> up<00:49:13.800> here,<00:49:14.080> which<00:49:14.280> is<00:49:14.359> just"
+ },
+ {
+ "start": 2954.63,
+ "duration": 0.0,
+ "text": "a very toy set up here, which is just"
+ },
+ {
+ "start": 2954.64,
+ "duration": 0.0,
+ "text": "a very toy set up here, which is just using<00:49:15.240> again<00:49:15.600> a<00:49:15.680> one-dimensional<00:49:16.440> cellular"
+ },
+ {
+ "start": 2956.67,
+ "duration": 0.0,
+ "text": "using again a one-dimensional cellular"
+ },
+ {
+ "start": 2956.68,
+ "duration": 0.0,
+ "text": "using again a one-dimensional cellular automaton.<00:49:17.040> We'd<00:49:17.160> like<00:49:17.280> to<00:49:17.359> repeat<00:49:17.600> this<00:49:17.880> for"
+ },
+ {
+ "start": 2958.15,
+ "duration": 0.0,
+ "text": "automaton. We'd like to repeat this for"
+ },
+ {
+ "start": 2958.16,
+ "duration": 0.0,
+ "text": "automaton. We'd like to repeat this for a<00:49:18.200> more<00:49:18.400> complex<00:49:18.800> one.<00:49:19.520> Um<00:49:19.880> but<00:49:20.040> again,<00:49:20.280> with"
+ },
+ {
+ "start": 2960.39,
+ "duration": 0.0,
+ "text": "a more complex one. Um but again, with"
+ },
+ {
+ "start": 2960.4,
+ "duration": 0.0,
+ "text": "a more complex one. Um but again, with the<00:49:20.840> this<00:49:21.080> this<00:49:21.280> rule<00:49:21.400> 54.<00:49:22.440> And<00:49:22.560> then<00:49:22.680> we<00:49:22.800> use<00:49:23.240> a"
+ },
+ {
+ "start": 2963.27,
+ "duration": 0.0,
+ "text": "the this this rule 54. And then we use a"
+ },
+ {
+ "start": 2963.28,
+ "duration": 0.0,
+ "text": "the this this rule 54. And then we use a version<00:49:23.760> of<00:49:23.920> a<00:49:24.000> loop<00:49:24.240> transformer<00:49:25.280> so<00:49:25.600> that<00:49:26.640> um"
+ },
+ {
+ "start": 2967.31,
+ "duration": 0.0,
+ "text": "version of a loop transformer so that um"
+ },
+ {
+ "start": 2967.32,
+ "duration": 0.0,
+ "text": "version of a loop transformer so that um if<00:49:27.720> we<00:49:27.960> find<00:49:29.120> a<00:49:29.359> neural<00:49:29.600> network<00:49:29.960> that<00:49:30.120> does"
+ },
+ {
+ "start": 2970.51,
+ "duration": 0.0,
+ "text": "if we find a neural network that does"
+ },
+ {
+ "start": 2970.52,
+ "duration": 0.0,
+ "text": "if we find a neural network that does fit<00:49:31.160> this<00:49:31.359> rule<00:49:31.520> directly,<00:49:32.080> that<00:49:32.280> it<00:49:32.400> can"
+ },
+ {
+ "start": 2972.55,
+ "duration": 0.0,
+ "text": "fit this rule directly, that it can"
+ },
+ {
+ "start": 2972.56,
+ "duration": 0.0,
+ "text": "fit this rule directly, that it can actually<00:49:32.840> be<00:49:32.920> simple."
+ },
+ {
+ "start": 2974.03,
+ "duration": 0.0,
+ "text": "actually be simple."
+ },
+ {
+ "start": 2974.04,
+ "duration": 0.0,
+ "text": "actually be simple. We<00:49:34.200> include<00:49:34.520> this<00:49:34.640> in<00:49:34.720> the<00:49:34.800> hypothesis<00:49:35.240> space."
+ },
+ {
+ "start": 2976.15,
+ "duration": 0.0,
+ "text": "We include this in the hypothesis space."
+ },
+ {
+ "start": 2976.16,
+ "duration": 0.0,
+ "text": "We include this in the hypothesis space. And<00:49:36.280> what<00:49:36.400> we<00:49:36.480> find<00:49:36.800> is<00:49:36.960> that<00:49:37.120> at<00:49:37.240> some"
+ },
+ {
+ "start": 2977.51,
+ "duration": 0.0,
+ "text": "And what we find is that at some"
+ },
+ {
+ "start": 2977.52,
+ "duration": 0.0,
+ "text": "And what we find is that at some threshold<00:49:38.200> for<00:49:38.360> compute,<00:49:39.520> the<00:49:39.760> optimal"
+ },
+ {
+ "start": 2980.67,
+ "duration": 0.0,
+ "text": "threshold for compute, the optimal"
+ },
+ {
+ "start": 2980.68,
+ "duration": 0.0,
+ "text": "threshold for compute, the optimal two-part<00:49:41.040> code<00:49:41.280> length<00:49:41.600> goes<00:49:42.000> from<00:49:42.160> being"
+ },
+ {
+ "start": 2983.19,
+ "duration": 0.0,
+ "text": "two-part code length goes from being"
+ },
+ {
+ "start": 2983.2,
+ "duration": 0.0,
+ "text": "two-part code length goes from being the<00:49:43.360> ordinary<00:49:44.000> transformer<00:49:45.000> to<00:49:45.120> the<00:49:45.200> loop"
+ },
+ {
+ "start": 2985.39,
+ "duration": 0.0,
+ "text": "the ordinary transformer to the loop"
+ },
+ {
+ "start": 2985.4,
+ "duration": 0.0,
+ "text": "the ordinary transformer to the loop transformer,<00:49:45.960> although<00:49:46.200> we<00:49:46.320> consider<00:49:46.640> both"
+ },
+ {
+ "start": 2987.31,
+ "duration": 0.0,
+ "text": "transformer, although we consider both"
+ },
+ {
+ "start": 2987.32,
+ "duration": 0.0,
+ "text": "transformer, although we consider both across<00:49:47.720> the<00:49:47.840> compute<00:49:48.160> range."
+ },
+ {
+ "start": 2989.55,
+ "duration": 0.0,
+ "text": "across the compute range."
+ },
+ {
+ "start": 2989.56,
+ "duration": 0.0,
+ "text": "across the compute range. And<00:49:49.680> when<00:49:49.840> that<00:49:50.000> happens,<00:49:51.040> right,<00:49:51.400> the"
+ },
+ {
+ "start": 2992.75,
+ "duration": 0.0,
+ "text": "And when that happens, right, the"
+ },
+ {
+ "start": 2992.76,
+ "duration": 0.0,
+ "text": "And when that happens, right, the the<00:49:52.880> model<00:49:53.240> finally<00:49:53.560> has<00:49:53.720> enough<00:49:53.880> compute<00:49:54.280> to"
+ },
+ {
+ "start": 2994.39,
+ "duration": 0.0,
+ "text": "the model finally has enough compute to"
+ },
+ {
+ "start": 2994.4,
+ "duration": 0.0,
+ "text": "the model finally has enough compute to actually<00:49:54.760> implement<00:49:55.120> this<00:49:55.280> rule.<00:49:55.880> And<00:49:56.040> so"
+ },
+ {
+ "start": 2996.15,
+ "duration": 0.0,
+ "text": "actually implement this rule. And so"
+ },
+ {
+ "start": 2996.16,
+ "duration": 0.0,
+ "text": "actually implement this rule. And so then<00:49:56.560> the<00:49:56.880> two-part<00:49:57.200> code<00:49:57.400> length<00:49:57.560> goes<00:49:57.760> way"
+ },
+ {
+ "start": 2997.87,
+ "duration": 0.0,
+ "text": "then the two-part code length goes way"
+ },
+ {
+ "start": 2997.88,
+ "duration": 0.0,
+ "text": "then the two-part code length goes way down."
+ },
+ {
+ "start": 2998.91,
+ "duration": 0.0,
+ "text": "down."
+ },
+ {
+ "start": 2998.92,
+ "duration": 0.0,
+ "text": "down. And<00:49:59.120> so<00:49:59.400> also<00:49:59.760> does<00:50:00.120> the<00:50:00.320> epiplexity."
+ },
+ {
+ "start": 3001.79,
+ "duration": 0.0,
+ "text": "And so also does the epiplexity."
+ },
+ {
+ "start": 3001.8,
+ "duration": 0.0,
+ "text": "And so also does the epiplexity. So<00:50:01.920> the<00:50:01.960> epiplexity<00:50:02.440> actually<00:50:02.680> goes<00:50:02.920> up<00:50:03.840> with"
+ },
+ {
+ "start": 3003.95,
+ "duration": 0.0,
+ "text": "So the epiplexity actually goes up with"
+ },
+ {
+ "start": 3003.96,
+ "duration": 0.0,
+ "text": "So the epiplexity actually goes up with compute<00:50:04.440> and<00:50:04.560> then<00:50:04.920> eventually<00:50:05.320> comes<00:50:05.520> down."
+ },
+ {
+ "start": 3007.27,
+ "duration": 0.0,
+ "text": "compute and then eventually comes down."
+ },
+ {
+ "start": 3007.28,
+ "duration": 0.0,
+ "text": "compute and then eventually comes down. And<00:50:07.320> we<00:50:07.440> attempt<00:50:07.760> to<00:50:07.960> mathematize,<00:50:08.680> so<00:50:08.800> that's"
+ },
+ {
+ "start": 3009.59,
+ "duration": 0.0,
+ "text": "And we attempt to mathematize, so that's"
+ },
+ {
+ "start": 3009.6,
+ "duration": 0.0,
+ "text": "And we attempt to mathematize, so that's this<00:50:09.920> phenomenon<00:50:10.280> that<00:50:10.480> we<00:50:10.600> were<00:50:11.360> um"
+ },
+ {
+ "start": 3012.03,
+ "duration": 0.0,
+ "text": "this phenomenon that we were um"
+ },
+ {
+ "start": 3012.04,
+ "duration": 0.0,
+ "text": "this phenomenon that we were um uh<00:50:12.400> just<00:50:12.560> speaking<00:50:12.720> about<00:50:12.840> before.<00:50:13.040> And<00:50:13.120> we"
+ },
+ {
+ "start": 3013.19,
+ "duration": 0.0,
+ "text": "uh just speaking about before. And we"
+ },
+ {
+ "start": 3013.2,
+ "duration": 0.0,
+ "text": "uh just speaking about before. And we attempt<00:50:13.360> to<00:50:13.440> mathematize<00:50:13.960> this<00:50:14.200> with<00:50:14.800> with"
+ },
+ {
+ "start": 3015.03,
+ "duration": 0.0,
+ "text": "attempt to mathematize this with with"
+ },
+ {
+ "start": 3015.04,
+ "duration": 0.0,
+ "text": "attempt to mathematize this with with this<00:50:15.520> um<00:50:16.000> description<00:50:16.360> here<00:50:16.720> where<00:50:17.280> we"
+ },
+ {
+ "start": 3017.75,
+ "duration": 0.0,
+ "text": "this um description here where we"
+ },
+ {
+ "start": 3017.76,
+ "duration": 0.0,
+ "text": "this um description here where we consider<00:50:18.160> two<00:50:18.400> time<00:50:18.680> bounds.<00:50:19.320> One<00:50:19.600> of<00:50:19.680> them"
+ },
+ {
+ "start": 3020.11,
+ "duration": 0.0,
+ "text": "consider two time bounds. One of them"
+ },
+ {
+ "start": 3020.12,
+ "duration": 0.0,
+ "text": "consider two time bounds. One of them where<00:50:20.920> uh<00:50:21.360> T1,<00:50:22.040> where<00:50:22.280> you<00:50:22.360> do<00:50:22.520> have<00:50:22.640> enough"
+ },
+ {
+ "start": 3022.87,
+ "duration": 0.0,
+ "text": "where uh T1, where you do have enough"
+ },
+ {
+ "start": 3022.88,
+ "duration": 0.0,
+ "text": "where uh T1, where you do have enough time<00:50:23.240> to<00:50:23.680> essentially<00:50:24.000> just<00:50:24.200> run<00:50:24.400> this<00:50:24.560> rule."
+ },
+ {
+ "start": 3025.19,
+ "duration": 0.0,
+ "text": "time to essentially just run this rule."
+ },
+ {
+ "start": 3025.2,
+ "duration": 0.0,
+ "text": "time to essentially just run this rule. And<00:50:25.360> T2,<00:50:25.760> where<00:50:25.920> you<00:50:26.040> don't<00:50:26.320> have<00:50:26.440> enough<00:50:26.640> time"
+ },
+ {
+ "start": 3026.87,
+ "duration": 0.0,
+ "text": "And T2, where you don't have enough time"
+ },
+ {
+ "start": 3026.88,
+ "duration": 0.0,
+ "text": "And T2, where you don't have enough time to<00:50:27.040> run<00:50:27.640> the<00:50:27.760> full<00:50:27.920> step<00:50:28.200> rule,<00:50:28.560> although<00:50:28.800> you"
+ },
+ {
+ "start": 3028.91,
+ "duration": 0.0,
+ "text": "to run the full step rule, although you"
+ },
+ {
+ "start": 3028.92,
+ "duration": 0.0,
+ "text": "to run the full step rule, although you do<00:50:29.280> have<00:50:29.440> enough<00:50:29.600> time<00:50:29.880> to<00:50:30.000> run<00:50:30.280> the<00:50:30.440> one<00:50:30.600> step"
+ },
+ {
+ "start": 3030.83,
+ "duration": 0.0,
+ "text": "do have enough time to run the one step"
+ },
+ {
+ "start": 3030.84,
+ "duration": 0.0,
+ "text": "do have enough time to run the one step rule.<00:50:31.240> So<00:50:31.320> it's<00:50:31.440> not<00:50:31.600> that<00:50:31.760> you<00:50:32.080> you<00:50:32.560> you<00:50:32.640> know"
+ },
+ {
+ "start": 3032.75,
+ "duration": 0.0,
+ "text": "rule. So it's not that you you you know"
+ },
+ {
+ "start": 3032.76,
+ "duration": 0.0,
+ "text": "rule. So it's not that you you you know you<00:50:32.920> can't<00:50:33.160> you<00:50:33.280> can't<00:50:33.760> uh<00:50:33.840> run<00:50:33.960> that.<00:50:34.680> Um"
+ },
+ {
+ "start": 3035.51,
+ "duration": 0.0,
+ "text": "you can't you can't uh run that. Um"
+ },
+ {
+ "start": 3035.52,
+ "duration": 0.0,
+ "text": "you can't you can't uh run that. Um and<00:50:36.320> uh"
+ },
+ {
+ "start": 3037.35,
+ "duration": 0.0,
+ "text": "and uh"
+ },
+ {
+ "start": 3037.36,
+ "duration": 0.0,
+ "text": "and uh what<00:50:37.480> we<00:50:37.560> say<00:50:37.720> here<00:50:38.160> is"
+ },
+ {
+ "start": 3039.43,
+ "duration": 0.0,
+ "text": "what we say here is"
+ },
+ {
+ "start": 3039.44,
+ "duration": 0.0,
+ "text": "what we say here is um"
+ },
+ {
+ "start": 3040.55,
+ "duration": 0.0,
+ "text": "um"
+ },
+ {
+ "start": 3040.56,
+ "duration": 0.0,
+ "text": "um the<00:50:40.680> thought<00:50:41.000> is<00:50:41.600> hm"
+ },
+ {
+ "start": 3042.27,
+ "duration": 0.0,
+ "text": "the thought is hm"
+ },
+ {
+ "start": 3042.28,
+ "duration": 0.0,
+ "text": "the thought is hm perhaps"
+ },
+ {
+ "start": 3043.59,
+ "duration": 0.0,
+ "text": "perhaps"
+ },
+ {
+ "start": 3043.6,
+ "duration": 0.0,
+ "text": "perhaps uh<00:50:43.840> the"
+ },
+ {
+ "start": 3044.91,
+ "duration": 0.0,
+ "text": "uh the"
+ },
+ {
+ "start": 3044.92,
+ "duration": 0.0,
+ "text": "uh the uh<00:50:45.000> what's<00:50:45.120> going<00:50:45.280> on<00:50:45.360> here<00:50:45.760> is<00:50:46.000> that<00:50:46.760> the"
+ },
+ {
+ "start": 3047.95,
+ "duration": 0.0,
+ "text": "uh what's going on here is that the"
+ },
+ {
+ "start": 3047.96,
+ "duration": 0.0,
+ "text": "uh what's going on here is that the uh<00:50:48.240> the<00:50:48.320> difference<00:50:48.760> between<00:50:49.040> these<00:50:49.200> two"
+ },
+ {
+ "start": 3049.31,
+ "duration": 0.0,
+ "text": "uh the difference between these two"
+ },
+ {
+ "start": 3049.32,
+ "duration": 0.0,
+ "text": "uh the difference between these two epiplexities<00:50:50.360> for<00:50:50.680> the<00:50:50.800> one<00:50:51.000> step<00:50:51.240> rule"
+ },
+ {
+ "start": 3052.15,
+ "duration": 0.0,
+ "text": "epiplexities for the one step rule"
+ },
+ {
+ "start": 3052.16,
+ "duration": 0.0,
+ "text": "epiplexities for the one step rule is"
+ },
+ {
+ "start": 3053.03,
+ "duration": 0.0,
+ "text": "is"
+ },
+ {
+ "start": 3053.04,
+ "duration": 0.0,
+ "text": "is constant.<00:50:54.000> But<00:50:54.320> that<00:50:55.080> um"
+ },
+ {
+ "start": 3056.43,
+ "duration": 0.0,
+ "text": "constant. But that um"
+ },
+ {
+ "start": 3056.44,
+ "duration": 0.0,
+ "text": "constant. But that um your<00:50:57.120> the<00:50:57.200> difference<00:50:57.520> in<00:50:57.600> epiplexities<00:50:58.240> for"
+ },
+ {
+ "start": 3058.35,
+ "duration": 0.0,
+ "text": "your the difference in epiplexities for"
+ },
+ {
+ "start": 3058.36,
+ "duration": 0.0,
+ "text": "your the difference in epiplexities for the<00:50:58.440> case<00:50:58.760> step<00:50:59.280> rule<00:50:59.520> for<00:50:59.640> these<00:50:59.800> two<00:50:59.920> time"
+ },
+ {
+ "start": 3060.11,
+ "duration": 0.0,
+ "text": "the case step rule for these two time"
+ },
+ {
+ "start": 3060.12,
+ "duration": 0.0,
+ "text": "the case step rule for these two time bounds<00:51:00.880> is<00:51:01.040> actually"
+ },
+ {
+ "start": 3062.27,
+ "duration": 0.0,
+ "text": "bounds is actually"
+ },
+ {
+ "start": 3062.28,
+ "duration": 0.0,
+ "text": "bounds is actually asymptotically<00:51:02.880> greater<00:51:03.120> than<00:51:03.240> constant,"
+ },
+ {
+ "start": 3063.67,
+ "duration": 0.0,
+ "text": "asymptotically greater than constant,"
+ },
+ {
+ "start": 3063.68,
+ "duration": 0.0,
+ "text": "asymptotically greater than constant, right?<00:51:03.880> Essentially<00:51:04.200> growing<00:51:04.880> with<00:51:05.160> the"
+ },
+ {
+ "start": 3065.27,
+ "duration": 0.0,
+ "text": "right? Essentially growing with the"
+ },
+ {
+ "start": 3065.28,
+ "duration": 0.0,
+ "text": "right? Essentially growing with the state<00:51:05.560> size"
+ },
+ {
+ "start": 3066.87,
+ "duration": 0.0,
+ "text": "state size"
+ },
+ {
+ "start": 3066.88,
+ "duration": 0.0,
+ "text": "state size and<00:51:07.080> the<00:51:07.160> number<00:51:07.360> of<00:51:07.440> steps<00:51:08.160> or<00:51:08.320> the<00:51:08.400> number<00:51:08.600> of"
+ },
+ {
+ "start": 3068.67,
+ "duration": 0.0,
+ "text": "and the number of steps or the number of"
+ },
+ {
+ "start": 3068.68,
+ "duration": 0.0,
+ "text": "and the number of steps or the number of steps."
+ },
+ {
+ "start": 3069.55,
+ "duration": 0.0,
+ "text": "steps."
+ },
+ {
+ "start": 3069.56,
+ "duration": 0.0,
+ "text": "steps. Um<00:51:09.960> right.<00:51:10.200> So<00:51:10.360> the<00:51:10.480> thing<00:51:10.720> that<00:51:10.880> like<00:51:11.080> as<00:51:11.200> you"
+ },
+ {
+ "start": 3071.27,
+ "duration": 0.0,
+ "text": "Um right. So the thing that like as you"
+ },
+ {
+ "start": 3071.28,
+ "duration": 0.0,
+ "text": "Um right. So the thing that like as you make<00:51:11.400> the<00:51:11.480> state<00:51:11.720> larger,<00:51:12.160> there<00:51:12.280> are<00:51:12.360> more"
+ },
+ {
+ "start": 3072.51,
+ "duration": 0.0,
+ "text": "make the state larger, there are more"
+ },
+ {
+ "start": 3072.52,
+ "duration": 0.0,
+ "text": "make the state larger, there are more and<00:51:12.600> more<00:51:12.720> structures<00:51:13.120> they<00:51:13.240> actually<00:51:13.520> need"
+ },
+ {
+ "start": 3073.67,
+ "duration": 0.0,
+ "text": "and more structures they actually need"
+ },
+ {
+ "start": 3073.68,
+ "duration": 0.0,
+ "text": "and more structures they actually need to<00:51:14.280> to<00:51:15.000> the<00:51:15.240> that<00:51:15.440> are<00:51:15.520> possible<00:51:15.880> to<00:51:15.960> configure"
+ },
+ {
+ "start": 3076.23,
+ "duration": 0.0,
+ "text": "to to the that are possible to configure"
+ },
+ {
+ "start": 3076.24,
+ "duration": 0.0,
+ "text": "to to the that are possible to configure inside<00:51:16.560> there<00:51:16.680> that<00:51:16.800> you<00:51:16.880> need<00:51:17.000> to<00:51:17.080> know"
+ },
+ {
+ "start": 3077.19,
+ "duration": 0.0,
+ "text": "inside there that you need to know"
+ },
+ {
+ "start": 3077.2,
+ "duration": 0.0,
+ "text": "inside there that you need to know about.<00:51:17.920> Okay.<00:51:18.720> Um<00:51:19.440> I<00:51:19.520> guess<00:51:19.720> in<00:51:19.800> the<00:51:19.840> interest"
+ },
+ {
+ "start": 3080.07,
+ "duration": 0.0,
+ "text": "about. Okay. Um I guess in the interest"
+ },
+ {
+ "start": 3080.08,
+ "duration": 0.0,
+ "text": "about. Okay. Um I guess in the interest of<00:51:20.160> time<00:51:20.320> we'll<00:51:20.440> just<00:51:20.880> uh<00:51:21.000> continue,<00:51:21.520> but<00:51:21.800> um"
+ },
+ {
+ "start": 3082.07,
+ "duration": 0.0,
+ "text": "of time we'll just uh continue, but um"
+ },
+ {
+ "start": 3082.08,
+ "duration": 0.0,
+ "text": "of time we'll just uh continue, but um we'd<00:51:22.200> love<00:51:22.400> to<00:51:22.640> talk<00:51:22.880> about<00:51:23.080> this<00:51:23.440> uh<00:51:23.920> later"
+ },
+ {
+ "start": 3084.23,
+ "duration": 0.0,
+ "text": "we'd love to talk about this uh later"
+ },
+ {
+ "start": 3084.24,
+ "duration": 0.0,
+ "text": "we'd love to talk about this uh later on.<00:51:24.640> So<00:51:24.760> then<00:51:24.960> yeah,<00:51:25.080> we<00:51:25.200> also<00:51:25.440> look<00:51:25.640> at<00:51:25.920> um<00:51:26.440> uh"
+ },
+ {
+ "start": 3087.03,
+ "duration": 0.0,
+ "text": "on. So then yeah, we also look at um uh"
+ },
+ {
+ "start": 3087.04,
+ "duration": 0.0,
+ "text": "on. So then yeah, we also look at um uh you<00:51:27.120> know,<00:51:27.200> we<00:51:27.280> have<00:51:27.440> this"
+ },
+ {
+ "start": 3088.35,
+ "duration": 0.0,
+ "text": "you know, we have this"
+ },
+ {
+ "start": 3088.36,
+ "duration": 0.0,
+ "text": "you know, we have this the<00:51:28.560> thing<00:51:28.760> about<00:51:29.000> this<00:51:29.200> the<00:51:29.320> structure<00:51:29.680> in"
+ },
+ {
+ "start": 3089.75,
+ "duration": 0.0,
+ "text": "the thing about this the structure in"
+ },
+ {
+ "start": 3089.76,
+ "duration": 0.0,
+ "text": "the thing about this the structure in the<00:51:29.800> model.<00:51:30.520> Well,<00:51:30.760> is<00:51:30.880> the<00:51:31.000> structure<00:51:31.800> how"
+ },
+ {
+ "start": 3091.87,
+ "duration": 0.0,
+ "text": "the model. Well, is the structure how"
+ },
+ {
+ "start": 3091.88,
+ "duration": 0.0,
+ "text": "the model. Well, is the structure how does<00:51:32.000> the<00:51:32.080> structure<00:51:32.440> relate<00:51:32.760> to<00:51:32.880> what<00:51:33.040> we're"
+ },
+ {
+ "start": 3093.15,
+ "duration": 0.0,
+ "text": "does the structure relate to what we're"
+ },
+ {
+ "start": 3093.16,
+ "duration": 0.0,
+ "text": "does the structure relate to what we're interested<00:51:33.560> in<00:51:34.040> in<00:51:34.160> machine<00:51:34.400> learning<00:51:35.080> for"
+ },
+ {
+ "start": 3095.19,
+ "duration": 0.0,
+ "text": "interested in in machine learning for"
+ },
+ {
+ "start": 3095.2,
+ "duration": 0.0,
+ "text": "interested in in machine learning for making<00:51:35.560> more<00:51:36.400> uh<00:51:36.600> performant<00:51:36.920> models,"
+ },
+ {
+ "start": 3097.63,
+ "duration": 0.0,
+ "text": "making more uh performant models,"
+ },
+ {
+ "start": 3097.64,
+ "duration": 0.0,
+ "text": "making more uh performant models, thinking<00:51:37.840> about<00:51:38.160> OD<00:51:38.600> transfer<00:51:39.080> OD"
+ },
+ {
+ "start": 3099.67,
+ "duration": 0.0,
+ "text": "thinking about OD transfer OD"
+ },
+ {
+ "start": 3099.68,
+ "duration": 0.0,
+ "text": "thinking about OD transfer OD generalization<00:51:40.200> OD<00:51:40.400> performance."
+ },
+ {
+ "start": 3101.87,
+ "duration": 0.0,
+ "text": "generalization OD performance."
+ },
+ {
+ "start": 3101.88,
+ "duration": 0.0,
+ "text": "generalization OD performance. And<00:51:41.960> I<00:51:42.000> think<00:51:42.160> there's<00:51:42.280> a<00:51:42.320> nice<00:51:42.480> story<00:51:42.760> here"
+ },
+ {
+ "start": 3102.99,
+ "duration": 0.0,
+ "text": "And I think there's a nice story here"
+ },
+ {
+ "start": 3103.0,
+ "duration": 0.0,
+ "text": "And I think there's a nice story here that<00:51:43.560> um"
+ },
+ {
+ "start": 3104.39,
+ "duration": 0.0,
+ "text": "that um"
+ },
+ {
+ "start": 3104.4,
+ "duration": 0.0,
+ "text": "that um with<00:51:45.520> a<00:51:45.600> lot<00:51:45.880> of<00:51:46.000> structures<00:51:46.600> in<00:51:46.680> the<00:51:46.760> model,"
+ },
+ {
+ "start": 3108.11,
+ "duration": 0.0,
+ "text": "with a lot of structures in the model,"
+ },
+ {
+ "start": 3108.12,
+ "duration": 0.0,
+ "text": "with a lot of structures in the model, circuits,<00:51:48.680> induction<00:51:49.040> heads,<00:51:49.560> so<00:51:49.720> forth,"
+ },
+ {
+ "start": 3110.59,
+ "duration": 0.0,
+ "text": "circuits, induction heads, so forth,"
+ },
+ {
+ "start": 3110.6,
+ "duration": 0.0,
+ "text": "circuits, induction heads, so forth, there's<00:51:50.720> a<00:51:50.760> lot<00:51:50.960> more<00:51:51.520> to<00:51:51.640> draw<00:51:51.880> upon<00:51:52.320> for"
+ },
+ {
+ "start": 3112.43,
+ "duration": 0.0,
+ "text": "there's a lot more to draw upon for"
+ },
+ {
+ "start": 3112.44,
+ "duration": 0.0,
+ "text": "there's a lot more to draw upon for transfer,<00:51:53.120> right?<00:51:53.400> So<00:51:54.000> at<00:51:54.200> least<00:51:54.520> in"
+ },
+ {
+ "start": 3114.59,
+ "duration": 0.0,
+ "text": "transfer, right? So at least in"
+ },
+ {
+ "start": 3114.6,
+ "duration": 0.0,
+ "text": "transfer, right? So at least in principle,<00:51:55.160> if<00:51:55.280> we<00:51:55.360> have<00:51:55.520> some<00:51:55.720> other<00:51:55.920> task,"
+ },
+ {
+ "start": 3116.75,
+ "duration": 0.0,
+ "text": "principle, if we have some other task,"
+ },
+ {
+ "start": 3116.76,
+ "duration": 0.0,
+ "text": "principle, if we have some other task, there's<00:51:56.960> more<00:51:57.360> that<00:51:58.120> might<00:51:58.560> be<00:51:59.080> uh<00:51:59.200> that<00:51:59.280> we"
+ },
+ {
+ "start": 3119.35,
+ "duration": 0.0,
+ "text": "there's more that might be uh that we"
+ },
+ {
+ "start": 3119.36,
+ "duration": 0.0,
+ "text": "there's more that might be uh that we can<00:51:59.600> leverage<00:52:00.000> those<00:52:00.160> existing<00:52:00.520> circuits."
+ },
+ {
+ "start": 3121.23,
+ "duration": 0.0,
+ "text": "can leverage those existing circuits."
+ },
+ {
+ "start": 3121.24,
+ "duration": 0.0,
+ "text": "can leverage those existing circuits. Versus<00:52:01.560> if<00:52:01.720> you<00:52:01.800> have<00:52:02.040> a<00:52:02.080> very<00:52:02.280> small"
+ },
+ {
+ "start": 3122.59,
+ "duration": 0.0,
+ "text": "Versus if you have a very small"
+ },
+ {
+ "start": 3122.6,
+ "duration": 0.0,
+ "text": "Versus if you have a very small epiplexity<00:52:03.280> and<00:52:03.400> the<00:52:03.480> model<00:52:03.920> ends<00:52:04.080> up<00:52:04.160> very"
+ },
+ {
+ "start": 3124.31,
+ "duration": 0.0,
+ "text": "epiplexity and the model ends up very"
+ },
+ {
+ "start": 3124.32,
+ "duration": 0.0,
+ "text": "epiplexity and the model ends up very small,<00:52:05.000> then<00:52:05.120> there's<00:52:05.280> very<00:52:05.480> little<00:52:05.840> reuse"
+ },
+ {
+ "start": 3126.19,
+ "duration": 0.0,
+ "text": "small, then there's very little reuse"
+ },
+ {
+ "start": 3126.2,
+ "duration": 0.0,
+ "text": "small, then there's very little reuse that<00:52:06.320> can<00:52:06.440> happen."
+ },
+ {
+ "start": 3127.95,
+ "duration": 0.0,
+ "text": "that can happen."
+ },
+ {
+ "start": 3127.96,
+ "duration": 0.0,
+ "text": "that can happen. So<00:52:08.040> we<00:52:08.160> do<00:52:08.320> some<00:52:08.640> interesting<00:52:09.000> analysis<00:52:09.560> of<00:52:10.280> um"
+ },
+ {
+ "start": 3130.51,
+ "duration": 0.0,
+ "text": "So we do some interesting analysis of um"
+ },
+ {
+ "start": 3130.52,
+ "duration": 0.0,
+ "text": "So we do some interesting analysis of um now<00:52:11.000> this<00:52:11.200> is<00:52:11.600> uh"
+ },
+ {
+ "start": 3132.15,
+ "duration": 0.0,
+ "text": "now this is uh"
+ },
+ {
+ "start": 3132.16,
+ "duration": 0.0,
+ "text": "now this is uh uh"
+ },
+ {
+ "start": 3132.95,
+ "duration": 0.0,
+ "text": "uh"
+ },
+ {
+ "start": 3132.96,
+ "duration": 0.0,
+ "text": "uh we<00:52:13.040> do<00:52:13.160> some<00:52:13.280> analysis<00:52:13.680> based<00:52:13.880> on<00:52:14.000> scaling"
+ },
+ {
+ "start": 3134.31,
+ "duration": 0.0,
+ "text": "we do some analysis based on scaling"
+ },
+ {
+ "start": 3134.32,
+ "duration": 0.0,
+ "text": "we do some analysis based on scaling laws<00:52:14.720> of<00:52:15.160> um<00:52:15.400> of<00:52:15.480> different<00:52:16.040> uh<00:52:16.360> natural"
+ },
+ {
+ "start": 3136.67,
+ "duration": 0.0,
+ "text": "laws of um of different uh natural"
+ },
+ {
+ "start": 3136.68,
+ "duration": 0.0,
+ "text": "laws of um of different uh natural domains<00:52:17.200> uh<00:52:17.640> language,<00:52:18.560> images<00:52:19.120> with<00:52:19.240> vector"
+ },
+ {
+ "start": 3139.47,
+ "duration": 0.0,
+ "text": "domains uh language, images with vector"
+ },
+ {
+ "start": 3139.48,
+ "duration": 0.0,
+ "text": "domains uh language, images with vector quantization."
+ },
+ {
+ "start": 3141.31,
+ "duration": 0.0,
+ "text": "quantization."
+ },
+ {
+ "start": 3141.32,
+ "duration": 0.0,
+ "text": "quantization. Now<00:52:21.480> I<00:52:21.520> will<00:52:21.640> say<00:52:21.840> that<00:52:22.200> this<00:52:22.440> estimation<00:52:22.840> of"
+ },
+ {
+ "start": 3142.91,
+ "duration": 0.0,
+ "text": "Now I will say that this estimation of"
+ },
+ {
+ "start": 3142.92,
+ "duration": 0.0,
+ "text": "Now I will say that this estimation of epiplexity<00:52:23.400> is<00:52:23.520> much<00:52:24.120> uh<00:52:24.320> not<00:52:24.520> nearly<00:52:25.320> done<00:52:25.560> as"
+ },
+ {
+ "start": 3145.79,
+ "duration": 0.0,
+ "text": "epiplexity is much uh not nearly done as"
+ },
+ {
+ "start": 3145.8,
+ "duration": 0.0,
+ "text": "epiplexity is much uh not nearly done as as<00:52:26.000> precisely<00:52:26.520> and<00:52:26.640> I<00:52:26.680> think<00:52:26.840> that<00:52:26.920> there<00:52:27.040> are"
+ },
+ {
+ "start": 3147.07,
+ "duration": 0.0,
+ "text": "as precisely and I think that there are"
+ },
+ {
+ "start": 3147.08,
+ "duration": 0.0,
+ "text": "as precisely and I think that there are some<00:52:27.520> some<00:52:27.680> challenges<00:52:28.040> there.<00:52:28.520> Uh<00:52:28.640> we're"
+ },
+ {
+ "start": 3148.71,
+ "duration": 0.0,
+ "text": "some some challenges there. Uh we're"
+ },
+ {
+ "start": 3148.72,
+ "duration": 0.0,
+ "text": "some some challenges there. Uh we're just<00:52:28.920> taking<00:52:29.160> it<00:52:29.280> from<00:52:29.400> scaling<00:52:29.640> laws,<00:52:29.840> but<00:52:29.920> we"
+ },
+ {
+ "start": 3149.99,
+ "duration": 0.0,
+ "text": "just taking it from scaling laws, but we"
+ },
+ {
+ "start": 3150.0,
+ "duration": 0.0,
+ "text": "just taking it from scaling laws, but we try<00:52:30.120> to<00:52:30.200> do<00:52:30.280> our<00:52:30.400> best.<00:52:31.040> Um<00:52:31.400> and<00:52:31.560> we<00:52:31.680> find<00:52:31.960> that"
+ },
+ {
+ "start": 3152.39,
+ "duration": 0.0,
+ "text": "try to do our best. Um and we find that"
+ },
+ {
+ "start": 3152.4,
+ "duration": 0.0,
+ "text": "try to do our best. Um and we find that um<00:52:33.040> that<00:52:33.800> uh<00:52:33.880> for<00:52:34.040> the<00:52:34.160> same<00:52:34.400> compute,<00:52:35.360> um<00:52:35.600> the"
+ },
+ {
+ "start": 3155.71,
+ "duration": 0.0,
+ "text": "um that uh for the same compute, um the"
+ },
+ {
+ "start": 3155.72,
+ "duration": 0.0,
+ "text": "um that uh for the same compute, um the language<00:52:36.080> has<00:52:36.200> a<00:52:36.280> higher<00:52:36.640> epiplexity<00:52:37.320> than<00:52:37.840> um"
+ },
+ {
+ "start": 3158.07,
+ "duration": 0.0,
+ "text": "language has a higher epiplexity than um"
+ },
+ {
+ "start": 3158.08,
+ "duration": 0.0,
+ "text": "language has a higher epiplexity than um than<00:52:38.240> images,<00:52:38.760> which<00:52:38.960> is<00:52:39.120> is<00:52:39.280> kind<00:52:39.440> of"
+ },
+ {
+ "start": 3159.51,
+ "duration": 0.0,
+ "text": "than images, which is is kind of"
+ },
+ {
+ "start": 3159.52,
+ "duration": 0.0,
+ "text": "than images, which is is kind of interesting<00:52:39.960> that<00:52:40.040> is<00:52:40.240> what<00:52:40.480> we're<00:52:40.560> following"
+ },
+ {
+ "start": 3160.83,
+ "duration": 0.0,
+ "text": "interesting that is what we're following"
+ },
+ {
+ "start": 3160.84,
+ "duration": 0.0,
+ "text": "interesting that is what we're following up<00:52:40.960> on."
+ },
+ {
+ "start": 3161.75,
+ "duration": 0.0,
+ "text": "up on."
+ },
+ {
+ "start": 3161.76,
+ "duration": 0.0,
+ "text": "up on. Um<00:52:42.000> okay.<00:52:42.440> So<00:52:43.000> uh<00:52:43.080> we<00:52:43.200> also<00:52:43.560> look<00:52:43.800> at<00:52:44.160> uh<00:52:44.280> some"
+ },
+ {
+ "start": 3165.11,
+ "duration": 0.0,
+ "text": "Um okay. So uh we also look at uh some"
+ },
+ {
+ "start": 3165.12,
+ "duration": 0.0,
+ "text": "Um okay. So uh we also look at uh some uh<00:52:45.240> downstream<00:52:45.560> performance.<00:52:46.120> Maybe<00:52:46.440> I<00:52:46.560> will"
+ },
+ {
+ "start": 3166.87,
+ "duration": 0.0,
+ "text": "uh downstream performance. Maybe I will"
+ },
+ {
+ "start": 3166.88,
+ "duration": 0.0,
+ "text": "uh downstream performance. Maybe I will uh<00:52:46.920> skip<00:52:47.120> past<00:52:47.400> this,<00:52:47.560> but<00:52:47.680> we<00:52:47.760> do<00:52:47.880> some"
+ },
+ {
+ "start": 3168.19,
+ "duration": 0.0,
+ "text": "uh skip past this, but we do some"
+ },
+ {
+ "start": 3168.2,
+ "duration": 0.0,
+ "text": "uh skip past this, but we do some preliminary<00:52:48.680> investigation<00:52:49.240> showing<00:52:49.520> that"
+ },
+ {
+ "start": 3170.19,
+ "duration": 0.0,
+ "text": "preliminary investigation showing that"
+ },
+ {
+ "start": 3170.2,
+ "duration": 0.0,
+ "text": "preliminary investigation showing that um<00:52:50.840> at<00:52:50.960> least<00:52:51.120> in<00:52:51.200> some<00:52:51.400> cases,<00:52:51.880> training<00:52:52.120> LLMs"
+ },
+ {
+ "start": 3172.55,
+ "duration": 0.0,
+ "text": "um at least in some cases, training LLMs"
+ },
+ {
+ "start": 3172.56,
+ "duration": 0.0,
+ "text": "um at least in some cases, training LLMs on<00:52:52.680> data<00:52:52.840> with<00:52:52.960> higher<00:52:53.160> epiplexity<00:52:53.840> leads<00:52:54.080> to"
+ },
+ {
+ "start": 3174.43,
+ "duration": 0.0,
+ "text": "on data with higher epiplexity leads to"
+ },
+ {
+ "start": 3174.44,
+ "duration": 0.0,
+ "text": "on data with higher epiplexity leads to higher<00:52:54.640> downstream<00:52:55.000> performance<00:52:55.560> for"
+ },
+ {
+ "start": 3176.19,
+ "duration": 0.0,
+ "text": "higher downstream performance for"
+ },
+ {
+ "start": 3176.2,
+ "duration": 0.0,
+ "text": "higher downstream performance for downstream<00:52:56.520> tasks.<00:52:57.200> But<00:52:57.320> of<00:52:57.400> course<00:52:57.560> this"
+ },
+ {
+ "start": 3177.67,
+ "duration": 0.0,
+ "text": "downstream tasks. But of course this"
+ },
+ {
+ "start": 3177.68,
+ "duration": 0.0,
+ "text": "downstream tasks. But of course this won't<00:52:57.840> always<00:52:58.080> be<00:52:58.160> the<00:52:58.240> case.<00:52:59.000> You<00:52:59.320> need<00:52:59.920> some"
+ },
+ {
+ "start": 3180.39,
+ "duration": 0.0,
+ "text": "won't always be the case. You need some"
+ },
+ {
+ "start": 3180.4,
+ "duration": 0.0,
+ "text": "won't always be the case. You need some shared<00:53:00.680> structure<00:53:01.080> between<00:53:01.440> the<00:53:01.520> tasks."
+ },
+ {
+ "start": 3183.63,
+ "duration": 0.0,
+ "text": "shared structure between the tasks."
+ },
+ {
+ "start": 3183.64,
+ "duration": 0.0,
+ "text": "shared structure between the tasks. Um"
+ },
+ {
+ "start": 3184.63,
+ "duration": 0.0,
+ "text": "Um"
+ },
+ {
+ "start": 3184.64,
+ "duration": 0.0,
+ "text": "Um and<00:53:04.840> then<00:53:05.560> uh"
+ },
+ {
+ "start": 3186.35,
+ "duration": 0.0,
+ "text": "and then uh"
+ },
+ {
+ "start": 3186.36,
+ "duration": 0.0,
+ "text": "and then uh yeah,<00:53:06.520> so<00:53:06.760> there<00:53:06.880> are<00:53:06.920> a<00:53:06.960> lot<00:53:07.080> of<00:53:07.160> things<00:53:07.320> that"
+ },
+ {
+ "start": 3187.39,
+ "duration": 0.0,
+ "text": "yeah, so there are a lot of things that"
+ },
+ {
+ "start": 3187.4,
+ "duration": 0.0,
+ "text": "yeah, so there are a lot of things that we're<00:53:07.520> we're<00:53:07.720> really<00:53:07.920> excited<00:53:08.160> about<00:53:08.560> um<00:53:09.360> uh"
+ },
+ {
+ "start": 3189.63,
+ "duration": 0.0,
+ "text": "we're we're really excited about um uh"
+ },
+ {
+ "start": 3189.64,
+ "duration": 0.0,
+ "text": "we're we're really excited about um uh doing<00:53:09.840> with<00:53:09.960> this<00:53:10.080> work.<00:53:10.320> I<00:53:10.360> think<00:53:10.520> there's<00:53:10.640> a"
+ },
+ {
+ "start": 3190.67,
+ "duration": 0.0,
+ "text": "doing with this work. I think there's a"
+ },
+ {
+ "start": 3190.68,
+ "duration": 0.0,
+ "text": "doing with this work. I think there's a lot<00:53:10.840> of<00:53:10.880> different<00:53:11.120> things<00:53:11.280> to<00:53:11.360> do.<00:53:11.480> Here<00:53:11.640> are"
+ },
+ {
+ "start": 3191.71,
+ "duration": 0.0,
+ "text": "lot of different things to do. Here are"
+ },
+ {
+ "start": 3191.72,
+ "duration": 0.0,
+ "text": "lot of different things to do. Here are a<00:53:11.760> few<00:53:11.960> things<00:53:12.200> that<00:53:12.280> we're<00:53:12.400> interested<00:53:12.760> in."
+ },
+ {
+ "start": 3193.23,
+ "duration": 0.0,
+ "text": "a few things that we're interested in."
+ },
+ {
+ "start": 3193.24,
+ "duration": 0.0,
+ "text": "a few things that we're interested in. Um<00:53:13.840> you<00:53:13.920> know,<00:53:14.000> there's<00:53:14.200> this<00:53:14.360> recent<00:53:14.600> paper"
+ },
+ {
+ "start": 3194.99,
+ "duration": 0.0,
+ "text": "Um you know, there's this recent paper"
+ },
+ {
+ "start": 3195.0,
+ "duration": 0.0,
+ "text": "Um you know, there's this recent paper on<00:53:15.240> neural<00:53:15.440> cellular<00:53:15.680> automaton.<00:53:16.200> I<00:53:16.240> know"
+ },
+ {
+ "start": 3196.39,
+ "duration": 0.0,
+ "text": "on neural cellular automaton. I know"
+ },
+ {
+ "start": 3196.4,
+ "duration": 0.0,
+ "text": "on neural cellular automaton. I know neural<00:53:16.640> cellular<00:53:16.840> automaton,<00:53:17.200> you<00:53:17.360> know,<00:53:17.480> is"
+ },
+ {
+ "start": 3197.63,
+ "duration": 0.0,
+ "text": "neural cellular automaton, you know, is"
+ },
+ {
+ "start": 3197.64,
+ "duration": 0.0,
+ "text": "neural cellular automaton, you know, is is<00:53:17.840> something<00:53:18.040> that<00:53:18.120> came<00:53:18.280> out<00:53:18.360> of<00:53:18.840> uh<00:53:19.040> your"
+ },
+ {
+ "start": 3199.15,
+ "duration": 0.0,
+ "text": "is something that came out of uh your"
+ },
+ {
+ "start": 3199.16,
+ "duration": 0.0,
+ "text": "is something that came out of uh your group,<00:53:19.400> but<00:53:19.480> you<00:53:19.560> have<00:53:19.640> basically"
+ },
+ {
+ "start": 3199.95,
+ "duration": 0.0,
+ "text": "group, but you have basically"
+ },
+ {
+ "start": 3199.96,
+ "duration": 0.0,
+ "text": "group, but you have basically pre-training<00:53:20.560> pre-pre-training<00:53:21.200> on<00:53:21.280> neural"
+ },
+ {
+ "start": 3201.47,
+ "duration": 0.0,
+ "text": "pre-training pre-pre-training on neural"
+ },
+ {
+ "start": 3201.48,
+ "duration": 0.0,
+ "text": "pre-training pre-pre-training on neural cellular<00:53:21.680> automaton<00:53:22.000> data<00:53:22.560> and<00:53:22.640> how<00:53:22.760> that"
+ },
+ {
+ "start": 3202.87,
+ "duration": 0.0,
+ "text": "cellular automaton data and how that"
+ },
+ {
+ "start": 3202.88,
+ "duration": 0.0,
+ "text": "cellular automaton data and how that could<00:53:23.000> actually<00:53:23.240> be<00:53:23.320> useful<00:53:23.720> for<00:53:24.200> um<00:53:24.760> you"
+ },
+ {
+ "start": 3204.83,
+ "duration": 0.0,
+ "text": "could actually be useful for um you"
+ },
+ {
+ "start": 3204.84,
+ "duration": 0.0,
+ "text": "could actually be useful for um you know,<00:53:25.000> uh<00:53:25.280> language<00:53:26.120> uh<00:53:26.200> for<00:53:26.360> code,<00:53:26.840> for<00:53:27.120> math."
+ },
+ {
+ "start": 3207.87,
+ "duration": 0.0,
+ "text": "know, uh language uh for code, for math."
+ },
+ {
+ "start": 3207.88,
+ "duration": 0.0,
+ "text": "know, uh language uh for code, for math. Um<00:53:28.480> and<00:53:28.680> I<00:53:28.720> think<00:53:29.320> very<00:53:29.560> interesting<00:53:30.360> also"
+ },
+ {
+ "start": 3210.83,
+ "duration": 0.0,
+ "text": "Um and I think very interesting also"
+ },
+ {
+ "start": 3210.84,
+ "duration": 0.0,
+ "text": "Um and I think very interesting also other<00:53:31.080> things<00:53:31.280> about<00:53:31.440> synthetic<00:53:31.760> data.<00:53:31.880> I"
+ },
+ {
+ "start": 3211.91,
+ "duration": 0.0,
+ "text": "other things about synthetic data. I"
+ },
+ {
+ "start": 3211.92,
+ "duration": 0.0,
+ "text": "other things about synthetic data. I think<00:53:32.080> that's<00:53:32.240> something<00:53:32.480> that<00:53:32.600> has<00:53:32.680> been"
+ },
+ {
+ "start": 3212.83,
+ "duration": 0.0,
+ "text": "think that's something that has been"
+ },
+ {
+ "start": 3212.84,
+ "duration": 0.0,
+ "text": "think that's something that has been under<00:53:33.600> uh"
+ },
+ {
+ "start": 3214.23,
+ "duration": 0.0,
+ "text": "under uh"
+ },
+ {
+ "start": 3214.24,
+ "duration": 0.0,
+ "text": "under uh uh<00:53:34.320> appreciated.<00:53:34.920> Um"
+ },
+ {
+ "start": 3215.55,
+ "duration": 0.0,
+ "text": "uh appreciated. Um"
+ },
+ {
+ "start": 3215.56,
+ "duration": 0.0,
+ "text": "uh appreciated. Um Okay,<00:53:35.760> yeah.<00:53:36.120> Interconnecting<00:53:36.640> this"
+ },
+ {
+ "start": 3216.83,
+ "duration": 0.0,
+ "text": "Okay, yeah. Interconnecting this"
+ },
+ {
+ "start": 3216.84,
+ "duration": 0.0,
+ "text": "Okay, yeah. Interconnecting this different<00:53:37.120> demands,<00:53:37.920> thinking<00:53:38.080> more<00:53:38.240> about"
+ },
+ {
+ "start": 3218.47,
+ "duration": 0.0,
+ "text": "different demands, thinking more about"
+ },
+ {
+ "start": 3218.48,
+ "duration": 0.0,
+ "text": "different demands, thinking more about emergent<00:53:38.800> phenomena,<00:53:39.280> thinking<00:53:39.520> about"
+ },
+ {
+ "start": 3219.67,
+ "duration": 0.0,
+ "text": "emergent phenomena, thinking about"
+ },
+ {
+ "start": 3219.68,
+ "duration": 0.0,
+ "text": "emergent phenomena, thinking about chaos.<00:53:40.560> Um<00:53:40.960> yeah,<00:53:41.160> and<00:53:41.240> I<00:53:41.320> guess<00:53:41.520> maybe<00:53:41.760> I'll"
+ },
+ {
+ "start": 3221.83,
+ "duration": 0.0,
+ "text": "chaos. Um yeah, and I guess maybe I'll"
+ },
+ {
+ "start": 3221.84,
+ "duration": 0.0,
+ "text": "chaos. Um yeah, and I guess maybe I'll just<00:53:42.440> open<00:53:42.680> up<00:53:42.760> for<00:53:42.880> your<00:53:42.960> questions.<00:53:43.640> Uh<00:53:43.800> all"
+ },
+ {
+ "start": 3223.87,
+ "duration": 0.0,
+ "text": "just open up for your questions. Uh all"
+ },
+ {
+ "start": 3223.88,
+ "duration": 0.0,
+ "text": "just open up for your questions. Uh all right,<00:53:44.000> so<00:53:44.120> so<00:53:44.280> here<00:53:44.360> here<00:53:44.600> is<00:53:44.760> just<00:53:45.040> um<00:53:45.680> just<00:53:45.880> a"
+ },
+ {
+ "start": 3226.03,
+ "duration": 0.0,
+ "text": "right, so so here here is just um just a"
+ },
+ {
+ "start": 3226.04,
+ "duration": 0.0,
+ "text": "right, so so here here is just um just a nice<00:53:46.240> highlight<00:53:46.520> of<00:53:46.880> okay,<00:53:47.720> some<00:53:47.920> of<00:53:48.000> the<00:53:48.320> the"
+ },
+ {
+ "start": 3228.39,
+ "duration": 0.0,
+ "text": "nice highlight of okay, some of the the"
+ },
+ {
+ "start": 3228.4,
+ "duration": 0.0,
+ "text": "nice highlight of okay, some of the the different<00:53:48.920> objects<00:53:49.240> that<00:53:49.320> we<00:53:49.400> talked<00:53:49.640> about,"
+ },
+ {
+ "start": 3229.87,
+ "duration": 0.0,
+ "text": "different objects that we talked about,"
+ },
+ {
+ "start": 3229.88,
+ "duration": 0.0,
+ "text": "different objects that we talked about, right?<00:53:50.160> Um<00:53:50.920> ones<00:53:51.160> which<00:53:51.359> have<00:53:51.800> high<00:53:52.040> time<00:53:52.280> data"
+ },
+ {
+ "start": 3232.51,
+ "duration": 0.0,
+ "text": "right? Um ones which have high time data"
+ },
+ {
+ "start": 3232.52,
+ "duration": 0.0,
+ "text": "right? Um ones which have high time data entropy<00:53:53.040> and<00:53:53.840> also<00:53:54.160> high<00:53:54.320> complexity,<00:53:54.840> things"
+ },
+ {
+ "start": 3234.99,
+ "duration": 0.0,
+ "text": "entropy and also high complexity, things"
+ },
+ {
+ "start": 3235.0,
+ "duration": 0.0,
+ "text": "entropy and also high complexity, things that<00:53:55.120> are<00:53:55.160> actually<00:53:55.440> random,<00:53:56.040> right?<00:53:56.320> Things"
+ },
+ {
+ "start": 3236.51,
+ "duration": 0.0,
+ "text": "that are actually random, right? Things"
+ },
+ {
+ "start": 3236.52,
+ "duration": 0.0,
+ "text": "that are actually random, right? Things that<00:53:56.600> have<00:53:56.720> high<00:53:56.880> time<00:53:57.120> data<00:53:57.320> complexity,<00:53:57.920> but"
+ },
+ {
+ "start": 3238.11,
+ "duration": 0.0,
+ "text": "that have high time data complexity, but"
+ },
+ {
+ "start": 3238.12,
+ "duration": 0.0,
+ "text": "that have high time data complexity, but actually<00:53:58.440> low<00:53:59.040> Kolmogorov<00:53:59.400> complexity,<00:53:59.960> low"
+ },
+ {
+ "start": 3240.19,
+ "duration": 0.0,
+ "text": "actually low Kolmogorov complexity, low"
+ },
+ {
+ "start": 3240.2,
+ "duration": 0.0,
+ "text": "actually low Kolmogorov complexity, low entropy<00:54:00.920> because<00:54:01.600> they're<00:54:01.720> somehow"
+ },
+ {
+ "start": 3242.11,
+ "duration": 0.0,
+ "text": "entropy because they're somehow"
+ },
+ {
+ "start": 3242.12,
+ "duration": 0.0,
+ "text": "entropy because they're somehow computationally<00:54:02.760> random,<00:54:03.440> but<00:54:03.600> not<00:54:04.320> uh<00:54:04.520> but"
+ },
+ {
+ "start": 3244.67,
+ "duration": 0.0,
+ "text": "computationally random, but not uh but"
+ },
+ {
+ "start": 3244.68,
+ "duration": 0.0,
+ "text": "computationally random, but not uh but not<00:54:05.000> if<00:54:05.040> you<00:54:05.120> have<00:54:05.240> infinite<00:54:05.520> computation,"
+ },
+ {
+ "start": 3246.39,
+ "duration": 0.0,
+ "text": "not if you have infinite computation,"
+ },
+ {
+ "start": 3246.4,
+ "duration": 0.0,
+ "text": "not if you have infinite computation, right?<00:54:06.680> And<00:54:06.800> then<00:54:07.000> things<00:54:07.200> that<00:54:07.280> have<00:54:07.400> high<00:54:08.200> uh"
+ },
+ {
+ "start": 3249.07,
+ "duration": 0.0,
+ "text": "right? And then things that have high uh"
+ },
+ {
+ "start": 3249.08,
+ "duration": 0.0,
+ "text": "right? And then things that have high uh epiplexity<00:54:10.320> um<00:54:10.640> like<00:54:10.800> these<00:54:10.960> things<00:54:11.160> here."
+ },
+ {
+ "start": 3251.43,
+ "duration": 0.0,
+ "text": "epiplexity um like these things here."
+ },
+ {
+ "start": 3251.44,
+ "duration": 0.0,
+ "text": "epiplexity um like these things here. And<00:54:11.560> most<00:54:11.880> of<00:54:11.960> these,<00:54:12.359> you<00:54:12.440> know,<00:54:12.560> of<00:54:12.680> course"
+ },
+ {
+ "start": 3252.83,
+ "duration": 0.0,
+ "text": "And most of these, you know, of course"
+ },
+ {
+ "start": 3252.84,
+ "duration": 0.0,
+ "text": "And most of these, you know, of course you<00:54:12.920> have<00:54:13.000> natural<00:54:13.280> phenomena,<00:54:13.640> maybe<00:54:13.880> those"
+ },
+ {
+ "start": 3254.07,
+ "duration": 0.0,
+ "text": "you have natural phenomena, maybe those"
+ },
+ {
+ "start": 3254.08,
+ "duration": 0.0,
+ "text": "you have natural phenomena, maybe those are<00:54:14.200> actually<00:54:14.440> high<00:54:14.560> complexity.<00:54:15.359> But<00:54:15.480> most"
+ },
+ {
+ "start": 3255.71,
+ "duration": 0.0,
+ "text": "are actually high complexity. But most"
+ },
+ {
+ "start": 3255.72,
+ "duration": 0.0,
+ "text": "are actually high complexity. But most of<00:54:15.800> these<00:54:16.240> but<00:54:16.359> all<00:54:16.520> of<00:54:16.600> these<00:54:16.920> are<00:54:17.080> actually"
+ },
+ {
+ "start": 3257.349,
+ "duration": 0.0,
+ "text": "of these but all of these are actually"
+ },
+ {
+ "start": 3257.359,
+ "duration": 0.0,
+ "text": "of these but all of these are actually ones<00:54:17.680> where<00:54:18.120> we<00:54:18.240> can<00:54:18.359> say<00:54:18.520> that<00:54:18.680> the<00:54:19.000> the"
+ },
+ {
+ "start": 3259.15,
+ "duration": 0.0,
+ "text": "ones where we can say that the the"
+ },
+ {
+ "start": 3259.16,
+ "duration": 0.0,
+ "text": "ones where we can say that the the Kolmogorov<00:54:19.560> complexity,<00:54:20.120> the<00:54:20.240> entropy<00:54:20.720> are"
+ },
+ {
+ "start": 3260.79,
+ "duration": 0.0,
+ "text": "Kolmogorov complexity, the entropy are"
+ },
+ {
+ "start": 3260.8,
+ "duration": 0.0,
+ "text": "Kolmogorov complexity, the entropy are very<00:54:21.000> low,<00:54:21.600> but<00:54:21.760> somehow<00:54:22.400> they<00:54:22.520> have<00:54:22.720> high"
+ },
+ {
+ "start": 3262.95,
+ "duration": 0.0,
+ "text": "very low, but somehow they have high"
+ },
+ {
+ "start": 3262.96,
+ "duration": 0.0,
+ "text": "very low, but somehow they have high epiplexity."
+ },
+ {
+ "start": 3264.15,
+ "duration": 0.0,
+ "text": "epiplexity."
+ },
+ {
+ "start": 3264.16,
+ "duration": 0.0,
+ "text": "epiplexity. Um<00:54:24.680> maybe<00:54:24.840> I'll<00:54:24.920> just<00:54:25.080> open<00:54:25.280> up<00:54:25.359> for"
+ },
+ {
+ "start": 3265.47,
+ "duration": 0.0,
+ "text": "Um maybe I'll just open up for"
+ },
+ {
+ "start": 3265.48,
+ "duration": 0.0,
+ "text": "Um maybe I'll just open up for questions.<00:54:26.120> Yeah,<00:54:26.600> uh"
+ },
+ {
+ "start": 3268.39,
+ "duration": 0.0,
+ "text": "questions. Yeah, uh"
+ },
+ {
+ "start": 3268.4,
+ "duration": 0.0,
+ "text": "questions. Yeah, uh Yeah."
+ },
+ {
+ "start": 3269.31,
+ "duration": 0.0,
+ "text": "Yeah."
+ },
+ {
+ "start": 3269.32,
+ "duration": 0.0,
+ "text": "Yeah. Thank<00:54:29.440> you<00:54:29.520> very<00:54:29.680> much.<00:54:30.160> I<00:54:30.280> have<00:54:30.480> some"
+ },
+ {
+ "start": 3270.91,
+ "duration": 0.0,
+ "text": "Thank you very much. I have some"
+ },
+ {
+ "start": 3270.92,
+ "duration": 0.0,
+ "text": "Thank you very much. I have some question<00:54:31.520> uh<00:54:31.680> so<00:54:31.840> so<00:54:32.600> uh"
+ },
+ {
+ "start": 3273.349,
+ "duration": 0.0,
+ "text": "question uh so so uh"
+ },
+ {
+ "start": 3273.359,
+ "duration": 0.0,
+ "text": "question uh so so uh the<00:54:33.480> first<00:54:33.800> question<00:54:34.120> is<00:54:34.480> a<00:54:34.560> little<00:54:34.800> bit<00:54:35.320> uh"
+ },
+ {
+ "start": 3275.39,
+ "duration": 0.0,
+ "text": "the first question is a little bit uh"
+ },
+ {
+ "start": 3275.4,
+ "duration": 0.0,
+ "text": "the first question is a little bit uh technical.<00:54:36.359> So<00:54:36.760> when<00:54:37.000> you<00:54:37.760> use<00:54:38.000> a<00:54:38.080> method<00:54:38.520> to"
+ },
+ {
+ "start": 3278.63,
+ "duration": 0.0,
+ "text": "technical. So when you use a method to"
+ },
+ {
+ "start": 3278.64,
+ "duration": 0.0,
+ "text": "technical. So when you use a method to train<00:54:39.120> on<00:54:39.400> cellular<00:54:39.680> automaton,"
+ },
+ {
+ "start": 3280.91,
+ "duration": 0.0,
+ "text": "train on cellular automaton,"
+ },
+ {
+ "start": 3280.92,
+ "duration": 0.0,
+ "text": "train on cellular automaton, do<00:54:41.000> you<00:54:41.080> predict<00:54:41.680> a<00:54:42.120> T<00:54:42.280> plus<00:54:42.560> one<00:54:42.840> from<00:54:43.120> T<00:54:43.440> or<00:54:43.720> T"
+ },
+ {
+ "start": 3283.95,
+ "duration": 0.0,
+ "text": "do you predict a T plus one from T or T"
+ },
+ {
+ "start": 3283.96,
+ "duration": 0.0,
+ "text": "do you predict a T plus one from T or T plus<00:54:44.400> like<00:54:44.640> delta<00:54:45.000> T<00:54:45.280> from<00:54:45.520> T?<00:54:46.040> Yeah,<00:54:46.240> so<00:54:46.400> we"
+ },
+ {
+ "start": 3286.51,
+ "duration": 0.0,
+ "text": "plus like delta T from T? Yeah, so we"
+ },
+ {
+ "start": 3286.52,
+ "duration": 0.0,
+ "text": "plus like delta T from T? Yeah, so we predict<00:54:46.920> T<00:54:47.120> T<00:54:47.320> plus<00:54:47.800> uh<00:54:47.920> delta<00:54:48.160> T.<00:54:48.320> So<00:54:48.520> it's"
+ },
+ {
+ "start": 3288.83,
+ "duration": 0.0,
+ "text": "predict T T plus uh delta T. So it's"
+ },
+ {
+ "start": 3288.84,
+ "duration": 0.0,
+ "text": "predict T T plus uh delta T. So it's something<00:54:49.120> like<00:54:49.480> um<00:54:49.760> in<00:54:49.840> some<00:54:50.000> of<00:54:50.040> the"
+ },
+ {
+ "start": 3290.11,
+ "duration": 0.0,
+ "text": "something like um in some of the"
+ },
+ {
+ "start": 3290.12,
+ "duration": 0.0,
+ "text": "something like um in some of the experiments<00:54:50.440> we<00:54:50.520> do,<00:54:50.760> 16<00:54:51.120> steps<00:54:51.359> ahead,<00:54:51.720> some"
+ },
+ {
+ "start": 3291.87,
+ "duration": 0.0,
+ "text": "experiments we do, 16 steps ahead, some"
+ },
+ {
+ "start": 3291.88,
+ "duration": 0.0,
+ "text": "experiments we do, 16 steps ahead, some of<00:54:51.960> them<00:54:52.120> 64<00:54:52.560> steps.<00:54:53.440> Um<00:54:54.040> somewhere<00:54:54.320> around"
+ },
+ {
+ "start": 3294.47,
+ "duration": 0.0,
+ "text": "of them 64 steps. Um somewhere around"
+ },
+ {
+ "start": 3294.48,
+ "duration": 0.0,
+ "text": "of them 64 steps. Um somewhere around this,<00:54:54.640> but<00:54:54.800> a<00:54:54.840> lot<00:54:55.120> of<00:54:55.200> steps<00:54:55.440> ahead.<00:54:55.880> Yeah."
+ },
+ {
+ "start": 3296.55,
+ "duration": 0.0,
+ "text": "this, but a lot of steps ahead. Yeah."
+ },
+ {
+ "start": 3296.56,
+ "duration": 0.0,
+ "text": "this, but a lot of steps ahead. Yeah. And<00:54:57.200> um<00:54:57.680> that<00:54:57.920> that<00:54:58.120> being<00:54:58.280> a<00:54:58.320> key<00:54:58.520> part.<00:54:58.760> So<00:54:58.880> if"
+ },
+ {
+ "start": 3298.99,
+ "duration": 0.0,
+ "text": "And um that that being a key part. So if"
+ },
+ {
+ "start": 3299.0,
+ "duration": 0.0,
+ "text": "And um that that being a key part. So if you<00:54:59.120> only<00:54:59.359> predicted<00:54:59.800> one<00:54:59.920> step<00:55:00.120> ahead,<00:55:00.400> then"
+ },
+ {
+ "start": 3301.07,
+ "duration": 0.0,
+ "text": "you only predicted one step ahead, then"
+ },
+ {
+ "start": 3301.08,
+ "duration": 0.0,
+ "text": "you only predicted one step ahead, then uh"
+ },
+ {
+ "start": 3301.83,
+ "duration": 0.0,
+ "text": "uh"
+ },
+ {
+ "start": 3301.84,
+ "duration": 0.0,
+ "text": "uh yeah,<00:55:02.040> then<00:55:02.280> then<00:55:02.720> in<00:55:02.800> in"
+ },
+ {
+ "start": 3303.47,
+ "duration": 0.0,
+ "text": "yeah, then then in in"
+ },
+ {
+ "start": 3303.48,
+ "duration": 0.0,
+ "text": "yeah, then then in in in<00:55:03.640> most<00:55:03.920> of<00:55:03.960> the<00:55:04.040> cases<00:55:04.400> that<00:55:04.680> I<00:55:04.760> mean<00:55:05.080> I<00:55:05.160> think"
+ },
+ {
+ "start": 3305.71,
+ "duration": 0.0,
+ "text": "in most of the cases that I mean I think"
+ },
+ {
+ "start": 3305.72,
+ "duration": 0.0,
+ "text": "in most of the cases that I mean I think in<00:55:05.800> essentially<00:55:06.160> all<00:55:06.280> of<00:55:06.359> the<00:55:06.400> cases<00:55:06.640> the"
+ },
+ {
+ "start": 3306.67,
+ "duration": 0.0,
+ "text": "in essentially all of the cases the"
+ },
+ {
+ "start": 3306.68,
+ "duration": 0.0,
+ "text": "in essentially all of the cases the model<00:55:06.880> would<00:55:06.960> just<00:55:07.120> be<00:55:07.200> able<00:55:07.359> to<00:55:07.960> um<00:55:08.480> to<00:55:08.640> do"
+ },
+ {
+ "start": 3308.91,
+ "duration": 0.0,
+ "text": "model would just be able to um to do"
+ },
+ {
+ "start": 3308.92,
+ "duration": 0.0,
+ "text": "model would just be able to um to do this<00:55:09.098> [clears throat]<00:55:09.480> to<00:55:09.600> implement<00:55:10.000> that"
+ },
+ {
+ "start": 3310.11,
+ "duration": 0.0,
+ "text": "this [clears throat] to implement that"
+ },
+ {
+ "start": 3310.12,
+ "duration": 0.0,
+ "text": "this [clears throat] to implement that one<00:55:10.280> step<00:55:10.520> rule."
+ },
+ {
+ "start": 3311.51,
+ "duration": 0.0,
+ "text": "one step rule."
+ },
+ {
+ "start": 3311.52,
+ "duration": 0.0,
+ "text": "one step rule. Yeah,<00:55:11.680> how<00:55:11.960> do<00:55:12.040> you<00:55:12.120> choose<00:55:12.440> the<00:55:12.560> delta<00:55:12.880> T?"
+ },
+ {
+ "start": 3313.79,
+ "duration": 0.0,
+ "text": "Yeah, how do you choose the delta T?"
+ },
+ {
+ "start": 3313.8,
+ "duration": 0.0,
+ "text": "Yeah, how do you choose the delta T? Yeah,<00:55:13.960> so<00:55:14.320> um<00:55:14.960> and<00:55:15.080> that<00:55:15.240> depends<00:55:15.640> on<00:55:15.800> kind<00:55:15.920> of"
+ },
+ {
+ "start": 3316.03,
+ "duration": 0.0,
+ "text": "Yeah, so um and that depends on kind of"
+ },
+ {
+ "start": 3316.04,
+ "duration": 0.0,
+ "text": "Yeah, so um and that depends on kind of which<00:55:16.680> uh<00:55:16.920> which<00:55:17.080> phenomena<00:55:17.440> we're<00:55:17.560> trying<00:55:18.040> to"
+ },
+ {
+ "start": 3318.23,
+ "duration": 0.0,
+ "text": "which uh which phenomena we're trying to"
+ },
+ {
+ "start": 3318.24,
+ "duration": 0.0,
+ "text": "which uh which phenomena we're trying to see.<00:55:18.840> So<00:55:19.440> um"
+ },
+ {
+ "start": 3319.99,
+ "duration": 0.0,
+ "text": "see. So um"
+ },
+ {
+ "start": 3320.0,
+ "duration": 0.0,
+ "text": "see. So um for<00:55:21.040> uh"
+ },
+ {
+ "start": 3322.31,
+ "duration": 0.0,
+ "text": "for uh"
+ },
+ {
+ "start": 3322.32,
+ "duration": 0.0,
+ "text": "for uh uh<00:55:22.640> yeah,<00:55:23.080> so<00:55:23.320> for<00:55:23.640> these<00:55:23.920> experiments,<00:55:24.400> we"
+ },
+ {
+ "start": 3324.47,
+ "duration": 0.0,
+ "text": "uh yeah, so for these experiments, we"
+ },
+ {
+ "start": 3324.48,
+ "duration": 0.0,
+ "text": "uh yeah, so for these experiments, we choose<00:55:24.840> the<00:55:25.080> delta<00:55:25.400> T<00:55:25.600> pretty<00:55:26.200> um"
+ },
+ {
+ "start": 3326.95,
+ "duration": 0.0,
+ "text": "choose the delta T pretty um"
+ },
+ {
+ "start": 3326.96,
+ "duration": 0.0,
+ "text": "choose the delta T pretty um uh<00:55:27.040> pretty<00:55:27.240> large,<00:55:27.600> right?<00:55:27.760> So<00:55:27.880> we<00:55:28.000> want<00:55:28.240> the"
+ },
+ {
+ "start": 3328.27,
+ "duration": 0.0,
+ "text": "uh pretty large, right? So we want the"
+ },
+ {
+ "start": 3328.28,
+ "duration": 0.0,
+ "text": "uh pretty large, right? So we want the delta<00:55:28.560> T<00:55:28.800> to<00:55:28.880> be<00:55:29.000> large<00:55:29.280> enough<00:55:29.480> that<00:55:29.600> the"
+ },
+ {
+ "start": 3329.63,
+ "duration": 0.0,
+ "text": "delta T to be large enough that the"
+ },
+ {
+ "start": 3329.64,
+ "duration": 0.0,
+ "text": "delta T to be large enough that the model<00:55:29.920> actually<00:55:30.280> cannot<00:55:30.880> learn<00:55:31.160> that"
+ },
+ {
+ "start": 3331.39,
+ "duration": 0.0,
+ "text": "model actually cannot learn that"
+ },
+ {
+ "start": 3331.4,
+ "duration": 0.0,
+ "text": "model actually cannot learn that multi-step<00:55:31.880> rule,<00:55:32.200> right?<00:55:32.880> Uh<00:55:32.960> so<00:55:33.080> I<00:55:33.120> think"
+ },
+ {
+ "start": 3333.31,
+ "duration": 0.0,
+ "text": "multi-step rule, right? Uh so I think"
+ },
+ {
+ "start": 3333.32,
+ "duration": 0.0,
+ "text": "multi-step rule, right? Uh so I think this<00:55:33.520> was<00:55:33.640> 64."
+ },
+ {
+ "start": 3335.15,
+ "duration": 0.0,
+ "text": "this was 64."
+ },
+ {
+ "start": 3335.16,
+ "duration": 0.0,
+ "text": "this was 64. Um<00:55:35.800> for<00:55:36.080> some<00:55:36.359> experiments,<00:55:36.920> we<00:55:37.080> might<00:55:37.359> want"
+ },
+ {
+ "start": 3337.59,
+ "duration": 0.0,
+ "text": "Um for some experiments, we might want"
+ },
+ {
+ "start": 3337.6,
+ "duration": 0.0,
+ "text": "Um for some experiments, we might want to<00:55:37.720> be<00:55:37.800> in<00:55:37.880> this<00:55:38.040> regime<00:55:38.560> where<00:55:39.160> um<00:55:39.600> where<00:55:39.800> we"
+ },
+ {
+ "start": 3339.91,
+ "duration": 0.0,
+ "text": "to be in this regime where um where we"
+ },
+ {
+ "start": 3339.92,
+ "duration": 0.0,
+ "text": "to be in this regime where um where we actually<00:55:40.240> can<00:55:41.160> uh<00:55:41.320> learn<00:55:41.840> this<00:55:42.040> forward"
+ },
+ {
+ "start": 3342.27,
+ "duration": 0.0,
+ "text": "actually can uh learn this forward"
+ },
+ {
+ "start": 3342.28,
+ "duration": 0.0,
+ "text": "actually can uh learn this forward function,<00:55:42.800> right?<00:55:43.040> So<00:55:43.760> um<00:55:43.960> say<00:55:44.160> like<00:55:44.440> in<00:55:44.560> in"
+ },
+ {
+ "start": 3344.83,
+ "duration": 0.0,
+ "text": "function, right? So um say like in in"
+ },
+ {
+ "start": 3344.84,
+ "duration": 0.0,
+ "text": "function, right? So um say like in in this<00:55:45.000> setup<00:55:45.560> or<00:55:46.400> um"
+ },
+ {
+ "start": 3347.39,
+ "duration": 0.0,
+ "text": "this setup or um"
+ },
+ {
+ "start": 3347.4,
+ "duration": 0.0,
+ "text": "this setup or um uh<00:55:47.480> or<00:55:47.760> or<00:55:47.880> in<00:55:47.960> this<00:55:48.280> actually<00:55:48.520> this<00:55:48.840> is<00:55:48.960> one,"
+ },
+ {
+ "start": 3349.23,
+ "duration": 0.0,
+ "text": "uh or or in this actually this is one,"
+ },
+ {
+ "start": 3349.24,
+ "duration": 0.0,
+ "text": "uh or or in this actually this is one, right?<00:55:49.600> Um<00:55:49.880> so<00:55:50.160> actually<00:55:50.400> that's<00:55:50.600> where<00:55:50.720> this"
+ },
+ {
+ "start": 3350.91,
+ "duration": 0.0,
+ "text": "right? Um so actually that's where this"
+ },
+ {
+ "start": 3350.92,
+ "duration": 0.0,
+ "text": "right? Um so actually that's where this this<00:55:51.080> hard<00:55:51.240> function<00:55:51.560> came<00:55:51.720> from.<00:55:52.160> We<00:55:52.359> we<00:55:52.520> we"
+ },
+ {
+ "start": 3352.63,
+ "duration": 0.0,
+ "text": "this hard function came from. We we we"
+ },
+ {
+ "start": 3352.64,
+ "duration": 0.0,
+ "text": "this hard function came from. We we we use<00:55:52.800> it<00:55:52.880> quite<00:55:53.040> a<00:55:53.080> bit.<00:55:53.680> Um<00:55:54.080> so<00:55:54.200> this<00:55:54.400> is<00:55:54.520> where"
+ },
+ {
+ "start": 3354.67,
+ "duration": 0.0,
+ "text": "use it quite a bit. Um so this is where"
+ },
+ {
+ "start": 3354.68,
+ "duration": 0.0,
+ "text": "use it quite a bit. Um so this is where we<00:55:54.840> we<00:55:55.000> set<00:55:55.200> that<00:55:55.320> delta<00:55:55.560> T<00:55:55.680> to<00:55:55.760> be<00:55:56.200> much"
+ },
+ {
+ "start": 3356.43,
+ "duration": 0.0,
+ "text": "we we set that delta T to be much"
+ },
+ {
+ "start": 3356.44,
+ "duration": 0.0,
+ "text": "we we set that delta T to be much smaller,<00:55:56.760> something<00:55:57.040> like<00:55:57.200> 10<00:55:57.400> steps,<00:55:58.080> where"
+ },
+ {
+ "start": 3358.55,
+ "duration": 0.0,
+ "text": "smaller, something like 10 steps, where"
+ },
+ {
+ "start": 3358.56,
+ "duration": 0.0,
+ "text": "smaller, something like 10 steps, where um<00:55:58.640> with<00:55:58.800> 10<00:55:59.000> steps,<00:56:00.000> if<00:56:00.040> you<00:56:00.120> train<00:56:00.320> a<00:56:00.359> large"
+ },
+ {
+ "start": 3360.59,
+ "duration": 0.0,
+ "text": "um with 10 steps, if you train a large"
+ },
+ {
+ "start": 3360.6,
+ "duration": 0.0,
+ "text": "um with 10 steps, if you train a large enough<00:56:00.760> model,<00:56:01.200> it<00:56:01.280> can<00:56:01.520> eventually<00:56:01.840> learn"
+ },
+ {
+ "start": 3362.03,
+ "duration": 0.0,
+ "text": "enough model, it can eventually learn"
+ },
+ {
+ "start": 3362.04,
+ "duration": 0.0,
+ "text": "enough model, it can eventually learn it,<00:56:02.200> but<00:56:02.320> it's<00:56:02.480> difficult."
+ },
+ {
+ "start": 3363.79,
+ "duration": 0.0,
+ "text": "it, but it's difficult."
+ },
+ {
+ "start": 3363.8,
+ "duration": 0.0,
+ "text": "it, but it's difficult. Okay.<00:56:04.359> Yeah,<00:56:04.800> the<00:56:04.960> reason<00:56:05.280> I<00:56:05.400> ask<00:56:05.760> you<00:56:05.880> this"
+ },
+ {
+ "start": 3366.07,
+ "duration": 0.0,
+ "text": "Okay. Yeah, the reason I ask you this"
+ },
+ {
+ "start": 3366.08,
+ "duration": 0.0,
+ "text": "Okay. Yeah, the reason I ask you this question<00:56:06.400> because<00:56:06.640> this<00:56:07.120> really<00:56:07.440> reminds<00:56:08.000> me"
+ },
+ {
+ "start": 3368.15,
+ "duration": 0.0,
+ "text": "question because this really reminds me"
+ },
+ {
+ "start": 3368.16,
+ "duration": 0.0,
+ "text": "question because this really reminds me of<00:56:08.680> uh<00:56:09.200> Stephen<00:56:09.560> Wolfram's<00:56:10.240> uh<00:56:10.359> computational"
+ },
+ {
+ "start": 3371.03,
+ "duration": 0.0,
+ "text": "of uh Stephen Wolfram's uh computational"
+ },
+ {
+ "start": 3371.04,
+ "duration": 0.0,
+ "text": "of uh Stephen Wolfram's uh computational irreducibility."
+ },
+ {
+ "start": 3372.55,
+ "duration": 0.0,
+ "text": "irreducibility."
+ },
+ {
+ "start": 3372.56,
+ "duration": 0.0,
+ "text": "irreducibility. It's<00:56:12.840> it's<00:56:13.000> saying<00:56:13.480> when<00:56:13.680> you<00:56:13.880> have<00:56:14.120> some<00:56:14.520> some"
+ },
+ {
+ "start": 3374.79,
+ "duration": 0.0,
+ "text": "It's it's saying when you have some some"
+ },
+ {
+ "start": 3374.8,
+ "duration": 0.0,
+ "text": "It's it's saying when you have some some model<00:56:15.400> like<00:56:16.240> rule<00:56:16.440> 30,<00:56:17.320> when<00:56:17.480> you<00:56:17.600> want<00:56:17.880> to"
+ },
+ {
+ "start": 3377.95,
+ "duration": 0.0,
+ "text": "model like rule 30, when you want to"
+ },
+ {
+ "start": 3377.96,
+ "duration": 0.0,
+ "text": "model like rule 30, when you want to predict<00:56:18.359> the<00:56:18.440> future,<00:56:18.840> you<00:56:18.920> can't"
+ },
+ {
+ "start": 3380.23,
+ "duration": 0.0,
+ "text": "predict the future, you can't"
+ },
+ {
+ "start": 3380.24,
+ "duration": 0.0,
+ "text": "predict the future, you can't jump<00:56:20.560> to<00:56:20.680> the<00:56:20.800> future.<00:56:21.160> You<00:56:21.320> must<00:56:21.680> do<00:56:22.080> step<00:56:22.359> by"
+ },
+ {
+ "start": 3382.47,
+ "duration": 0.0,
+ "text": "jump to the future. You must do step by"
+ },
+ {
+ "start": 3382.48,
+ "duration": 0.0,
+ "text": "jump to the future. You must do step by step.<00:56:22.880> So<00:56:23.120> I<00:56:23.320> I<00:56:23.440> wondering<00:56:24.440> how<00:56:24.680> how<00:56:24.800> do<00:56:24.880> you"
+ },
+ {
+ "start": 3384.99,
+ "duration": 0.0,
+ "text": "step. So I I wondering how how do you"
+ },
+ {
+ "start": 3385.0,
+ "duration": 0.0,
+ "text": "step. So I I wondering how how do you see<00:56:25.280> the<00:56:25.560> relationship<00:56:26.320> between<00:56:26.640> your<00:56:27.000> work"
+ },
+ {
+ "start": 3387.39,
+ "duration": 0.0,
+ "text": "see the relationship between your work"
+ },
+ {
+ "start": 3387.4,
+ "duration": 0.0,
+ "text": "see the relationship between your work and<00:56:28.040> uh<00:56:28.120> this<00:56:28.440> computational"
+ },
+ {
+ "start": 3389.07,
+ "duration": 0.0,
+ "text": "and uh this computational"
+ },
+ {
+ "start": 3389.08,
+ "duration": 0.0,
+ "text": "and uh this computational irreducibility?"
+ },
+ {
+ "start": 3390.83,
+ "duration": 0.0,
+ "text": "irreducibility?"
+ },
+ {
+ "start": 3390.84,
+ "duration": 0.0,
+ "text": "irreducibility? Yeah,<00:56:31.040> so<00:56:31.240> I<00:56:31.280> mean<00:56:31.440> we're<00:56:31.560> definitely<00:56:31.840> heavily"
+ },
+ {
+ "start": 3392.03,
+ "duration": 0.0,
+ "text": "Yeah, so I mean we're definitely heavily"
+ },
+ {
+ "start": 3392.04,
+ "duration": 0.0,
+ "text": "Yeah, so I mean we're definitely heavily inspired<00:56:32.440> by<00:56:32.760> you<00:56:32.800> know,<00:56:32.920> some<00:56:33.120> of<00:56:33.240> Wolfram's"
+ },
+ {
+ "start": 3393.67,
+ "duration": 0.0,
+ "text": "inspired by you know, some of Wolfram's"
+ },
+ {
+ "start": 3393.68,
+ "duration": 0.0,
+ "text": "inspired by you know, some of Wolfram's work.<00:56:34.400> Um<00:56:34.800> and<00:56:35.000> I<00:56:35.080> think<00:56:35.359> that<00:56:35.800> the<00:56:36.560> uh<00:56:36.760> right,"
+ },
+ {
+ "start": 3396.95,
+ "duration": 0.0,
+ "text": "work. Um and I think that the uh right,"
+ },
+ {
+ "start": 3396.96,
+ "duration": 0.0,
+ "text": "work. Um and I think that the uh right, the<00:56:37.200> the<00:56:37.480> computational<00:56:38.000> irreducibility"
+ },
+ {
+ "start": 3398.83,
+ "duration": 0.0,
+ "text": "the the computational irreducibility"
+ },
+ {
+ "start": 3398.84,
+ "duration": 0.0,
+ "text": "the the computational irreducibility speaks<00:56:39.200> to<00:56:39.760> um"
+ },
+ {
+ "start": 3401.31,
+ "duration": 0.0,
+ "text": "speaks to um"
+ },
+ {
+ "start": 3401.32,
+ "duration": 0.0,
+ "text": "speaks to um uh<00:56:41.680> right,<00:56:41.880> there<00:56:42.000> are<00:56:42.040> there<00:56:42.160> are<00:56:42.200> certain"
+ },
+ {
+ "start": 3402.39,
+ "duration": 0.0,
+ "text": "uh right, there are there are certain"
+ },
+ {
+ "start": 3402.4,
+ "duration": 0.0,
+ "text": "uh right, there are there are certain elements<00:56:42.680> where<00:56:43.080> yeah,<00:56:43.240> you<00:56:43.320> you're<00:56:43.680> right,"
+ },
+ {
+ "start": 3403.79,
+ "duration": 0.0,
+ "text": "elements where yeah, you you're right,"
+ },
+ {
+ "start": 3403.8,
+ "duration": 0.0,
+ "text": "elements where yeah, you you're right, you<00:56:43.920> can't<00:56:44.280> you<00:56:44.359> can't<00:56:44.600> jump<00:56:44.800> ahead<00:56:45.320> um"
+ },
+ {
+ "start": 3405.47,
+ "duration": 0.0,
+ "text": "you can't you can't jump ahead um"
+ },
+ {
+ "start": 3405.48,
+ "duration": 0.0,
+ "text": "you can't you can't jump ahead um completely,<00:56:45.840> but<00:56:45.960> I<00:56:46.040> think<00:56:46.320> that<00:56:47.080> even<00:56:47.720> in"
+ },
+ {
+ "start": 3407.83,
+ "duration": 0.0,
+ "text": "completely, but I think that even in"
+ },
+ {
+ "start": 3407.84,
+ "duration": 0.0,
+ "text": "completely, but I think that even in many<00:56:48.040> of<00:56:48.120> these<00:56:48.280> cases,<00:56:49.440> um<00:56:50.280> say<00:56:51.200> uh<00:56:51.440> with<00:56:52.359> rule"
+ },
+ {
+ "start": 3412.51,
+ "duration": 0.0,
+ "text": "many of these cases, um say uh with rule"
+ },
+ {
+ "start": 3412.52,
+ "duration": 0.0,
+ "text": "many of these cases, um say uh with rule 54<00:56:53.520> or<00:56:54.160> ones<00:56:54.600> that<00:56:54.960> you<00:56:55.160> do<00:56:55.280> not<00:56:55.520> have<00:56:55.680> this"
+ },
+ {
+ "start": 3415.83,
+ "duration": 0.0,
+ "text": "54 or ones that you do not have this"
+ },
+ {
+ "start": 3415.84,
+ "duration": 0.0,
+ "text": "54 or ones that you do not have this completely<00:56:56.200> unpredictable<00:56:56.680> output,<00:56:57.400> there"
+ },
+ {
+ "start": 3417.71,
+ "duration": 0.0,
+ "text": "completely unpredictable output, there"
+ },
+ {
+ "start": 3417.72,
+ "duration": 0.0,
+ "text": "completely unpredictable output, there are<00:56:58.080> there<00:56:58.359> is<00:56:58.560> a<00:56:58.640> lot<00:56:59.240> that<00:56:59.400> you<00:56:59.520> can<00:56:59.720> jump"
+ },
+ {
+ "start": 3419.91,
+ "duration": 0.0,
+ "text": "are there is a lot that you can jump"
+ },
+ {
+ "start": 3419.92,
+ "duration": 0.0,
+ "text": "are there is a lot that you can jump ahead<00:57:00.160> for.<00:57:00.600> And<00:57:00.760> that<00:57:00.960> part<00:57:01.240> is<00:57:01.640> where"
+ },
+ {
+ "start": 3422.47,
+ "duration": 0.0,
+ "text": "ahead for. And that part is where"
+ },
+ {
+ "start": 3422.48,
+ "duration": 0.0,
+ "text": "ahead for. And that part is where actually<00:57:02.920> with<00:57:03.120> small<00:57:03.480> compute,<00:57:04.040> you<00:57:04.120> can"
+ },
+ {
+ "start": 3424.27,
+ "duration": 0.0,
+ "text": "actually with small compute, you can"
+ },
+ {
+ "start": 3424.28,
+ "duration": 0.0,
+ "text": "actually with small compute, you can still<00:57:04.480> make<00:57:04.680> progress.<00:57:05.720> Um<00:57:06.240> right,<00:57:06.720> with<00:57:07.040> with"
+ },
+ {
+ "start": 3427.23,
+ "duration": 0.0,
+ "text": "still make progress. Um right, with with"
+ },
+ {
+ "start": 3427.24,
+ "duration": 0.0,
+ "text": "still make progress. Um right, with with not<00:57:07.640> enough<00:57:07.880> compute<00:57:08.200> to<00:57:08.320> run<00:57:08.480> the<00:57:08.560> full"
+ },
+ {
+ "start": 3428.83,
+ "duration": 0.0,
+ "text": "not enough compute to run the full"
+ },
+ {
+ "start": 3428.84,
+ "duration": 0.0,
+ "text": "not enough compute to run the full cellular<00:57:09.120> automaton.<00:57:09.520> So<00:57:09.640> that's<00:57:09.880> that's<00:57:10.080> the"
+ },
+ {
+ "start": 3430.15,
+ "duration": 0.0,
+ "text": "cellular automaton. So that's that's the"
+ },
+ {
+ "start": 3430.16,
+ "duration": 0.0,
+ "text": "cellular automaton. So that's that's the regime<00:57:10.480> that<00:57:10.640> these<00:57:11.040> are<00:57:11.320> in.<00:57:11.960> Um<00:57:12.440> and<00:57:12.760> so<00:57:13.480> in"
+ },
+ {
+ "start": 3433.59,
+ "duration": 0.0,
+ "text": "regime that these are in. Um and so in"
+ },
+ {
+ "start": 3433.6,
+ "duration": 0.0,
+ "text": "regime that these are in. Um and so in this<00:57:13.800> setting,<00:57:14.480> uh<00:57:14.680> you<00:57:14.760> know,<00:57:14.840> what<00:57:14.960> I'd<00:57:15.120> say"
+ },
+ {
+ "start": 3435.349,
+ "duration": 0.0,
+ "text": "this setting, uh you know, what I'd say"
+ },
+ {
+ "start": 3435.359,
+ "duration": 0.0,
+ "text": "this setting, uh you know, what I'd say is<00:57:15.520> that<00:57:16.240> the<00:57:16.400> the<00:57:16.520> fact<00:57:16.800> that<00:57:16.920> we<00:57:17.000> can<00:57:17.120> make"
+ },
+ {
+ "start": 3437.31,
+ "duration": 0.0,
+ "text": "is that the the fact that we can make"
+ },
+ {
+ "start": 3437.32,
+ "duration": 0.0,
+ "text": "is that the the fact that we can make continued<00:57:17.760> gains<00:57:18.359> with<00:57:18.720> compute<00:57:19.240> that<00:57:19.400> is<00:57:19.520> not"
+ },
+ {
+ "start": 3439.71,
+ "duration": 0.0,
+ "text": "continued gains with compute that is not"
+ },
+ {
+ "start": 3439.72,
+ "duration": 0.0,
+ "text": "continued gains with compute that is not enough<00:57:20.080> to<00:57:20.359> fit<00:57:20.640> the<00:57:20.920> the<00:57:21.000> final<00:57:21.240> function"
+ },
+ {
+ "start": 3441.95,
+ "duration": 0.0,
+ "text": "enough to fit the the final function"
+ },
+ {
+ "start": 3441.96,
+ "duration": 0.0,
+ "text": "enough to fit the the final function says<00:57:22.280> that<00:57:22.400> there's<00:57:22.560> actually<00:57:22.840> a<00:57:22.880> lot<00:57:23.280> of<00:57:23.440> kind"
+ },
+ {
+ "start": 3443.59,
+ "duration": 0.0,
+ "text": "says that there's actually a lot of kind"
+ },
+ {
+ "start": 3443.6,
+ "duration": 0.0,
+ "text": "says that there's actually a lot of kind of<00:57:23.800> reducible<00:57:24.440> components<00:57:24.960> along<00:57:25.280> the<00:57:25.400> way,"
+ },
+ {
+ "start": 3446.11,
+ "duration": 0.0,
+ "text": "of reducible components along the way,"
+ },
+ {
+ "start": 3446.12,
+ "duration": 0.0,
+ "text": "of reducible components along the way, ways<00:57:26.520> that<00:57:26.640> you<00:57:26.760> can<00:57:27.000> make<00:57:27.160> predictions"
+ },
+ {
+ "start": 3447.79,
+ "duration": 0.0,
+ "text": "ways that you can make predictions"
+ },
+ {
+ "start": 3447.8,
+ "duration": 0.0,
+ "text": "ways that you can make predictions effectively<00:57:28.760> without<00:57:29.280> running<00:57:29.520> the<00:57:29.640> full"
+ },
+ {
+ "start": 3450.07,
+ "duration": 0.0,
+ "text": "effectively without running the full"
+ },
+ {
+ "start": 3450.08,
+ "duration": 0.0,
+ "text": "effectively without running the full rule.<00:57:30.680> And<00:57:31.160> um<00:57:31.600> of<00:57:31.720> course<00:57:32.000> with<00:57:32.160> rule<00:57:32.320> 30,"
+ },
+ {
+ "start": 3453.349,
+ "duration": 0.0,
+ "text": "rule. And um of course with rule 30,"
+ },
+ {
+ "start": 3453.359,
+ "duration": 0.0,
+ "text": "rule. And um of course with rule 30, the<00:57:33.840> one<00:57:34.040> that<00:57:34.160> is<00:57:34.400> is<00:57:34.600> conjectured<00:57:35.040> to<00:57:35.120> be,"
+ },
+ {
+ "start": 3455.23,
+ "duration": 0.0,
+ "text": "the one that is is conjectured to be,"
+ },
+ {
+ "start": 3455.24,
+ "duration": 0.0,
+ "text": "the one that is is conjectured to be, you<00:57:35.320> know,<00:57:35.520> a<00:57:35.600> computationally<00:57:36.160> irreducible,"
+ },
+ {
+ "start": 3456.99,
+ "duration": 0.0,
+ "text": "you know, a computationally irreducible,"
+ },
+ {
+ "start": 3457.0,
+ "duration": 0.0,
+ "text": "you know, a computationally irreducible, um<00:57:37.280> you<00:57:37.440> you<00:57:37.520> don't<00:57:37.720> see<00:57:37.840> that<00:57:38.000> happening."
+ },
+ {
+ "start": 3459.15,
+ "duration": 0.0,
+ "text": "um you you don't see that happening."
+ },
+ {
+ "start": 3459.16,
+ "duration": 0.0,
+ "text": "um you you don't see that happening. So<00:57:39.359> I<00:57:39.440> think<00:57:39.720> that<00:57:40.480> um<00:57:41.240> that<00:57:42.320> uh<00:57:42.680> thinking"
+ },
+ {
+ "start": 3462.99,
+ "duration": 0.0,
+ "text": "So I think that um that uh thinking"
+ },
+ {
+ "start": 3463.0,
+ "duration": 0.0,
+ "text": "So I think that um that uh thinking about<00:57:43.400> useful<00:57:43.760> data<00:57:44.359> for<00:57:44.480> us<00:57:44.600> to<00:57:44.680> train<00:57:44.920> on,<00:57:45.240> it"
+ },
+ {
+ "start": 3465.39,
+ "duration": 0.0,
+ "text": "about useful data for us to train on, it"
+ },
+ {
+ "start": 3465.4,
+ "duration": 0.0,
+ "text": "about useful data for us to train on, it is<00:57:45.600> data<00:57:45.880> that<00:57:46.240> has<00:57:46.560> some<00:57:46.720> level<00:57:46.960> of<00:57:47.040> computa-"
+ },
+ {
+ "start": 3467.55,
+ "duration": 0.0,
+ "text": "is data that has some level of computa-"
+ },
+ {
+ "start": 3467.56,
+ "duration": 0.0,
+ "text": "is data that has some level of computa- that<00:57:47.680> is<00:57:47.880> some<00:57:48.080> level<00:57:48.280> of<00:57:48.359> computationally"
+ },
+ {
+ "start": 3469.03,
+ "duration": 0.0,
+ "text": "that is some level of computationally"
+ },
+ {
+ "start": 3469.04,
+ "duration": 0.0,
+ "text": "that is some level of computationally reducible"
+ },
+ {
+ "start": 3470.31,
+ "duration": 0.0,
+ "text": "reducible"
+ },
+ {
+ "start": 3470.32,
+ "duration": 0.0,
+ "text": "reducible um<00:57:50.520> is<00:57:50.720> is<00:57:50.880> what<00:57:51.040> I<00:57:51.359> how<00:57:51.800> I<00:57:51.880> think<00:57:52.080> about<00:57:52.240> that,"
+ },
+ {
+ "start": 3472.39,
+ "duration": 0.0,
+ "text": "um is is what I how I think about that,"
+ },
+ {
+ "start": 3472.4,
+ "duration": 0.0,
+ "text": "um is is what I how I think about that, which<00:57:52.600> where<00:57:53.040> people<00:57:53.400> with<00:57:53.640> limited"
+ },
+ {
+ "start": 3473.99,
+ "duration": 0.0,
+ "text": "which where people with limited"
+ },
+ {
+ "start": 3474.0,
+ "duration": 0.0,
+ "text": "which where people with limited computation<00:57:54.520> looking<00:57:54.720> at<00:57:54.800> the<00:57:54.880> data<00:57:55.400> that"
+ },
+ {
+ "start": 3475.51,
+ "duration": 0.0,
+ "text": "computation looking at the data that"
+ },
+ {
+ "start": 3475.52,
+ "duration": 0.0,
+ "text": "computation looking at the data that don't<00:57:55.760> have<00:57:55.920> enough<00:57:56.400> that<00:57:56.520> can't<00:57:56.720> just<00:57:56.880> run"
+ },
+ {
+ "start": 3477.07,
+ "duration": 0.0,
+ "text": "don't have enough that can't just run"
+ },
+ {
+ "start": 3477.08,
+ "duration": 0.0,
+ "text": "don't have enough that can't just run the<00:57:57.320> the<00:57:57.600> computation<00:57:58.000> directly<00:57:58.400> can<00:57:58.560> still"
+ },
+ {
+ "start": 3479.11,
+ "duration": 0.0,
+ "text": "the the computation directly can still"
+ },
+ {
+ "start": 3479.12,
+ "duration": 0.0,
+ "text": "the the computation directly can still um"
+ },
+ {
+ "start": 3479.79,
+ "duration": 0.0,
+ "text": "um"
+ },
+ {
+ "start": 3479.8,
+ "duration": 0.0,
+ "text": "um uh<00:57:59.840> make<00:58:00.080> interesting<00:58:00.480> predictions,<00:58:00.920> can"
+ },
+ {
+ "start": 3481.03,
+ "duration": 0.0,
+ "text": "uh make interesting predictions, can"
+ },
+ {
+ "start": 3481.04,
+ "duration": 0.0,
+ "text": "uh make interesting predictions, can still<00:58:01.200> learn<00:58:01.400> interesting<00:58:01.880> things,<00:58:02.560> you"
+ },
+ {
+ "start": 3482.63,
+ "duration": 0.0,
+ "text": "still learn interesting things, you"
+ },
+ {
+ "start": 3482.64,
+ "duration": 0.0,
+ "text": "still learn interesting things, you know,<00:58:02.800> like<00:58:03.600> say<00:58:03.800> how<00:58:04.280> uh"
+ },
+ {
+ "start": 3485.07,
+ "duration": 0.0,
+ "text": "know, like say how uh"
+ },
+ {
+ "start": 3485.08,
+ "duration": 0.0,
+ "text": "know, like say how uh how<00:58:05.240> you<00:58:05.320> don't<00:58:05.480> need<00:58:05.640> to<00:58:05.760> know<00:58:06.040> all<00:58:06.280> of<00:58:06.440> the<00:58:06.960> uh"
+ },
+ {
+ "start": 3487.31,
+ "duration": 0.0,
+ "text": "how you don't need to know all of the uh"
+ },
+ {
+ "start": 3487.32,
+ "duration": 0.0,
+ "text": "how you don't need to know all of the uh the<00:58:07.400> positions<00:58:07.920> of<00:58:08.040> the<00:58:08.240> atoms<00:58:08.640> in<00:58:08.720> a<00:58:08.760> gas<00:58:09.480> to"
+ },
+ {
+ "start": 3489.59,
+ "duration": 0.0,
+ "text": "the positions of the atoms in a gas to"
+ },
+ {
+ "start": 3489.6,
+ "duration": 0.0,
+ "text": "the positions of the atoms in a gas to be<00:58:09.680> able<00:58:09.880> to<00:58:09.960> say<00:58:10.120> something<00:58:10.480> about<00:58:10.960> its"
+ },
+ {
+ "start": 3491.19,
+ "duration": 0.0,
+ "text": "be able to say something about its"
+ },
+ {
+ "start": 3491.2,
+ "duration": 0.0,
+ "text": "be able to say something about its pressure<00:58:11.640> or<00:58:11.760> temperature<00:58:12.359> or<00:58:12.600> volume,<00:58:13.080> these"
+ },
+ {
+ "start": 3493.23,
+ "duration": 0.0,
+ "text": "pressure or temperature or volume, these"
+ },
+ {
+ "start": 3493.24,
+ "duration": 0.0,
+ "text": "pressure or temperature or volume, these kinds<00:58:13.440> of<00:58:13.520> things."
+ },
+ {
+ "start": 3497.76,
+ "duration": 0.0,
+ "text": "Thank<00:58:17.920> you."
+ },
+ {
+ "start": 3502.08,
+ "duration": 0.0,
+ "text": "Uh"
+ },
+ {
+ "start": 3502.79,
+ "duration": 0.0,
+ "text": "Uh"
+ },
+ {
+ "start": 3502.8,
+ "duration": 0.0,
+ "text": "Uh do<00:58:22.920> do<00:58:23.080> you<00:58:23.120> mind<00:58:23.880> uh<00:58:23.960> going<00:58:24.320> back<00:58:24.680> to<00:58:24.800> that"
+ },
+ {
+ "start": 3504.99,
+ "duration": 0.0,
+ "text": "do do you mind uh going back to that"
+ },
+ {
+ "start": 3505.0,
+ "duration": 0.0,
+ "text": "do do you mind uh going back to that example<00:58:26.120> uh<00:58:26.200> with<00:58:26.440> low<00:58:26.920> Kolmogorov"
+ },
+ {
+ "start": 3507.67,
+ "duration": 0.0,
+ "text": "example uh with low Kolmogorov"
+ },
+ {
+ "start": 3507.68,
+ "duration": 0.0,
+ "text": "example uh with low Kolmogorov complexity<00:58:28.240> and<00:58:28.400> high<00:58:28.960> epiplexity?<00:58:29.920> I<00:58:30.040> I<00:58:30.080> I<00:58:30.120> I"
+ },
+ {
+ "start": 3510.95,
+ "duration": 0.0,
+ "text": "complexity and high epiplexity? I I I I"
+ },
+ {
+ "start": 3510.96,
+ "duration": 0.0,
+ "text": "complexity and high epiplexity? I I I I I'd<00:58:31.080> like<00:58:31.280> to<00:58:31.359> understand<00:58:31.800> that<00:58:31.920> a<00:58:31.960> little"
+ },
+ {
+ "start": 3512.23,
+ "duration": 0.0,
+ "text": "I'd like to understand that a little"
+ },
+ {
+ "start": 3512.24,
+ "duration": 0.0,
+ "text": "I'd like to understand that a little bit."
+ },
+ {
+ "start": 3513.71,
+ "duration": 0.0,
+ "text": "bit."
+ },
+ {
+ "start": 3513.72,
+ "duration": 0.0,
+ "text": "bit. Uh<00:58:33.920> low<00:58:34.120> Kolmogorov<00:58:34.480> complexity?<00:58:35.080> Yeah,<00:58:35.760> uh"
+ },
+ {
+ "start": 3515.83,
+ "duration": 0.0,
+ "text": "Uh low Kolmogorov complexity? Yeah, uh"
+ },
+ {
+ "start": 3515.84,
+ "duration": 0.0,
+ "text": "Uh low Kolmogorov complexity? Yeah, uh right.<00:58:36.440> So<00:58:37.200> um"
+ },
+ {
+ "start": 3518.79,
+ "duration": 0.0,
+ "text": "right. So um"
+ },
+ {
+ "start": 3518.8,
+ "duration": 0.0,
+ "text": "right. So um uh"
+ },
+ {
+ "start": 3519.99,
+ "duration": 0.0,
+ "text": "uh"
+ },
+ {
+ "start": 3520.0,
+ "duration": 0.0,
+ "text": "uh Do<00:58:40.040> you<00:58:40.120> remember<00:58:40.359> which<00:58:40.600> one<00:58:40.800> that<00:58:40.920> was?<00:58:41.720> You"
+ },
+ {
+ "start": 3521.75,
+ "duration": 0.0,
+ "text": "Do you remember which one that was? You"
+ },
+ {
+ "start": 3521.76,
+ "duration": 0.0,
+ "text": "Do you remember which one that was? You mean<00:58:41.880> the<00:58:41.960> one<00:58:42.080> that"
+ },
+ {
+ "start": 3522.15,
+ "duration": 0.0,
+ "text": "mean the one that"
+ },
+ {
+ "start": 3522.16,
+ "duration": 0.0,
+ "text": "mean the one that >> I<00:58:42.359> I<00:58:42.400> think<00:58:42.560> it<00:58:42.640> was<00:58:42.760> towards<00:58:43.000> the<00:58:43.120> end.<00:58:43.840> Yeah,"
+ },
+ {
+ "start": 3523.91,
+ "duration": 0.0,
+ "text": ">> I I think it was towards the end. Yeah,"
+ },
+ {
+ "start": 3523.92,
+ "duration": 0.0,
+ "text": ">> I I think it was towards the end. Yeah, this<00:58:44.080> this<00:58:44.240> one<00:58:44.359> here?"
+ },
+ {
+ "start": 3525.75,
+ "duration": 0.0,
+ "text": "this this one here?"
+ },
+ {
+ "start": 3525.76,
+ "duration": 0.0,
+ "text": "this this one here? Right."
+ },
+ {
+ "start": 3527.03,
+ "duration": 0.0,
+ "text": "Right."
+ },
+ {
+ "start": 3527.04,
+ "duration": 0.0,
+ "text": "Right. Uh<00:58:47.359> is<00:58:47.520> it<00:58:47.600> this<00:58:47.800> slide?"
+ },
+ {
+ "start": 3529.59,
+ "duration": 0.0,
+ "text": "Uh is it this slide?"
+ },
+ {
+ "start": 3529.6,
+ "duration": 0.0,
+ "text": "Uh is it this slide? Uh<00:58:50.400> So<00:58:50.560> here<00:58:50.920> is<00:58:51.000> maybe<00:58:51.200> a<00:58:51.240> summary<00:58:51.560> of<00:58:51.640> what"
+ },
+ {
+ "start": 3531.75,
+ "duration": 0.0,
+ "text": "Uh So here is maybe a summary of what"
+ },
+ {
+ "start": 3531.76,
+ "duration": 0.0,
+ "text": "Uh So here is maybe a summary of what you<00:58:51.920> Yeah,<00:58:52.120> I<00:58:52.359> I<00:58:52.440> think<00:58:52.640> this<00:58:52.760> is<00:58:52.800> the<00:58:52.840> one."
+ },
+ {
+ "start": 3533.03,
+ "duration": 0.0,
+ "text": "you Yeah, I I think this is the one."
+ },
+ {
+ "start": 3533.04,
+ "duration": 0.0,
+ "text": "you Yeah, I I think this is the one. Yeah,<00:58:53.160> yeah,<00:58:53.240> yeah.<00:58:53.640> Right."
+ },
+ {
+ "start": 3534.51,
+ "duration": 0.0,
+ "text": "Yeah, yeah, yeah. Right."
+ },
+ {
+ "start": 3534.52,
+ "duration": 0.0,
+ "text": "Yeah, yeah, yeah. Right. So<00:58:54.920> um<00:58:55.320> so<00:58:55.520> these<00:58:55.920> guys<00:58:56.160> here,<00:58:56.560> right?<00:58:56.920> Uh"
+ },
+ {
+ "start": 3537.71,
+ "duration": 0.0,
+ "text": "So um so these guys here, right? Uh"
+ },
+ {
+ "start": 3537.72,
+ "duration": 0.0,
+ "text": "So um so these guys here, right? Uh low<00:58:58.040> Kolmogorov<00:58:58.400> complexity<00:58:59.080> and<00:58:59.280> oh<00:58:59.359> sorry,"
+ },
+ {
+ "start": 3539.59,
+ "duration": 0.0,
+ "text": "low Kolmogorov complexity and oh sorry,"
+ },
+ {
+ "start": 3539.6,
+ "duration": 0.0,
+ "text": "low Kolmogorov complexity and oh sorry, low<00:58:59.760> Kolmogorov<00:59:00.080> complexity<00:59:00.400> and<00:59:00.480> high"
+ },
+ {
+ "start": 3540.83,
+ "duration": 0.0,
+ "text": "low Kolmogorov complexity and high"
+ },
+ {
+ "start": 3540.84,
+ "duration": 0.0,
+ "text": "low Kolmogorov complexity and high epiplexity.<00:59:01.560> That<00:59:01.760> that's<00:59:02.040> the<00:59:02.160> these<00:59:02.400> ones."
+ },
+ {
+ "start": 3542.95,
+ "duration": 0.0,
+ "text": "epiplexity. That that's the these ones."
+ },
+ {
+ "start": 3542.96,
+ "duration": 0.0,
+ "text": "epiplexity. That that's the these ones. >> Yeah."
+ },
+ {
+ "start": 3543.91,
+ "duration": 0.0,
+ "text": ">> Yeah."
+ },
+ {
+ "start": 3543.92,
+ "duration": 0.0,
+ "text": ">> Yeah. Right.<00:59:04.520> So<00:59:04.680> that<00:59:05.120> um<00:59:05.520> you<00:59:05.600> know,<00:59:05.720> key<00:59:05.840> example"
+ },
+ {
+ "start": 3546.19,
+ "duration": 0.0,
+ "text": "Right. So that um you know, key example"
+ },
+ {
+ "start": 3546.2,
+ "duration": 0.0,
+ "text": "Right. So that um you know, key example is<00:59:06.280> being<00:59:06.520> right<00:59:06.680> like<00:59:07.280> uh<00:59:07.600> rule<00:59:07.760> 54,<00:59:08.960> um<00:59:09.200> this"
+ },
+ {
+ "start": 3549.43,
+ "duration": 0.0,
+ "text": "is being right like uh rule 54, um this"
+ },
+ {
+ "start": 3549.44,
+ "duration": 0.0,
+ "text": "is being right like uh rule 54, um this AlphaZero,<00:59:10.359> say<00:59:10.840> like<00:59:11.200> a<00:59:11.240> data<00:59:11.600> produced<00:59:11.840> from"
+ },
+ {
+ "start": 3551.95,
+ "duration": 0.0,
+ "text": "AlphaZero, say like a data produced from"
+ },
+ {
+ "start": 3551.96,
+ "duration": 0.0,
+ "text": "AlphaZero, say like a data produced from a<00:59:12.000> fractal.<00:59:12.760> In<00:59:12.880> each<00:59:13.040> of<00:59:13.120> these<00:59:13.240> cases,<00:59:13.680> we"
+ },
+ {
+ "start": 3553.83,
+ "duration": 0.0,
+ "text": "a fractal. In each of these cases, we"
+ },
+ {
+ "start": 3553.84,
+ "duration": 0.0,
+ "text": "a fractal. In each of these cases, we have<00:59:14.320> a<00:59:14.520> short<00:59:14.760> program<00:59:15.200> that<00:59:15.480> can<00:59:15.720> produce"
+ },
+ {
+ "start": 3556.51,
+ "duration": 0.0,
+ "text": "have a short program that can produce"
+ },
+ {
+ "start": 3556.52,
+ "duration": 0.0,
+ "text": "have a short program that can produce the<00:59:16.640> outputs,<00:59:17.120> right?<00:59:17.359> In<00:59:17.440> the<00:59:17.520> case<00:59:17.680> of<00:59:17.760> the"
+ },
+ {
+ "start": 3557.79,
+ "duration": 0.0,
+ "text": "the outputs, right? In the case of the"
+ },
+ {
+ "start": 3557.8,
+ "duration": 0.0,
+ "text": "the outputs, right? In the case of the fractal,<00:59:18.240> we<00:59:18.320> just<00:59:18.480> have<00:59:18.640> this<00:59:19.240> iterating<00:59:19.600> the"
+ },
+ {
+ "start": 3559.67,
+ "duration": 0.0,
+ "text": "fractal, we just have this iterating the"
+ },
+ {
+ "start": 3559.68,
+ "duration": 0.0,
+ "text": "fractal, we just have this iterating the complex<00:59:20.040> plane,<00:59:20.560> right?<00:59:21.280> Um<00:59:21.720> it<00:59:21.800> just<00:59:21.920> takes<00:59:22.080> a"
+ },
+ {
+ "start": 3562.11,
+ "duration": 0.0,
+ "text": "complex plane, right? Um it just takes a"
+ },
+ {
+ "start": 3562.12,
+ "duration": 0.0,
+ "text": "complex plane, right? Um it just takes a lot<00:59:22.240> of<00:59:22.320> computation<00:59:22.840> to<00:59:22.920> make<00:59:23.120> all<00:59:23.240> these"
+ },
+ {
+ "start": 3563.349,
+ "duration": 0.0,
+ "text": "lot of computation to make all these"
+ },
+ {
+ "start": 3563.359,
+ "duration": 0.0,
+ "text": "lot of computation to make all these different<00:59:23.840> uh"
+ },
+ {
+ "start": 3564.51,
+ "duration": 0.0,
+ "text": "different uh"
+ },
+ {
+ "start": 3564.52,
+ "duration": 0.0,
+ "text": "different uh uh<00:59:24.800> you<00:59:24.880> know,<00:59:25.040> pixels.<00:59:26.000> Um<00:59:26.920> uh"
+ },
+ {
+ "start": 3567.55,
+ "duration": 0.0,
+ "text": "uh you know, pixels. Um uh"
+ },
+ {
+ "start": 3567.56,
+ "duration": 0.0,
+ "text": "uh you know, pixels. Um uh and<00:59:28.080> for<00:59:28.680> uh<00:59:29.000> right,<00:59:29.520> uh"
+ },
+ {
+ "start": 3570.11,
+ "duration": 0.0,
+ "text": "and for uh right, uh"
+ },
+ {
+ "start": 3570.12,
+ "duration": 0.0,
+ "text": "and for uh right, uh but<00:59:30.520> if<00:59:30.680> we<00:59:31.160> are<00:59:31.480> training<00:59:31.880> on<00:59:32.000> it<00:59:32.240> with<00:59:32.880> a"
+ },
+ {
+ "start": 3573.07,
+ "duration": 0.0,
+ "text": "but if we are training on it with a"
+ },
+ {
+ "start": 3573.08,
+ "duration": 0.0,
+ "text": "but if we are training on it with a model<00:59:33.600> that<00:59:34.520> has<00:59:34.960> limited<00:59:35.240> computation,<00:59:36.360> then"
+ },
+ {
+ "start": 3576.55,
+ "duration": 0.0,
+ "text": "model that has limited computation, then"
+ },
+ {
+ "start": 3576.56,
+ "duration": 0.0,
+ "text": "model that has limited computation, then actually<00:59:37.240> we<00:59:37.360> see<00:59:37.520> this<00:59:37.920> as<00:59:38.040> complex<00:59:38.600> and"
+ },
+ {
+ "start": 3578.75,
+ "duration": 0.0,
+ "text": "actually we see this as complex and"
+ },
+ {
+ "start": 3578.76,
+ "duration": 0.0,
+ "text": "actually we see this as complex and interesting."
+ },
+ {
+ "start": 3579.87,
+ "duration": 0.0,
+ "text": "interesting."
+ },
+ {
+ "start": 3579.88,
+ "duration": 0.0,
+ "text": "interesting. And<00:59:40.600> perhaps,<00:59:41.120> you<00:59:41.240> know,<00:59:41.480> mapping<00:59:42.000> a<00:59:42.040> little"
+ },
+ {
+ "start": 3582.23,
+ "duration": 0.0,
+ "text": "And perhaps, you know, mapping a little"
+ },
+ {
+ "start": 3582.24,
+ "duration": 0.0,
+ "text": "And perhaps, you know, mapping a little bit<00:59:42.440> on<00:59:42.600> to<00:59:43.320> I<00:59:43.360> mean<00:59:43.720> a<00:59:43.760> human<00:59:44.040> looks<00:59:44.280> at<00:59:44.400> this"
+ },
+ {
+ "start": 3584.67,
+ "duration": 0.0,
+ "text": "bit on to I mean a human looks at this"
+ },
+ {
+ "start": 3584.68,
+ "duration": 0.0,
+ "text": "bit on to I mean a human looks at this and<00:59:44.920> they<00:59:45.080> think<00:59:45.320> you<00:59:45.400> know<00:59:45.480> they<00:59:45.560> think<00:59:45.720> this"
+ },
+ {
+ "start": 3585.91,
+ "duration": 0.0,
+ "text": "and they think you know they think this"
+ },
+ {
+ "start": 3585.92,
+ "duration": 0.0,
+ "text": "and they think you know they think this is<00:59:46.120> really<00:59:46.760> this<00:59:47.000> this<00:59:47.200> is<00:59:47.280> really"
+ },
+ {
+ "start": 3587.43,
+ "duration": 0.0,
+ "text": "is really this this is really"
+ },
+ {
+ "start": 3587.44,
+ "duration": 0.0,
+ "text": "is really this this is really interesting<00:59:47.880> and<00:59:47.960> there's<00:59:48.080> things<00:59:48.280> to<00:59:48.400> learn"
+ },
+ {
+ "start": 3588.59,
+ "duration": 0.0,
+ "text": "interesting and there's things to learn"
+ },
+ {
+ "start": 3588.6,
+ "duration": 0.0,
+ "text": "interesting and there's things to learn here,<00:59:48.960> right?<00:59:49.840> Um<00:59:50.080> and<00:59:50.240> that<00:59:50.480> is<00:59:50.560> somehow<00:59:50.800> true"
+ },
+ {
+ "start": 3591.11,
+ "duration": 0.0,
+ "text": "here, right? Um and that is somehow true"
+ },
+ {
+ "start": 3591.12,
+ "duration": 0.0,
+ "text": "here, right? Um and that is somehow true at<00:59:51.200> the<00:59:51.280> same<00:59:51.480> time<00:59:51.960> as<00:59:52.240> there<00:59:52.400> being<00:59:52.560> a<00:59:52.600> very"
+ },
+ {
+ "start": 3592.75,
+ "duration": 0.0,
+ "text": "at the same time as there being a very"
+ },
+ {
+ "start": 3592.76,
+ "duration": 0.0,
+ "text": "at the same time as there being a very simple<00:59:53.000> rule<00:59:53.120> that<00:59:53.240> generated<00:59:53.680> it.<00:59:54.160> Um"
+ },
+ {
+ "start": 3594.63,
+ "duration": 0.0,
+ "text": "simple rule that generated it. Um"
+ },
+ {
+ "start": 3594.64,
+ "duration": 0.0,
+ "text": "simple rule that generated it. Um another<00:59:54.920> example,<00:59:55.200> right?<00:59:55.440> The<00:59:55.640> rule<00:59:55.760> 54,<00:59:56.720> the"
+ },
+ {
+ "start": 3596.91,
+ "duration": 0.0,
+ "text": "another example, right? The rule 54, the"
+ },
+ {
+ "start": 3596.92,
+ "duration": 0.0,
+ "text": "another example, right? The rule 54, the rule<00:59:57.240> itself<00:59:57.720> has<00:59:57.960> a<00:59:58.000> very<00:59:58.160> short"
+ },
+ {
+ "start": 3598.31,
+ "duration": 0.0,
+ "text": "rule itself has a very short"
+ },
+ {
+ "start": 3598.32,
+ "duration": 0.0,
+ "text": "rule itself has a very short description."
+ },
+ {
+ "start": 3599.75,
+ "duration": 0.0,
+ "text": "description."
+ },
+ {
+ "start": 3599.76,
+ "duration": 0.0,
+ "text": "description. Uh<01:00:00.080> if<01:00:00.440> we<01:00:01.280> uh"
+ },
+ {
+ "start": 3602.15,
+ "duration": 0.0,
+ "text": "Uh if we uh"
+ },
+ {
+ "start": 3602.16,
+ "duration": 0.0,
+ "text": "Uh if we uh I<01:00:02.240> guess<01:00:02.880> either<01:00:03.080> you<01:00:03.200> could<01:00:03.360> consider<01:00:03.680> the"
+ },
+ {
+ "start": 3603.79,
+ "duration": 0.0,
+ "text": "I guess either you could consider the"
+ },
+ {
+ "start": 3603.8,
+ "duration": 0.0,
+ "text": "I guess either you could consider the version<01:00:04.160> where<01:00:04.600> we<01:00:04.720> have<01:00:05.160> um"
+ },
+ {
+ "start": 3606.19,
+ "duration": 0.0,
+ "text": "version where we have um"
+ },
+ {
+ "start": 3606.2,
+ "duration": 0.0,
+ "text": "version where we have um random<01:00:06.640> initial<01:00:06.920> states<01:00:07.320> and<01:00:07.480> we're"
+ },
+ {
+ "start": 3607.55,
+ "duration": 0.0,
+ "text": "random initial states and we're"
+ },
+ {
+ "start": 3607.56,
+ "duration": 0.0,
+ "text": "random initial states and we're considering<01:00:07.880> the<01:00:07.960> prediction<01:00:08.320> problem<01:00:08.600> of"
+ },
+ {
+ "start": 3608.71,
+ "duration": 0.0,
+ "text": "considering the prediction problem of"
+ },
+ {
+ "start": 3608.72,
+ "duration": 0.0,
+ "text": "considering the prediction problem of the<01:00:08.800> final<01:00:09.080> state<01:00:09.320> given<01:00:09.520> the<01:00:09.600> initial"
+ },
+ {
+ "start": 3609.83,
+ "duration": 0.0,
+ "text": "the final state given the initial"
+ },
+ {
+ "start": 3609.84,
+ "duration": 0.0,
+ "text": "the final state given the initial states.<01:00:10.280> That<01:00:10.400> could<01:00:10.480> be<01:00:10.600> one<01:00:10.720> version<01:00:11.160> where"
+ },
+ {
+ "start": 3611.43,
+ "duration": 0.0,
+ "text": "states. That could be one version where"
+ },
+ {
+ "start": 3611.44,
+ "duration": 0.0,
+ "text": "states. That could be one version where that<01:00:11.560> would<01:00:11.680> be<01:00:12.080> high<01:00:12.240> epiplexity<01:00:12.880> but<01:00:13.080> low"
+ },
+ {
+ "start": 3613.59,
+ "duration": 0.0,
+ "text": "that would be high epiplexity but low"
+ },
+ {
+ "start": 3613.6,
+ "duration": 0.0,
+ "text": "that would be high epiplexity but low Kolmogorov<01:00:13.960> complexity<01:00:14.960> um<01:00:15.320> because<01:00:15.600> again,"
+ },
+ {
+ "start": 3616.15,
+ "duration": 0.0,
+ "text": "Kolmogorov complexity um because again,"
+ },
+ {
+ "start": 3616.16,
+ "duration": 0.0,
+ "text": "Kolmogorov complexity um because again, you<01:00:16.240> know,<01:00:16.320> you<01:00:16.760> you<01:00:16.880> know<01:00:17.040> the<01:00:17.120> rule,<01:00:17.440> you"
+ },
+ {
+ "start": 3617.51,
+ "duration": 0.0,
+ "text": "you know, you you know the rule, you"
+ },
+ {
+ "start": 3617.52,
+ "duration": 0.0,
+ "text": "you know, you you know the rule, you could<01:00:17.640> just<01:00:17.840> unroll<01:00:18.160> it.<01:00:18.680> Um<01:00:18.800> or<01:00:19.080> you<01:00:19.200> could<01:00:19.360> do"
+ },
+ {
+ "start": 3619.63,
+ "duration": 0.0,
+ "text": "could just unroll it. Um or you could do"
+ },
+ {
+ "start": 3619.64,
+ "duration": 0.0,
+ "text": "could just unroll it. Um or you could do say<01:00:20.040> uh"
+ },
+ {
+ "start": 3620.59,
+ "duration": 0.0,
+ "text": "say uh"
+ },
+ {
+ "start": 3620.6,
+ "duration": 0.0,
+ "text": "say uh where<01:00:20.920> you<01:00:21.040> just<01:00:21.240> have<01:00:21.360> some<01:00:21.480> deterministic"
+ },
+ {
+ "start": 3622.15,
+ "duration": 0.0,
+ "text": "where you just have some deterministic"
+ },
+ {
+ "start": 3622.16,
+ "duration": 0.0,
+ "text": "where you just have some deterministic initial<01:00:22.600> states<01:00:23.280> and<01:00:23.480> then<01:00:24.400> um"
+ },
+ {
+ "start": 3625.51,
+ "duration": 0.0,
+ "text": "initial states and then um"
+ },
+ {
+ "start": 3625.52,
+ "duration": 0.0,
+ "text": "initial states and then um uh<01:00:25.640> right<01:00:25.840> and<01:00:26.080> all<01:00:26.240> you're<01:00:26.320> doing<01:00:26.520> is<01:00:26.640> trying"
+ },
+ {
+ "start": 3626.75,
+ "duration": 0.0,
+ "text": "uh right and all you're doing is trying"
+ },
+ {
+ "start": 3626.76,
+ "duration": 0.0,
+ "text": "uh right and all you're doing is trying to<01:00:26.840> predict<01:00:27.080> the<01:00:27.160> final<01:00:27.400> state.<01:00:27.760> And<01:00:27.840> again,"
+ },
+ {
+ "start": 3628.15,
+ "duration": 0.0,
+ "text": "to predict the final state. And again,"
+ },
+ {
+ "start": 3628.16,
+ "duration": 0.0,
+ "text": "to predict the final state. And again, that<01:00:28.320> would<01:00:29.000> have<01:00:29.200> the<01:00:29.280> same<01:00:29.520> thing<01:00:29.720> of<01:00:29.920> low"
+ },
+ {
+ "start": 3630.15,
+ "duration": 0.0,
+ "text": "that would have the same thing of low"
+ },
+ {
+ "start": 3630.16,
+ "duration": 0.0,
+ "text": "that would have the same thing of low Kolmogorov<01:00:30.520> complexity<01:00:31.520> um<01:00:31.720> high<01:00:32.480> uh"
+ },
+ {
+ "start": 3632.95,
+ "duration": 0.0,
+ "text": "Kolmogorov complexity um high uh"
+ },
+ {
+ "start": 3632.96,
+ "duration": 0.0,
+ "text": "Kolmogorov complexity um high uh epiplexity.<01:00:34.080> Uh<01:00:34.240> also<01:00:34.520> the<01:00:34.600> AlphaZero,"
+ },
+ {
+ "start": 3635.35,
+ "duration": 0.0,
+ "text": "epiplexity. Uh also the AlphaZero,"
+ },
+ {
+ "start": 3635.36,
+ "duration": 0.0,
+ "text": "epiplexity. Uh also the AlphaZero, right?<01:00:35.680> Again,<01:00:36.040> the<01:00:36.200> this<01:00:36.720> the<01:00:36.840> seed,<01:00:37.280> the"
+ },
+ {
+ "start": 3637.35,
+ "duration": 0.0,
+ "text": "right? Again, the this the seed, the"
+ },
+ {
+ "start": 3637.36,
+ "duration": 0.0,
+ "text": "right? Again, the this the seed, the algorithm,<01:00:37.800> the<01:00:37.840> rules<01:00:38.040> of<01:00:38.120> the<01:00:38.200> game,<01:00:38.800> they"
+ },
+ {
+ "start": 3638.87,
+ "duration": 0.0,
+ "text": "algorithm, the rules of the game, they"
+ },
+ {
+ "start": 3638.88,
+ "duration": 0.0,
+ "text": "algorithm, the rules of the game, they all<01:00:39.000> have<01:00:39.080> a<01:00:39.120> short<01:00:39.320> description.<01:00:40.160> You<01:00:40.240> can"
+ },
+ {
+ "start": 3640.35,
+ "duration": 0.0,
+ "text": "all have a short description. You can"
+ },
+ {
+ "start": 3640.36,
+ "duration": 0.0,
+ "text": "all have a short description. You can write<01:00:40.520> that<01:00:40.640> down<01:00:40.840> as<01:00:41.000> a<01:00:41.080> computer<01:00:41.440> program<01:00:41.960> in"
+ },
+ {
+ "start": 3642.23,
+ "duration": 0.0,
+ "text": "write that down as a computer program in"
+ },
+ {
+ "start": 3642.24,
+ "duration": 0.0,
+ "text": "write that down as a computer program in in<01:00:42.480> just<01:00:42.680> a<01:00:42.760> few<01:00:42.920> thousand<01:00:43.200> lines<01:00:43.400> of<01:00:43.480> code."
+ },
+ {
+ "start": 3644.51,
+ "duration": 0.0,
+ "text": "in just a few thousand lines of code."
+ },
+ {
+ "start": 3644.52,
+ "duration": 0.0,
+ "text": "in just a few thousand lines of code. But<01:00:44.800> you<01:00:44.880> run<01:00:45.080> that<01:00:45.680> and<01:00:45.800> you<01:00:46.400> produce,<01:00:47.000> you"
+ },
+ {
+ "start": 3647.07,
+ "duration": 0.0,
+ "text": "But you run that and you produce, you"
+ },
+ {
+ "start": 3647.08,
+ "duration": 0.0,
+ "text": "But you run that and you produce, you know,<01:00:47.200> millions<01:00:47.760> or<01:00:47.880> billion<01:00:48.200> parameter"
+ },
+ {
+ "start": 3648.55,
+ "duration": 0.0,
+ "text": "know, millions or billion parameter"
+ },
+ {
+ "start": 3648.56,
+ "duration": 0.0,
+ "text": "know, millions or billion parameter models<01:00:49.440> um<01:00:49.600> that<01:00:49.840> seems<01:00:50.040> to<01:00:50.120> have<01:00:50.240> a<01:00:50.280> very<01:00:50.480> deep"
+ },
+ {
+ "start": 3650.71,
+ "duration": 0.0,
+ "text": "models um that seems to have a very deep"
+ },
+ {
+ "start": 3650.72,
+ "duration": 0.0,
+ "text": "models um that seems to have a very deep understanding<01:00:51.240> of<01:00:51.320> all<01:00:51.440> these<01:00:51.560> different<01:00:51.840> end"
+ },
+ {
+ "start": 3651.95,
+ "duration": 0.0,
+ "text": "understanding of all these different end"
+ },
+ {
+ "start": 3651.96,
+ "duration": 0.0,
+ "text": "understanding of all these different end game<01:00:52.120> variations.<01:00:53.120> Um"
+ },
+ {
+ "start": 3653.71,
+ "duration": 0.0,
+ "text": "game variations. Um"
+ },
+ {
+ "start": 3653.72,
+ "duration": 0.0,
+ "text": "game variations. Um and<01:00:54.160> to<01:00:54.280> human<01:00:54.560> they<01:00:54.680> would<01:00:54.800> say<01:00:54.920> that<01:00:55.080> the"
+ },
+ {
+ "start": 3655.15,
+ "duration": 0.0,
+ "text": "and to human they would say that the"
+ },
+ {
+ "start": 3655.16,
+ "duration": 0.0,
+ "text": "and to human they would say that the model<01:00:55.480> has<01:00:55.800> learned<01:00:56.080> all<01:00:56.200> this<01:00:56.360> information"
+ },
+ {
+ "start": 3656.83,
+ "duration": 0.0,
+ "text": "model has learned all this information"
+ },
+ {
+ "start": 3656.84,
+ "duration": 0.0,
+ "text": "model has learned all this information about<01:00:57.040> all<01:00:57.120> these<01:00:57.240> different<01:00:57.480> end<01:00:57.560> game"
+ },
+ {
+ "start": 3657.71,
+ "duration": 0.0,
+ "text": "about all these different end game"
+ },
+ {
+ "start": 3657.72,
+ "duration": 0.0,
+ "text": "about all these different end game variations<01:00:58.360> and<01:00:58.480> this<01:00:58.640> thing<01:00:58.840> and<01:00:58.920> that<01:00:59.200> and"
+ },
+ {
+ "start": 3659.75,
+ "duration": 0.0,
+ "text": "variations and this thing and that and"
+ },
+ {
+ "start": 3659.76,
+ "duration": 0.0,
+ "text": "variations and this thing and that and um"
+ },
+ {
+ "start": 3660.31,
+ "duration": 0.0,
+ "text": "um"
+ },
+ {
+ "start": 3660.32,
+ "duration": 0.0,
+ "text": "um right.<01:01:00.720> Uh<01:01:00.880> and<01:01:01.120> so<01:01:01.800> at<01:01:01.920> some<01:01:02.040> level<01:01:02.240> we<01:01:02.360> know"
+ },
+ {
+ "start": 3662.79,
+ "duration": 0.0,
+ "text": "right. Uh and so at some level we know"
+ },
+ {
+ "start": 3662.8,
+ "duration": 0.0,
+ "text": "right. Uh and so at some level we know that<01:01:03.000> the<01:01:03.120> Kolmogorov<01:01:03.440> complexity<01:01:03.960> is<01:01:04.080> low,"
+ },
+ {
+ "start": 3664.63,
+ "duration": 0.0,
+ "text": "that the Kolmogorov complexity is low,"
+ },
+ {
+ "start": 3664.64,
+ "duration": 0.0,
+ "text": "that the Kolmogorov complexity is low, Shannon<01:01:04.880> information<01:01:05.360> is<01:01:05.520> low<01:01:06.280> um<01:01:06.640> because<01:01:06.960> of"
+ },
+ {
+ "start": 3667.07,
+ "duration": 0.0,
+ "text": "Shannon information is low um because of"
+ },
+ {
+ "start": 3667.08,
+ "duration": 0.0,
+ "text": "Shannon information is low um because of just<01:01:07.400> what<01:01:07.640> went<01:01:07.840> into<01:01:08.080> this,<01:01:08.760> you<01:01:08.840> know,<01:01:09.280> the"
+ },
+ {
+ "start": 3669.43,
+ "duration": 0.0,
+ "text": "just what went into this, you know, the"
+ },
+ {
+ "start": 3669.44,
+ "duration": 0.0,
+ "text": "just what went into this, you know, the this<01:01:09.600> program<01:01:09.840> they<01:01:09.960> use<01:01:10.160> it.<01:01:10.520> But<01:01:10.680> then"
+ },
+ {
+ "start": 3671.75,
+ "duration": 0.0,
+ "text": "this program they use it. But then"
+ },
+ {
+ "start": 3671.76,
+ "duration": 0.0,
+ "text": "this program they use it. But then uh"
+ },
+ {
+ "start": 3672.63,
+ "duration": 0.0,
+ "text": "uh"
+ },
+ {
+ "start": 3672.64,
+ "duration": 0.0,
+ "text": "uh somehow<01:01:13.280> that's<01:01:13.480> not<01:01:13.640> mapping<01:01:13.920> on<01:01:14.000> to<01:01:14.080> the"
+ },
+ {
+ "start": 3674.15,
+ "duration": 0.0,
+ "text": "somehow that's not mapping on to the"
+ },
+ {
+ "start": 3674.16,
+ "duration": 0.0,
+ "text": "somehow that's not mapping on to the complexity<01:01:14.760> that<01:01:15.080> that<01:01:15.280> we<01:01:15.400> mean<01:01:15.720> when<01:01:15.880> we<01:01:15.960> say"
+ },
+ {
+ "start": 3676.27,
+ "duration": 0.0,
+ "text": "complexity that that we mean when we say"
+ },
+ {
+ "start": 3676.28,
+ "duration": 0.0,
+ "text": "complexity that that we mean when we say it<01:01:16.400> has<01:01:16.520> learned<01:01:16.720> all<01:01:16.800> these<01:01:16.960> end<01:01:17.080> game"
+ },
+ {
+ "start": 3677.27,
+ "duration": 0.0,
+ "text": "it has learned all these end game"
+ },
+ {
+ "start": 3677.28,
+ "duration": 0.0,
+ "text": "it has learned all these end game variations.<01:01:18.000> Um<01:01:18.200> so<01:01:18.920> uh<01:01:19.040> this<01:01:19.240> is<01:01:19.440> one<01:01:19.640> where"
+ },
+ {
+ "start": 3679.75,
+ "duration": 0.0,
+ "text": "variations. Um so uh this is one where"
+ },
+ {
+ "start": 3679.76,
+ "duration": 0.0,
+ "text": "variations. Um so uh this is one where we<01:01:19.880> would<01:01:20.000> expect<01:01:20.480> to<01:01:20.720> have<01:01:20.960> high<01:01:21.440> epiplexity"
+ },
+ {
+ "start": 3682.63,
+ "duration": 0.0,
+ "text": "we would expect to have high epiplexity"
+ },
+ {
+ "start": 3682.64,
+ "duration": 0.0,
+ "text": "we would expect to have high epiplexity um"
+ },
+ {
+ "start": 3683.19,
+ "duration": 0.0,
+ "text": "um"
+ },
+ {
+ "start": 3683.2,
+ "duration": 0.0,
+ "text": "um just<01:01:23.440> again<01:01:23.720> thinking<01:01:24.000> about<01:01:24.520> uh"
+ },
+ {
+ "start": 3685.15,
+ "duration": 0.0,
+ "text": "just again thinking about uh"
+ },
+ {
+ "start": 3685.16,
+ "duration": 0.0,
+ "text": "just again thinking about uh uh"
+ },
+ {
+ "start": 3686.15,
+ "duration": 0.0,
+ "text": "uh"
+ },
+ {
+ "start": 3686.16,
+ "duration": 0.0,
+ "text": "uh yeah,<01:01:26.760> basically<01:01:27.240> compressing<01:01:27.680> this<01:01:27.760> data"
+ },
+ {
+ "start": 3687.99,
+ "duration": 0.0,
+ "text": "yeah, basically compressing this data"
+ },
+ {
+ "start": 3688.0,
+ "duration": 0.0,
+ "text": "yeah, basically compressing this data that<01:01:28.120> was<01:01:28.240> produced<01:01:28.600> through<01:01:28.720> this<01:01:28.840> process."
+ },
+ {
+ "start": 3690.51,
+ "duration": 0.0,
+ "text": "that was produced through this process."
+ },
+ {
+ "start": 3690.52,
+ "duration": 0.0,
+ "text": "that was produced through this process. So<01:01:30.880> so"
+ },
+ {
+ "start": 3691.95,
+ "duration": 0.0,
+ "text": "So so"
+ },
+ {
+ "start": 3691.96,
+ "duration": 0.0,
+ "text": "So so So<01:01:32.120> what<01:01:32.240> you're<01:01:32.320> suggesting<01:01:32.920> is<01:01:33.040> if<01:01:33.160> you<01:01:33.280> push"
+ },
+ {
+ "start": 3693.59,
+ "duration": 0.0,
+ "text": "So what you're suggesting is if you push"
+ },
+ {
+ "start": 3693.6,
+ "duration": 0.0,
+ "text": "So what you're suggesting is if you push this<01:01:33.920> available<01:01:34.400> compute<01:01:34.800> time<01:01:35.080> to<01:01:35.200> infinity,"
+ },
+ {
+ "start": 3695.79,
+ "duration": 0.0,
+ "text": "this available compute time to infinity,"
+ },
+ {
+ "start": 3695.8,
+ "duration": 0.0,
+ "text": "this available compute time to infinity, then<01:01:36.040> the<01:01:36.280> plexity<01:01:37.080> would<01:01:37.240> reduce.<01:01:37.920> That's"
+ },
+ {
+ "start": 3698.19,
+ "duration": 0.0,
+ "text": "then the plexity would reduce. That's"
+ },
+ {
+ "start": 3698.2,
+ "duration": 0.0,
+ "text": "then the plexity would reduce. That's right.<01:01:38.440> Yeah,<01:01:38.520> okay.<01:01:38.800> Yeah,<01:01:39.000> I<01:01:39.040> should<01:01:39.440> have"
+ },
+ {
+ "start": 3699.51,
+ "duration": 0.0,
+ "text": "right. Yeah, okay. Yeah, I should have"
+ },
+ {
+ "start": 3699.52,
+ "duration": 0.0,
+ "text": "right. Yeah, okay. Yeah, I should have said<01:01:39.680> that.<01:01:39.840> Yeah,<01:01:40.000> so<01:01:40.360> uh"
+ },
+ {
+ "start": 3701.03,
+ "duration": 0.0,
+ "text": "said that. Yeah, so uh"
+ },
+ {
+ "start": 3701.04,
+ "duration": 0.0,
+ "text": "said that. Yeah, so uh um<01:01:41.520> here<01:01:41.800> I<01:01:41.840> meant<01:01:42.040> like<01:01:42.360> with<01:01:42.480> time<01:01:42.720> bounds"
+ },
+ {
+ "start": 3703.07,
+ "duration": 0.0,
+ "text": "um here I meant like with time bounds"
+ },
+ {
+ "start": 3703.08,
+ "duration": 0.0,
+ "text": "um here I meant like with time bounds that<01:01:43.320> are<01:01:43.880> um<01:01:44.400> are<01:01:44.520> modest.<01:01:44.880> So<01:01:45.040> in<01:01:45.160> this<01:01:45.320> case"
+ },
+ {
+ "start": 3705.59,
+ "duration": 0.0,
+ "text": "that are um are modest. So in this case"
+ },
+ {
+ "start": 3705.6,
+ "duration": 0.0,
+ "text": "that are um are modest. So in this case like<01:01:45.760> time<01:01:45.960> bounds<01:01:46.200> that<01:01:46.320> are<01:01:46.440> less<01:01:46.720> than<01:01:46.960> the"
+ },
+ {
+ "start": 3707.07,
+ "duration": 0.0,
+ "text": "like time bounds that are less than the"
+ },
+ {
+ "start": 3707.08,
+ "duration": 0.0,
+ "text": "like time bounds that are less than the amount<01:01:47.280> of<01:01:47.360> time<01:01:47.600> to<01:01:48.240> to<01:01:48.360> run<01:01:48.520> the<01:01:48.600> rule.<01:01:49.280> Um<01:01:49.560> in"
+ },
+ {
+ "start": 3709.67,
+ "duration": 0.0,
+ "text": "amount of time to to run the rule. Um in"
+ },
+ {
+ "start": 3709.68,
+ "duration": 0.0,
+ "text": "amount of time to to run the rule. Um in this<01:01:49.840> case<01:01:50.120> time<01:01:50.280> bounds<01:01:50.520> that<01:01:50.640> are<01:01:50.720> less<01:01:50.920> than"
+ },
+ {
+ "start": 3711.03,
+ "duration": 0.0,
+ "text": "this case time bounds that are less than"
+ },
+ {
+ "start": 3711.04,
+ "duration": 0.0,
+ "text": "this case time bounds that are less than the<01:01:51.120> amount<01:01:51.280> of<01:01:51.360> time<01:01:51.600> to<01:01:51.840> to<01:01:52.200> to<01:01:52.360> generate<01:01:52.880> the"
+ },
+ {
+ "start": 3713.55,
+ "duration": 0.0,
+ "text": "the amount of time to to to generate the"
+ },
+ {
+ "start": 3713.56,
+ "duration": 0.0,
+ "text": "the amount of time to to to generate the uh<01:01:53.640> you<01:01:53.720> know,<01:01:53.840> to<01:01:54.040> go<01:01:54.200> through<01:01:54.360> this"
+ },
+ {
+ "start": 3714.51,
+ "duration": 0.0,
+ "text": "uh you know, to go through this"
+ },
+ {
+ "start": 3714.52,
+ "duration": 0.0,
+ "text": "uh you know, to go through this recurrence<01:01:55.000> for<01:01:55.160> all<01:01:55.280> these<01:01:55.400> different"
+ },
+ {
+ "start": 3715.63,
+ "duration": 0.0,
+ "text": "recurrence for all these different"
+ },
+ {
+ "start": 3715.64,
+ "duration": 0.0,
+ "text": "recurrence for all these different points<01:01:55.880> that<01:01:56.000> you<01:01:56.120> care<01:01:56.280> about,<01:01:56.680> right?<01:01:57.400> Um"
+ },
+ {
+ "start": 3717.91,
+ "duration": 0.0,
+ "text": "points that you care about, right? Um"
+ },
+ {
+ "start": 3717.92,
+ "duration": 0.0,
+ "text": "points that you care about, right? Um you<01:01:58.000> know,<01:01:58.080> for<01:01:58.200> this<01:01:58.440> one<01:01:59.120> uh<01:01:59.240> time<01:01:59.640> in<01:01:59.760> this"
+ },
+ {
+ "start": 3719.91,
+ "duration": 0.0,
+ "text": "you know, for this one uh time in this"
+ },
+ {
+ "start": 3719.92,
+ "duration": 0.0,
+ "text": "you know, for this one uh time in this case<01:02:00.120> I'd<01:02:00.240> say<01:02:00.360> time<01:02:00.600> bound<01:02:00.880> less<01:02:01.240> than<01:02:01.760> enough"
+ },
+ {
+ "start": 3722.03,
+ "duration": 0.0,
+ "text": "case I'd say time bound less than enough"
+ },
+ {
+ "start": 3722.04,
+ "duration": 0.0,
+ "text": "case I'd say time bound less than enough to<01:02:02.160> run<01:02:02.400> the<01:02:02.480> AlphaZero<01:02:02.880> process,<01:02:03.440> right?<01:02:03.640> So"
+ },
+ {
+ "start": 3723.75,
+ "duration": 0.0,
+ "text": "to run the AlphaZero process, right? So"
+ },
+ {
+ "start": 3723.76,
+ "duration": 0.0,
+ "text": "to run the AlphaZero process, right? So this<01:02:03.920> would<01:02:04.040> actually<01:02:04.320> be<01:02:04.800> basically<01:02:05.320> if<01:02:05.520> you"
+ },
+ {
+ "start": 3725.67,
+ "duration": 0.0,
+ "text": "this would actually be basically if you"
+ },
+ {
+ "start": 3725.68,
+ "duration": 0.0,
+ "text": "this would actually be basically if you had<01:02:06.320> Look,<01:02:06.680> if<01:02:06.800> you're<01:02:06.920> looking<01:02:07.200> at<01:02:07.280> the"
+ },
+ {
+ "start": 3727.35,
+ "duration": 0.0,
+ "text": "had Look, if you're looking at the"
+ },
+ {
+ "start": 3727.36,
+ "duration": 0.0,
+ "text": "had Look, if you're looking at the weights,<01:02:07.840> right?<01:02:08.240> Um<01:02:08.680> or<01:02:09.080> the<01:02:09.200> predictions"
+ },
+ {
+ "start": 3729.63,
+ "duration": 0.0,
+ "text": "weights, right? Um or the predictions"
+ },
+ {
+ "start": 3729.64,
+ "duration": 0.0,
+ "text": "weights, right? Um or the predictions the<01:02:09.720> model<01:02:09.960> makes<01:02:10.520> and<01:02:10.640> you<01:02:10.680> don't<01:02:10.880> have"
+ },
+ {
+ "start": 3730.99,
+ "duration": 0.0,
+ "text": "the model makes and you don't have"
+ },
+ {
+ "start": 3731.0,
+ "duration": 0.0,
+ "text": "the model makes and you don't have enough<01:02:11.160> time<01:02:11.400> to<01:02:11.560> rerun<01:02:11.920> the<01:02:12.000> entire"
+ },
+ {
+ "start": 3732.43,
+ "duration": 0.0,
+ "text": "enough time to rerun the entire"
+ },
+ {
+ "start": 3732.44,
+ "duration": 0.0,
+ "text": "enough time to rerun the entire AlphaZero<01:02:12.800> process,<01:02:13.520> but<01:02:13.680> you're<01:02:13.800> trying<01:02:14.000> to"
+ },
+ {
+ "start": 3734.07,
+ "duration": 0.0,
+ "text": "AlphaZero process, but you're trying to"
+ },
+ {
+ "start": 3734.08,
+ "duration": 0.0,
+ "text": "AlphaZero process, but you're trying to say<01:02:14.280> like<01:02:14.560> hm<01:02:15.240> uh"
+ },
+ {
+ "start": 3735.83,
+ "duration": 0.0,
+ "text": "say like hm uh"
+ },
+ {
+ "start": 3735.84,
+ "duration": 0.0,
+ "text": "say like hm uh let<01:02:16.240> what<01:02:16.400> is<01:02:16.480> the<01:02:16.560> best<01:02:16.720> compression<01:02:17.200> I<01:02:17.240> can"
+ },
+ {
+ "start": 3737.35,
+ "duration": 0.0,
+ "text": "let what is the best compression I can"
+ },
+ {
+ "start": 3737.36,
+ "duration": 0.0,
+ "text": "let what is the best compression I can do<01:02:17.520> of<01:02:17.600> that<01:02:17.960> given<01:02:18.240> a<01:02:18.280> much<01:02:18.400> shorter<01:02:18.680> time,"
+ },
+ {
+ "start": 3739.15,
+ "duration": 0.0,
+ "text": "do of that given a much shorter time,"
+ },
+ {
+ "start": 3739.16,
+ "duration": 0.0,
+ "text": "do of that given a much shorter time, then<01:02:19.600> you<01:02:19.720> would<01:02:19.880> say,<01:02:20.120> \"Oh<01:02:20.240> wow,<01:02:20.480> there's"
+ },
+ {
+ "start": 3740.67,
+ "duration": 0.0,
+ "text": "then you would say, \"Oh wow, there's"
+ },
+ {
+ "start": 3740.68,
+ "duration": 0.0,
+ "text": "then you would say, \"Oh wow, there's just<01:02:20.840> like<01:02:21.000> there's<01:02:21.160> a<01:02:21.200> lot<01:02:21.480> to<01:02:21.560> compress"
+ },
+ {
+ "start": 3741.91,
+ "duration": 0.0,
+ "text": "just like there's a lot to compress"
+ },
+ {
+ "start": 3741.92,
+ "duration": 0.0,
+ "text": "just like there's a lot to compress here,<01:02:22.080> you<01:02:22.160> know,<01:02:22.240> there's<01:02:22.400> a<01:02:22.480> lot<01:02:22.640> of"
+ },
+ {
+ "start": 3742.71,
+ "duration": 0.0,
+ "text": "here, you know, there's a lot of"
+ },
+ {
+ "start": 3742.72,
+ "duration": 0.0,
+ "text": "here, you know, there's a lot of structure,<01:02:23.040> there's<01:02:23.240> a<01:02:23.280> lot<01:02:23.400> of<01:02:23.640> you<01:02:23.720> know,"
+ },
+ {
+ "start": 3744.19,
+ "duration": 0.0,
+ "text": "structure, there's a lot of you know,"
+ },
+ {
+ "start": 3744.2,
+ "duration": 0.0,
+ "text": "structure, there's a lot of you know, yeah.\""
+ },
+ {
+ "start": 3745.23,
+ "duration": 0.0,
+ "text": "yeah.\""
+ },
+ {
+ "start": 3745.24,
+ "duration": 0.0,
+ "text": "yeah.\" So<01:02:25.560> for<01:02:25.720> sure,<01:02:26.000> the<01:02:26.120> time<01:02:26.320> bound<01:02:26.480> is<01:02:26.920> is"
+ },
+ {
+ "start": 3747.07,
+ "duration": 0.0,
+ "text": "So for sure, the time bound is is"
+ },
+ {
+ "start": 3747.08,
+ "duration": 0.0,
+ "text": "So for sure, the time bound is is critical<01:02:27.480> here<01:02:27.840> and<01:02:28.600> if<01:02:28.840> you<01:02:29.040> set<01:02:29.520> this<01:02:29.800> time"
+ },
+ {
+ "start": 3750.03,
+ "duration": 0.0,
+ "text": "critical here and if you set this time"
+ },
+ {
+ "start": 3750.04,
+ "duration": 0.0,
+ "text": "critical here and if you set this time bound<01:02:30.680> to<01:02:31.160> as<01:02:31.320> it<01:02:31.440> gets<01:02:31.600> larger<01:02:31.840> and<01:02:31.920> larger<01:02:32.640> um"
+ },
+ {
+ "start": 3753.31,
+ "duration": 0.0,
+ "text": "bound to as it gets larger and larger um"
+ },
+ {
+ "start": 3753.32,
+ "duration": 0.0,
+ "text": "bound to as it gets larger and larger um in<01:02:33.520> in<01:02:33.600> many<01:02:33.760> of<01:02:33.840> these<01:02:33.960> cases,<01:02:34.400> then<01:02:35.280> the<01:02:36.080> uh"
+ },
+ {
+ "start": 3757.15,
+ "duration": 0.0,
+ "text": "in in many of these cases, then the uh"
+ },
+ {
+ "start": 3757.16,
+ "duration": 0.0,
+ "text": "in in many of these cases, then the uh time<01:02:37.400> bound<01:02:37.520> entropy<01:02:37.880> just<01:02:38.160> collapses<01:02:38.560> down"
+ },
+ {
+ "start": 3758.79,
+ "duration": 0.0,
+ "text": "time bound entropy just collapses down"
+ },
+ {
+ "start": 3758.8,
+ "duration": 0.0,
+ "text": "time bound entropy just collapses down to<01:02:39.440> um"
+ },
+ {
+ "start": 3759.99,
+ "duration": 0.0,
+ "text": "to um"
+ },
+ {
+ "start": 3760.0,
+ "duration": 0.0,
+ "text": "to um the<01:02:40.080> entropy,<01:02:40.640> right?<01:02:41.360> Uh"
+ },
+ {
+ "start": 3763.11,
+ "duration": 0.0,
+ "text": "the entropy, right? Uh"
+ },
+ {
+ "start": 3763.12,
+ "duration": 0.0,
+ "text": "the entropy, right? Uh Uh<01:02:43.640> yeah."
+ },
+ {
+ "start": 3764.67,
+ "duration": 0.0,
+ "text": "Uh yeah."
+ },
+ {
+ "start": 3764.68,
+ "duration": 0.0,
+ "text": "Uh yeah. Uh"
+ },
+ {
+ "start": 3765.43,
+ "duration": 0.0,
+ "text": "Uh"
+ },
+ {
+ "start": 3765.44,
+ "duration": 0.0,
+ "text": "Uh sorry.<01:02:45.760> No,<01:02:46.040> actually"
+ },
+ {
+ "start": 3767.23,
+ "duration": 0.0,
+ "text": "sorry. No, actually"
+ },
+ {
+ "start": 3767.24,
+ "duration": 0.0,
+ "text": "sorry. No, actually um<01:02:47.320> well,<01:02:47.520> right.<01:02:47.680> It<01:02:48.200> it<01:02:48.280> gets<01:02:48.520> it<01:02:48.640> gets<01:02:49.160> you"
+ },
+ {
+ "start": 3769.27,
+ "duration": 0.0,
+ "text": "um well, right. It it gets it gets you"
+ },
+ {
+ "start": 3769.28,
+ "duration": 0.0,
+ "text": "um well, right. It it gets it gets you basically<01:02:49.680> go<01:02:49.960> towards<01:02:50.360> the<01:02:50.480> time<01:02:50.680> bound"
+ },
+ {
+ "start": 3771.11,
+ "duration": 0.0,
+ "text": "basically go towards the time bound"
+ },
+ {
+ "start": 3771.12,
+ "duration": 0.0,
+ "text": "basically go towards the time bound sorry,<01:02:51.360> towards<01:02:51.720> um<01:02:51.960> Kolmogorov<01:02:52.360> complexity"
+ },
+ {
+ "start": 3772.99,
+ "duration": 0.0,
+ "text": "sorry, towards um Kolmogorov complexity"
+ },
+ {
+ "start": 3773.0,
+ "duration": 0.0,
+ "text": "sorry, towards um Kolmogorov complexity and<01:02:53.480> an<01:02:53.560> entropy<01:02:53.800> much<01:02:54.040> much<01:02:54.200> more<01:02:54.320> similar<01:02:54.600> to"
+ },
+ {
+ "start": 3774.67,
+ "duration": 0.0,
+ "text": "and an entropy much much more similar to"
+ },
+ {
+ "start": 3774.68,
+ "duration": 0.0,
+ "text": "and an entropy much much more similar to that<01:02:55.040> um<01:02:55.360> as<01:02:55.520> you<01:02:55.600> have<01:02:55.720> more<01:02:55.840> and<01:02:55.920> more"
+ },
+ {
+ "start": 3775.99,
+ "duration": 0.0,
+ "text": "that um as you have more and more"
+ },
+ {
+ "start": 3776.0,
+ "duration": 0.0,
+ "text": "that um as you have more and more compute."
+ },
+ {
+ "start": 3777.51,
+ "duration": 0.0,
+ "text": "compute."
+ },
+ {
+ "start": 3777.52,
+ "duration": 0.0,
+ "text": "compute. So<01:02:58.280> uh<01:02:58.680> thinking<01:02:58.920> about<01:02:59.200> like,<01:02:59.480> okay,<01:02:59.680> the"
+ },
+ {
+ "start": 3779.79,
+ "duration": 0.0,
+ "text": "So uh thinking about like, okay, the"
+ },
+ {
+ "start": 3779.8,
+ "duration": 0.0,
+ "text": "So uh thinking about like, okay, the AlphaZero<01:03:00.200> game<01:03:00.400> playing<01:03:00.640> agent,<01:03:01.120> right?<01:03:01.400> Can"
+ },
+ {
+ "start": 3781.55,
+ "duration": 0.0,
+ "text": "AlphaZero game playing agent, right? Can"
+ },
+ {
+ "start": 3781.56,
+ "duration": 0.0,
+ "text": "AlphaZero game playing agent, right? Can be<01:03:01.680> expressed<01:03:02.120> in<01:03:02.200> just<01:03:02.520> for<01:03:02.640> chess<01:03:02.920> can<01:03:03.040> just"
+ },
+ {
+ "start": 3783.19,
+ "duration": 0.0,
+ "text": "be expressed in just for chess can just"
+ },
+ {
+ "start": 3783.2,
+ "duration": 0.0,
+ "text": "be expressed in just for chess can just be<01:03:03.280> expressed<01:03:03.760> as<01:03:03.960> the<01:03:04.480> the<01:03:04.560> minimax<01:03:05.000> search."
+ },
+ {
+ "start": 3785.71,
+ "duration": 0.0,
+ "text": "be expressed as the the minimax search."
+ },
+ {
+ "start": 3785.72,
+ "duration": 0.0,
+ "text": "be expressed as the the minimax search. Um<01:03:06.040> that<01:03:06.320> can<01:03:06.440> be<01:03:06.520> done<01:03:06.680> a<01:03:06.720> very<01:03:06.880> short"
+ },
+ {
+ "start": 3787.03,
+ "duration": 0.0,
+ "text": "Um that can be done a very short"
+ },
+ {
+ "start": 3787.04,
+ "duration": 0.0,
+ "text": "Um that can be done a very short program.<01:03:07.920> Um<01:03:08.760> Right.<01:03:09.160> But<01:03:09.320> then<01:03:09.800> if<01:03:10.040> you<01:03:10.280> don't"
+ },
+ {
+ "start": 3790.47,
+ "duration": 0.0,
+ "text": "program. Um Right. But then if you don't"
+ },
+ {
+ "start": 3790.48,
+ "duration": 0.0,
+ "text": "program. Um Right. But then if you don't have<01:03:10.600> enough<01:03:10.880> time<01:03:11.240> to<01:03:11.360> run<01:03:11.560> that<01:03:11.680> search,"
+ },
+ {
+ "start": 3792.11,
+ "duration": 0.0,
+ "text": "have enough time to run that search,"
+ },
+ {
+ "start": 3792.12,
+ "duration": 0.0,
+ "text": "have enough time to run that search, then<01:03:12.480> the<01:03:12.600> moves<01:03:12.920> of<01:03:13.040> that<01:03:13.160> game<01:03:13.360> playing"
+ },
+ {
+ "start": 3793.55,
+ "duration": 0.0,
+ "text": "then the moves of that game playing"
+ },
+ {
+ "start": 3793.56,
+ "duration": 0.0,
+ "text": "then the moves of that game playing agent<01:03:13.880> could<01:03:14.040> look<01:03:14.240> very<01:03:14.480> interesting<01:03:14.920> and"
+ },
+ {
+ "start": 3794.99,
+ "duration": 0.0,
+ "text": "agent could look very interesting and"
+ },
+ {
+ "start": 3795.0,
+ "duration": 0.0,
+ "text": "agent could look very interesting and complex,<01:03:15.440> a<01:03:15.480> lot<01:03:15.720> to<01:03:15.840> learn<01:03:16.000> from."
+ },
+ {
+ "start": 3797.27,
+ "duration": 0.0,
+ "text": "complex, a lot to learn from."
+ },
+ {
+ "start": 3797.28,
+ "duration": 0.0,
+ "text": "complex, a lot to learn from. Yeah,<01:03:17.520> I<01:03:17.600> just<01:03:17.840> want<01:03:18.000> to<01:03:18.120> add<01:03:18.360> one<01:03:18.520> thing<01:03:18.840> uh"
+ },
+ {
+ "start": 3798.87,
+ "duration": 0.0,
+ "text": "Yeah, I just want to add one thing uh"
+ },
+ {
+ "start": 3798.88,
+ "duration": 0.0,
+ "text": "Yeah, I just want to add one thing uh real<01:03:19.160> quick.<01:03:19.800> It<01:03:19.960> reminds<01:03:20.400> me<01:03:21.320> uh"
+ },
+ {
+ "start": 3802.59,
+ "duration": 0.0,
+ "text": "real quick. It reminds me uh"
+ },
+ {
+ "start": 3802.6,
+ "duration": 0.0,
+ "text": "real quick. It reminds me uh some<01:03:22.800> of<01:03:22.880> the<01:03:23.080> theories<01:03:24.120> uh"
+ },
+ {
+ "start": 3804.75,
+ "duration": 0.0,
+ "text": "some of the theories uh"
+ },
+ {
+ "start": 3804.76,
+ "duration": 0.0,
+ "text": "some of the theories uh of<01:03:24.960> decision<01:03:25.480> making<01:03:26.040> under<01:03:26.360> uncertainty<01:03:26.960> in"
+ },
+ {
+ "start": 3807.07,
+ "duration": 0.0,
+ "text": "of decision making under uncertainty in"
+ },
+ {
+ "start": 3807.08,
+ "duration": 0.0,
+ "text": "of decision making under uncertainty in cognitive<01:03:27.560> science.<01:03:27.920> And<01:03:28.040> one<01:03:28.200> of<01:03:28.280> the<01:03:28.400> things"
+ },
+ {
+ "start": 3808.63,
+ "duration": 0.0,
+ "text": "cognitive science. And one of the things"
+ },
+ {
+ "start": 3808.64,
+ "duration": 0.0,
+ "text": "cognitive science. And one of the things they<01:03:28.760> have<01:03:29.000> this<01:03:29.400> is<01:03:29.560> is<01:03:29.720> called<01:03:30.040> the"
+ },
+ {
+ "start": 3810.11,
+ "duration": 0.0,
+ "text": "they have this is is called the"
+ },
+ {
+ "start": 3810.12,
+ "duration": 0.0,
+ "text": "they have this is is called the heuristics,<01:03:30.840> right?<01:03:31.080> It's<01:03:31.200> kind<01:03:31.400> of<01:03:31.960> rule<01:03:32.120> of"
+ },
+ {
+ "start": 3812.23,
+ "duration": 0.0,
+ "text": "heuristics, right? It's kind of rule of"
+ },
+ {
+ "start": 3812.24,
+ "duration": 0.0,
+ "text": "heuristics, right? It's kind of rule of thumb.<01:03:32.520> So<01:03:32.680> if<01:03:32.840> you<01:03:32.960> if<01:03:33.120> you<01:03:33.200> only<01:03:33.400> have<01:03:33.560> a"
+ },
+ {
+ "start": 3813.75,
+ "duration": 0.0,
+ "text": "thumb. So if you if you only have a"
+ },
+ {
+ "start": 3813.76,
+ "duration": 0.0,
+ "text": "thumb. So if you if you only have a limited<01:03:34.200> amount<01:03:34.440> of<01:03:34.560> time,<01:03:34.880> then<01:03:35.040> people"
+ },
+ {
+ "start": 3815.31,
+ "duration": 0.0,
+ "text": "limited amount of time, then people"
+ },
+ {
+ "start": 3815.32,
+ "duration": 0.0,
+ "text": "limited amount of time, then people resort<01:03:35.800> to<01:03:35.880> using<01:03:36.160> some<01:03:36.320> sort<01:03:36.520> of<01:03:37.040> rule<01:03:37.200> of"
+ },
+ {
+ "start": 3817.35,
+ "duration": 0.0,
+ "text": "resort to using some sort of rule of"
+ },
+ {
+ "start": 3817.36,
+ "duration": 0.0,
+ "text": "resort to using some sort of rule of thumb<01:03:37.600> kind<01:03:37.760> of<01:03:37.880> patterns<01:03:38.600> or<01:03:38.880> rules<01:03:39.960> um"
+ },
+ {
+ "start": 3820.75,
+ "duration": 0.0,
+ "text": "thumb kind of patterns or rules um"
+ },
+ {
+ "start": 3820.76,
+ "duration": 0.0,
+ "text": "thumb kind of patterns or rules um which<01:03:41.000> maximizes<01:03:41.760> their<01:03:42.240> decision<01:03:42.560> making."
+ },
+ {
+ "start": 3823.83,
+ "duration": 0.0,
+ "text": "which maximizes their decision making."
+ },
+ {
+ "start": 3823.84,
+ "duration": 0.0,
+ "text": "which maximizes their decision making. Uh<01:03:44.120> maybe<01:03:44.480> there<01:03:44.680> is<01:03:45.160> some<01:03:45.400> connection<01:03:45.920> there"
+ },
+ {
+ "start": 3826.15,
+ "duration": 0.0,
+ "text": "Uh maybe there is some connection there"
+ },
+ {
+ "start": 3826.16,
+ "duration": 0.0,
+ "text": "Uh maybe there is some connection there that<01:03:46.440> you<01:03:46.520> could<01:03:46.720> explore<01:03:47.000> if<01:03:47.120> you<01:03:47.200> have<01:03:47.359> any"
+ },
+ {
+ "start": 3827.75,
+ "duration": 0.0,
+ "text": "that you could explore if you have any"
+ },
+ {
+ "start": 3827.76,
+ "duration": 0.0,
+ "text": "that you could explore if you have any idea.<01:03:48.200> Absolutely."
+ },
+ {
+ "start": 3829.83,
+ "duration": 0.0,
+ "text": "idea. Absolutely."
+ },
+ {
+ "start": 3829.84,
+ "duration": 0.0,
+ "text": "idea. Absolutely. Yeah,<01:03:50.440> a<01:03:50.480> lot<01:03:50.680> of<01:03:50.760> things<01:03:50.920> that<01:03:51.040> I<01:03:51.080> would<01:03:51.200> like"
+ },
+ {
+ "start": 3831.31,
+ "duration": 0.0,
+ "text": "Yeah, a lot of things that I would like"
+ },
+ {
+ "start": 3831.32,
+ "duration": 0.0,
+ "text": "Yeah, a lot of things that I would like to<01:03:51.400> explore<01:03:51.720> and<01:03:51.800> that's<01:03:51.960> that's<01:03:52.280> something"
+ },
+ {
+ "start": 3832.55,
+ "duration": 0.0,
+ "text": "to explore and that's that's something"
+ },
+ {
+ "start": 3832.56,
+ "duration": 0.0,
+ "text": "to explore and that's that's something we'll<01:03:52.640> have<01:03:52.760> to<01:03:52.840> follow<01:03:53.000> up<01:03:53.120> on."
+ },
+ {
+ "start": 3835.8,
+ "duration": 0.0,
+ "text": "Uh<01:03:56.200> can<01:03:56.359> I<01:03:56.520> add<01:03:57.240> a<01:03:57.640> additional<01:03:58.000> question?<01:03:58.440> So<01:03:58.680> I"
+ },
+ {
+ "start": 3838.75,
+ "duration": 0.0,
+ "text": "Uh can I add a additional question? So I"
+ },
+ {
+ "start": 3838.76,
+ "duration": 0.0,
+ "text": "Uh can I add a additional question? So I just<01:03:59.040> shared<01:03:59.400> a<01:03:59.720> a<01:04:00.320> link<01:04:00.640> in<01:04:00.800> the<01:04:00.880> chat.<01:04:01.440> So"
+ },
+ {
+ "start": 3841.79,
+ "duration": 0.0,
+ "text": "just shared a a link in the chat. So"
+ },
+ {
+ "start": 3841.8,
+ "duration": 0.0,
+ "text": "just shared a a link in the chat. So there's"
+ },
+ {
+ "start": 3842.79,
+ "duration": 0.0,
+ "text": "there's"
+ },
+ {
+ "start": 3842.8,
+ "duration": 0.0,
+ "text": "there's I<01:04:02.880> think<01:04:03.200> a"
+ },
+ {
+ "start": 3844.55,
+ "duration": 0.0,
+ "text": "I think a"
+ },
+ {
+ "start": 3844.56,
+ "duration": 0.0,
+ "text": "I think a two<01:04:04.760> years<01:04:04.960> ago<01:04:05.200> or<01:04:05.400> one<01:04:05.560> years<01:04:05.720> ago<01:04:06.520> uh<01:04:06.840> some"
+ },
+ {
+ "start": 3847.07,
+ "duration": 0.0,
+ "text": "two years ago or one years ago uh some"
+ },
+ {
+ "start": 3847.08,
+ "duration": 0.0,
+ "text": "two years ago or one years ago uh some people<01:04:07.640> using<01:04:08.640> uh<01:04:09.160> MDL<01:04:09.800> to<01:04:10.440> to<01:04:10.720> to<01:04:10.920> solve<01:04:11.280> the"
+ },
+ {
+ "start": 3852.23,
+ "duration": 0.0,
+ "text": "people using uh MDL to to to solve the"
+ },
+ {
+ "start": 3852.24,
+ "duration": 0.0,
+ "text": "people using uh MDL to to to solve the ARC<01:04:12.600> AGI.<01:04:13.240> So<01:04:13.680> this<01:04:14.560> really<01:04:14.840> reminds<01:04:15.359> me<01:04:15.880> of<01:04:16.240> uh"
+ },
+ {
+ "start": 3856.27,
+ "duration": 0.0,
+ "text": "ARC AGI. So this really reminds me of uh"
+ },
+ {
+ "start": 3856.28,
+ "duration": 0.0,
+ "text": "ARC AGI. So this really reminds me of uh relates<01:04:16.760> to<01:04:16.960> to<01:04:17.120> your<01:04:17.280> work<01:04:17.600> because<01:04:18.359> first"
+ },
+ {
+ "start": 3859.07,
+ "duration": 0.0,
+ "text": "relates to to your work because first"
+ },
+ {
+ "start": 3859.08,
+ "duration": 0.0,
+ "text": "relates to to your work because first your<01:04:19.320> work<01:04:19.560> is<01:04:20.040> defined<01:04:20.520> based<01:04:20.840> on<01:04:21.480> MDL<01:04:22.480> and"
+ },
+ {
+ "start": 3862.99,
+ "duration": 0.0,
+ "text": "your work is defined based on MDL and"
+ },
+ {
+ "start": 3863.0,
+ "duration": 0.0,
+ "text": "your work is defined based on MDL and you<01:04:23.120> also<01:04:23.320> mentioned<01:04:24.359> by<01:04:24.560> choosing<01:04:25.040> a<01:04:25.120> better"
+ },
+ {
+ "start": 3866.03,
+ "duration": 0.0,
+ "text": "you also mentioned by choosing a better"
+ },
+ {
+ "start": 3866.04,
+ "duration": 0.0,
+ "text": "you also mentioned by choosing a better epiplexity"
+ },
+ {
+ "start": 3867.59,
+ "duration": 0.0,
+ "text": "epiplexity"
+ },
+ {
+ "start": 3867.6,
+ "duration": 0.0,
+ "text": "epiplexity uh"
+ },
+ {
+ "start": 3868.31,
+ "duration": 0.0,
+ "text": "uh"
+ },
+ {
+ "start": 3868.32,
+ "duration": 0.0,
+ "text": "uh uh<01:04:28.560> you<01:04:28.800> will<01:04:28.960> get<01:04:29.520> better<01:04:30.520> generalization."
+ },
+ {
+ "start": 3871.79,
+ "duration": 0.0,
+ "text": "uh you will get better generalization."
+ },
+ {
+ "start": 3871.8,
+ "duration": 0.0,
+ "text": "uh you will get better generalization. And<01:04:32.320> interestingly,<01:04:33.200> ARC<01:04:33.520> AGI<01:04:34.040> is<01:04:34.320> something"
+ },
+ {
+ "start": 3874.79,
+ "duration": 0.0,
+ "text": "And interestingly, ARC AGI is something"
+ },
+ {
+ "start": 3874.8,
+ "duration": 0.0,
+ "text": "And interestingly, ARC AGI is something that's<01:04:35.760> testing<01:04:36.320> how<01:04:36.640> how<01:04:36.800> fast<01:04:37.240> you<01:04:37.359> can"
+ },
+ {
+ "start": 3877.51,
+ "duration": 0.0,
+ "text": "that's testing how how fast you can"
+ },
+ {
+ "start": 3877.52,
+ "duration": 0.0,
+ "text": "that's testing how how fast you can generalize<01:04:38.200> or<01:04:38.400> how<01:04:38.600> good<01:04:39.080> you<01:04:39.200> can"
+ },
+ {
+ "start": 3879.31,
+ "duration": 0.0,
+ "text": "generalize or how good you can"
+ },
+ {
+ "start": 3879.32,
+ "duration": 0.0,
+ "text": "generalize or how good you can generalize.<01:04:40.400> And<01:04:40.920> I<01:04:41.040> just"
+ },
+ {
+ "start": 3882.15,
+ "duration": 0.0,
+ "text": "generalize. And I just"
+ },
+ {
+ "start": 3882.16,
+ "duration": 0.0,
+ "text": "generalize. And I just uh"
+ },
+ {
+ "start": 3883.19,
+ "duration": 0.0,
+ "text": "uh"
+ },
+ {
+ "start": 3883.2,
+ "duration": 0.0,
+ "text": "uh intuitively<01:04:43.920> feel<01:04:44.320> the"
+ },
+ {
+ "start": 3885.15,
+ "duration": 0.0,
+ "text": "intuitively feel the"
+ },
+ {
+ "start": 3885.16,
+ "duration": 0.0,
+ "text": "intuitively feel the their<01:04:45.480> work<01:04:46.000> might<01:04:46.920> deeply<01:04:47.280> relate<01:04:47.760> to<01:04:47.920> your"
+ },
+ {
+ "start": 3888.15,
+ "duration": 0.0,
+ "text": "their work might deeply relate to your"
+ },
+ {
+ "start": 3888.16,
+ "duration": 0.0,
+ "text": "their work might deeply relate to your to<01:04:48.320> your<01:04:48.960> to<01:04:49.080> your<01:04:49.240> method.<01:04:50.200> What<01:04:50.400> what<01:04:50.520> do<01:04:50.600> you"
+ },
+ {
+ "start": 3890.71,
+ "duration": 0.0,
+ "text": "to your to your method. What what do you"
+ },
+ {
+ "start": 3890.72,
+ "duration": 0.0,
+ "text": "to your to your method. What what do you think?"
+ },
+ {
+ "start": 3892.75,
+ "duration": 0.0,
+ "text": "think?"
+ },
+ {
+ "start": 3892.76,
+ "duration": 0.0,
+ "text": "think? Let's<01:04:53.080> see.<01:04:53.760> Um"
+ },
+ {
+ "start": 3898.0,
+ "duration": 0.0,
+ "text": "Yeah,<01:04:58.600> so<01:04:59.120> I<01:04:59.440> think"
+ },
+ {
+ "start": 3901.75,
+ "duration": 0.0,
+ "text": "Yeah, so I think"
+ },
+ {
+ "start": 3901.76,
+ "duration": 0.0,
+ "text": "Yeah, so I think um"
+ },
+ {
+ "start": 3903.71,
+ "duration": 0.0,
+ "text": "um"
+ },
+ {
+ "start": 3903.72,
+ "duration": 0.0,
+ "text": "um I<01:05:03.920> haven't<01:05:04.160> thought<01:05:04.320> about<01:05:04.520> it<01:05:04.560> very<01:05:04.720> much."
+ },
+ {
+ "start": 3905.59,
+ "duration": 0.0,
+ "text": "I haven't thought about it very much."
+ },
+ {
+ "start": 3905.6,
+ "duration": 0.0,
+ "text": "I haven't thought about it very much. Um<01:05:06.080> I<01:05:06.200> think"
+ },
+ {
+ "start": 3907.99,
+ "duration": 0.0,
+ "text": "Um I think"
+ },
+ {
+ "start": 3908.0,
+ "duration": 0.0,
+ "text": "Um I think at<01:05:08.240> some<01:05:08.400> level<01:05:08.600> it<01:05:08.680> makes<01:05:08.880> sense<01:05:09.240> that<01:05:10.200> uh"
+ },
+ {
+ "start": 3911.31,
+ "duration": 0.0,
+ "text": "at some level it makes sense that uh"
+ },
+ {
+ "start": 3911.32,
+ "duration": 0.0,
+ "text": "at some level it makes sense that uh Right.<01:05:11.800> ARC<01:05:12.000> AGI<01:05:12.280> is<01:05:12.400> testing<01:05:12.720> this<01:05:12.840> very"
+ },
+ {
+ "start": 3913.23,
+ "duration": 0.0,
+ "text": "Right. ARC AGI is testing this very"
+ },
+ {
+ "start": 3913.24,
+ "duration": 0.0,
+ "text": "Right. ARC AGI is testing this very high-level<01:05:13.920> pattern<01:05:14.240> matching<01:05:15.320> ability."
+ },
+ {
+ "start": 3916.19,
+ "duration": 0.0,
+ "text": "high-level pattern matching ability."
+ },
+ {
+ "start": 3916.2,
+ "duration": 0.0,
+ "text": "high-level pattern matching ability. Yeah,<01:05:17.000> similar<01:05:17.320> to<01:05:17.440> like<01:05:17.840> yeah,<01:05:18.200> um<01:05:19.080> and<01:05:20.320> it"
+ },
+ {
+ "start": 3920.43,
+ "duration": 0.0,
+ "text": "Yeah, similar to like yeah, um and it"
+ },
+ {
+ "start": 3920.44,
+ "duration": 0.0,
+ "text": "Yeah, similar to like yeah, um and it makes<01:05:20.600> sense<01:05:20.800> that<01:05:21.240> would<01:05:21.520> leverage<01:05:22.720> a<01:05:22.800> lot<01:05:23.040> of"
+ },
+ {
+ "start": 3923.19,
+ "duration": 0.0,
+ "text": "makes sense that would leverage a lot of"
+ },
+ {
+ "start": 3923.2,
+ "duration": 0.0,
+ "text": "makes sense that would leverage a lot of the<01:05:23.520> existing<01:05:24.040> circuits<01:05:24.520> and<01:05:24.640> patterns"
+ },
+ {
+ "start": 3924.91,
+ "duration": 0.0,
+ "text": "the existing circuits and patterns"
+ },
+ {
+ "start": 3924.92,
+ "duration": 0.0,
+ "text": "the existing circuits and patterns within<01:05:25.120> a<01:05:25.160> model.<01:05:25.480> So<01:05:25.720> think<01:05:25.960> about<01:05:26.760> working"
+ },
+ {
+ "start": 3927.07,
+ "duration": 0.0,
+ "text": "within a model. So think about working"
+ },
+ {
+ "start": 3927.08,
+ "duration": 0.0,
+ "text": "within a model. So think about working with<01:05:27.240> existing<01:05:27.560> models.<01:05:28.359> Yeah,<01:05:28.560> and<01:05:28.680> then"
+ },
+ {
+ "start": 3928.79,
+ "duration": 0.0,
+ "text": "with existing models. Yeah, and then"
+ },
+ {
+ "start": 3928.8,
+ "duration": 0.0,
+ "text": "with existing models. Yeah, and then again,<01:05:29.440> I<01:05:29.520> know<01:05:29.680> that<01:05:29.800> there's<01:05:30.000> some<01:05:30.400> you"
+ },
+ {
+ "start": 3930.55,
+ "duration": 0.0,
+ "text": "again, I know that there's some you"
+ },
+ {
+ "start": 3930.56,
+ "duration": 0.0,
+ "text": "again, I know that there's some you mentioned<01:05:30.840> there's<01:05:30.960> some<01:05:31.200> works<01:05:31.520> that"
+ },
+ {
+ "start": 3932.63,
+ "duration": 0.0,
+ "text": "mentioned there's some works that"
+ },
+ {
+ "start": 3932.64,
+ "duration": 0.0,
+ "text": "mentioned there's some works that that<01:05:33.120> don't<01:05:33.400> even<01:05:33.600> use<01:05:33.840> a<01:05:34.040> big<01:05:34.240> model<01:05:34.480> for"
+ },
+ {
+ "start": 3934.63,
+ "duration": 0.0,
+ "text": "that don't even use a big model for"
+ },
+ {
+ "start": 3934.64,
+ "duration": 0.0,
+ "text": "that don't even use a big model for that.<01:05:35.040> Um"
+ },
+ {
+ "start": 3936.91,
+ "duration": 0.0,
+ "text": "that. Um"
+ },
+ {
+ "start": 3936.92,
+ "duration": 0.0,
+ "text": "that. Um Yeah,<01:05:37.240> I<01:05:37.359> I<01:05:37.440> guess<01:05:38.120> in<01:05:38.240> terms<01:05:38.520> of<01:05:38.680> the<01:05:39.040> the<01:05:39.280> big"
+ },
+ {
+ "start": 3939.55,
+ "duration": 0.0,
+ "text": "Yeah, I I guess in terms of the the big"
+ },
+ {
+ "start": 3939.56,
+ "duration": 0.0,
+ "text": "Yeah, I I guess in terms of the the big model<01:05:39.840> or<01:05:39.920> small<01:05:40.160> model<01:05:40.800> being<01:05:41.080> useful.<01:05:41.359> I"
+ },
+ {
+ "start": 3941.39,
+ "duration": 0.0,
+ "text": "model or small model being useful. I"
+ },
+ {
+ "start": 3941.4,
+ "duration": 0.0,
+ "text": "model or small model being useful. I mean<01:05:41.880> there<01:05:42.200> there<01:05:42.359> are<01:05:42.400> also<01:05:42.600> points<01:05:42.840> that<01:05:42.920> go"
+ },
+ {
+ "start": 3943.03,
+ "duration": 0.0,
+ "text": "mean there there are also points that go"
+ },
+ {
+ "start": 3943.04,
+ "duration": 0.0,
+ "text": "mean there there are also points that go in<01:05:43.280> in<01:05:43.440> both<01:05:43.640> directions,<01:05:44.040> right?<01:05:44.240> There's<01:05:44.880> um"
+ },
+ {
+ "start": 3945.75,
+ "duration": 0.0,
+ "text": "in in both directions, right? There's um"
+ },
+ {
+ "start": 3945.76,
+ "duration": 0.0,
+ "text": "in in both directions, right? There's um I<01:05:45.880> guess"
+ },
+ {
+ "start": 3946.63,
+ "duration": 0.0,
+ "text": "I guess"
+ },
+ {
+ "start": 3946.64,
+ "duration": 0.0,
+ "text": "I guess you<01:05:46.720> know,<01:05:47.240> I<01:05:47.320> guess<01:05:47.640> you<01:05:47.720> know,<01:05:47.800> we<01:05:47.880> have<01:05:48.000> this"
+ },
+ {
+ "start": 3948.15,
+ "duration": 0.0,
+ "text": "you know, I guess you know, we have this"
+ },
+ {
+ "start": 3948.16,
+ "duration": 0.0,
+ "text": "you know, I guess you know, we have this perspective<01:05:48.560> about<01:05:49.440> the<01:05:49.560> reuse<01:05:50.600> a<01:05:50.960> big<01:05:51.160> model"
+ },
+ {
+ "start": 3951.39,
+ "duration": 0.0,
+ "text": "perspective about the reuse a big model"
+ },
+ {
+ "start": 3951.4,
+ "duration": 0.0,
+ "text": "perspective about the reuse a big model like<01:05:51.640> having<01:05:51.960> lots<01:05:52.240> inside<01:05:52.640> a<01:05:52.680> model<01:05:52.920> is<01:05:53.000> good"
+ },
+ {
+ "start": 3953.19,
+ "duration": 0.0,
+ "text": "like having lots inside a model is good"
+ },
+ {
+ "start": 3953.2,
+ "duration": 0.0,
+ "text": "like having lots inside a model is good because<01:05:53.520> then<01:05:53.720> there's<01:05:53.840> lots<01:05:54.080> of<01:05:54.120> reuse<01:05:54.480> for"
+ },
+ {
+ "start": 3954.55,
+ "duration": 0.0,
+ "text": "because then there's lots of reuse for"
+ },
+ {
+ "start": 3954.56,
+ "duration": 0.0,
+ "text": "because then there's lots of reuse for other<01:05:54.720> things.<01:05:55.480> Um<01:05:56.160> there's<01:05:56.320> also<01:05:56.560> another"
+ },
+ {
+ "start": 3956.79,
+ "duration": 0.0,
+ "text": "other things. Um there's also another"
+ },
+ {
+ "start": 3956.8,
+ "duration": 0.0,
+ "text": "other things. Um there's also another perspective"
+ },
+ {
+ "start": 3958.19,
+ "duration": 0.0,
+ "text": "perspective"
+ },
+ {
+ "start": 3958.2,
+ "duration": 0.0,
+ "text": "perspective uh<01:05:58.600> you<01:05:58.680> know,<01:05:58.760> the<01:05:58.840> more<01:05:58.960> classical<01:06:00.000> uh"
+ },
+ {
+ "start": 3960.07,
+ "duration": 0.0,
+ "text": "uh you know, the more classical uh"
+ },
+ {
+ "start": 3960.08,
+ "duration": 0.0,
+ "text": "uh you know, the more classical uh learning<01:06:00.320> theory<01:06:00.560> perspective<01:06:01.160> of<01:06:01.920> uh"
+ },
+ {
+ "start": 3962.63,
+ "duration": 0.0,
+ "text": "learning theory perspective of uh"
+ },
+ {
+ "start": 3962.64,
+ "duration": 0.0,
+ "text": "learning theory perspective of uh the<01:06:02.760> size<01:06:03.000> of<01:06:03.080> your<01:06:03.160> hypothesis<01:06:03.600> space<01:06:04.400> you"
+ },
+ {
+ "start": 3964.55,
+ "duration": 0.0,
+ "text": "the size of your hypothesis space you"
+ },
+ {
+ "start": 3964.56,
+ "duration": 0.0,
+ "text": "the size of your hypothesis space you want<01:06:04.880> to<01:06:05.000> be<01:06:05.120> small<01:06:06.359> um"
+ },
+ {
+ "start": 3967.47,
+ "duration": 0.0,
+ "text": "want to be small um"
+ },
+ {
+ "start": 3967.48,
+ "duration": 0.0,
+ "text": "want to be small um given<01:06:08.560> uh<01:06:08.880> all<01:06:09.040> things<01:06:09.240> being<01:06:09.440> equal<01:06:09.840> because"
+ },
+ {
+ "start": 3970.15,
+ "duration": 0.0,
+ "text": "given uh all things being equal because"
+ },
+ {
+ "start": 3970.16,
+ "duration": 0.0,
+ "text": "given uh all things being equal because then<01:06:10.600> you<01:06:11.160> will<01:06:11.280> have<01:06:11.440> less<01:06:11.640> overfitting,<01:06:12.280> you"
+ },
+ {
+ "start": 3972.43,
+ "duration": 0.0,
+ "text": "then you will have less overfitting, you"
+ },
+ {
+ "start": 3972.44,
+ "duration": 0.0,
+ "text": "then you will have less overfitting, you can<01:06:12.600> make<01:06:12.760> generalization<01:06:13.240> bounds.<01:06:14.120> So,<01:06:14.600> you"
+ },
+ {
+ "start": 3974.67,
+ "duration": 0.0,
+ "text": "can make generalization bounds. So, you"
+ },
+ {
+ "start": 3974.68,
+ "duration": 0.0,
+ "text": "can make generalization bounds. So, you know,<01:06:14.760> I<01:06:14.800> think<01:06:14.960> there's<01:06:15.120> a<01:06:15.200> bit<01:06:15.359> of<01:06:15.480> interplay"
+ },
+ {
+ "start": 3975.91,
+ "duration": 0.0,
+ "text": "know, I think there's a bit of interplay"
+ },
+ {
+ "start": 3975.92,
+ "duration": 0.0,
+ "text": "know, I think there's a bit of interplay between<01:06:16.200> those<01:06:16.400> two.<01:06:16.760> Um"
+ },
+ {
+ "start": 3977.51,
+ "duration": 0.0,
+ "text": "between those two. Um"
+ },
+ {
+ "start": 3977.52,
+ "duration": 0.0,
+ "text": "between those two. Um uh"
+ },
+ {
+ "start": 3978.47,
+ "duration": 0.0,
+ "text": "uh"
+ },
+ {
+ "start": 3978.48,
+ "duration": 0.0,
+ "text": "uh and<01:06:19.200> and<01:06:19.400> and<01:06:19.520> random<01:06:19.720> information."
+ },
+ {
+ "start": 3981.03,
+ "duration": 0.0,
+ "text": "and and and random information."
+ },
+ {
+ "start": 3981.04,
+ "duration": 0.0,
+ "text": "and and and random information. Um"
+ },
+ {
+ "start": 3982.87,
+ "duration": 0.0,
+ "text": "Um"
+ },
+ {
+ "start": 3982.88,
+ "duration": 0.0,
+ "text": "Um Yeah,<01:06:23.280> I<01:06:23.800> I<01:06:24.560> uh<01:06:25.000> I<01:06:25.080> don't<01:06:25.240> have<01:06:25.400> anything<01:06:26.200> uh"
+ },
+ {
+ "start": 3986.27,
+ "duration": 0.0,
+ "text": "Yeah, I I uh I don't have anything uh"
+ },
+ {
+ "start": 3986.28,
+ "duration": 0.0,
+ "text": "Yeah, I I uh I don't have anything uh very<01:06:27.040> uh"
+ },
+ {
+ "start": 3988.83,
+ "duration": 0.0,
+ "text": "very uh"
+ },
+ {
+ "start": 3988.84,
+ "duration": 0.0,
+ "text": "very uh yeah,<01:06:29.520> very<01:06:30.480> very<01:06:30.800> useful<01:06:31.080> to<01:06:31.200> say,<01:06:31.440> but<01:06:31.600> I<01:06:31.720> I"
+ },
+ {
+ "start": 3991.79,
+ "duration": 0.0,
+ "text": "yeah, very very useful to say, but I I"
+ },
+ {
+ "start": 3991.8,
+ "duration": 0.0,
+ "text": "yeah, very very useful to say, but I I think<01:06:32.040> it<01:06:32.120> would<01:06:32.240> be<01:06:32.440> Yeah,<01:06:32.640> any<01:06:32.960> any<01:06:33.160> more"
+ },
+ {
+ "start": 3993.31,
+ "duration": 0.0,
+ "text": "think it would be Yeah, any any more"
+ },
+ {
+ "start": 3993.32,
+ "duration": 0.0,
+ "text": "think it would be Yeah, any any more specific<01:06:33.760> questions<01:06:34.120> about<01:06:34.320> from<01:06:34.480> the<01:06:34.760> ARC"
+ },
+ {
+ "start": 3994.95,
+ "duration": 0.0,
+ "text": "specific questions about from the ARC"
+ },
+ {
+ "start": 3994.96,
+ "duration": 0.0,
+ "text": "specific questions about from the ARC AGI<01:06:35.640> pattern<01:06:35.880> like<01:06:36.120> anything"
+ },
+ {
+ "start": 3997.79,
+ "duration": 0.0,
+ "text": "AGI pattern like anything"
+ },
+ {
+ "start": 3997.8,
+ "duration": 0.0,
+ "text": "AGI pattern like anything specific<01:06:38.400> about<01:06:38.600> that<01:06:38.800> that<01:06:38.920> you<01:06:39.000> think<01:06:39.600> might"
+ },
+ {
+ "start": 4000.31,
+ "duration": 0.0,
+ "text": "specific about that that you think might"
+ },
+ {
+ "start": 4000.32,
+ "duration": 0.0,
+ "text": "specific about that that you think might Uh<01:06:40.640> so<01:06:40.960> so<01:06:41.200> so<01:06:41.440> they<01:06:41.640> they<01:06:41.760> actually<01:06:42.120> also<01:06:42.440> use"
+ },
+ {
+ "start": 4003.15,
+ "duration": 0.0,
+ "text": "Uh so so so they they actually also use"
+ },
+ {
+ "start": 4003.16,
+ "duration": 0.0,
+ "text": "Uh so so so they they actually also use a<01:06:43.280> a<01:06:43.320> neural<01:06:43.600> network<01:06:44.520> to<01:06:44.720> to<01:06:44.840> represent<01:06:45.320> the"
+ },
+ {
+ "start": 4005.39,
+ "duration": 0.0,
+ "text": "a a neural network to to represent the"
+ },
+ {
+ "start": 4005.4,
+ "duration": 0.0,
+ "text": "a a neural network to to represent the P.<01:06:45.760> So<01:06:46.120> actually<01:06:46.560> the<01:06:46.760> P<01:06:47.200> the<01:06:47.359> computation<01:06:47.880> of"
+ },
+ {
+ "start": 4008.03,
+ "duration": 0.0,
+ "text": "P. So actually the P the computation of"
+ },
+ {
+ "start": 4008.04,
+ "duration": 0.0,
+ "text": "P. So actually the P the computation of P<01:06:48.280> is<01:06:48.480> bounded.<01:06:49.560> And<01:06:50.560> the<01:06:50.920> the<01:06:51.040> introduce<01:06:51.880> some"
+ },
+ {
+ "start": 4012.15,
+ "duration": 0.0,
+ "text": "P is bounded. And the the introduce some"
+ },
+ {
+ "start": 4012.16,
+ "duration": 0.0,
+ "text": "P is bounded. And the the introduce some variational<01:06:52.840> way<01:06:53.160> to<01:06:53.520> to<01:06:54.280> to<01:06:54.680> optimize<01:06:55.200> the"
+ },
+ {
+ "start": 4015.349,
+ "duration": 0.0,
+ "text": "variational way to to to optimize the"
+ },
+ {
+ "start": 4015.359,
+ "duration": 0.0,
+ "text": "variational way to to to optimize the size<01:06:55.800> of<01:06:55.960> P,<01:06:56.359> like<01:06:56.600> the<01:06:56.960> number<01:06:57.320> of<01:06:57.440> bit.<01:06:58.120> It's"
+ },
+ {
+ "start": 4018.349,
+ "duration": 0.0,
+ "text": "size of P, like the number of bit. It's"
+ },
+ {
+ "start": 4018.359,
+ "duration": 0.0,
+ "text": "size of P, like the number of bit. It's basically<01:06:59.200> injecting<01:06:59.800> noise<01:07:00.280> to<01:07:00.440> your"
+ },
+ {
+ "start": 4020.63,
+ "duration": 0.0,
+ "text": "basically injecting noise to your"
+ },
+ {
+ "start": 4020.64,
+ "duration": 0.0,
+ "text": "basically injecting noise to your parameter<01:07:01.000> space<01:07:01.440> so<01:07:01.600> you<01:07:01.720> can<01:07:01.920> explicitly"
+ },
+ {
+ "start": 4023.43,
+ "duration": 0.0,
+ "text": "parameter space so you can explicitly"
+ },
+ {
+ "start": 4023.44,
+ "duration": 0.0,
+ "text": "parameter space so you can explicitly compute<01:07:04.080> the<01:07:04.240> the"
+ },
+ {
+ "start": 4025.03,
+ "duration": 0.0,
+ "text": "compute the the"
+ },
+ {
+ "start": 4025.04,
+ "duration": 0.0,
+ "text": "compute the the number<01:07:05.400> of<01:07:05.560> bits<01:07:05.960> in<01:07:06.120> your<01:07:06.280> model.<01:07:07.040> So<01:07:07.240> in<01:07:07.440> that"
+ },
+ {
+ "start": 4027.71,
+ "duration": 0.0,
+ "text": "number of bits in your model. So in that"
+ },
+ {
+ "start": 4027.72,
+ "duration": 0.0,
+ "text": "number of bits in your model. So in that way"
+ },
+ {
+ "start": 4028.95,
+ "duration": 0.0,
+ "text": "way"
+ },
+ {
+ "start": 4028.96,
+ "duration": 0.0,
+ "text": "way you<01:07:09.240> you<01:07:09.440> are<01:07:09.800> you<01:07:09.960> can<01:07:10.400> optimize<01:07:11.080> the<01:07:11.320> the"
+ },
+ {
+ "start": 4031.51,
+ "duration": 0.0,
+ "text": "you you are you can optimize the the"
+ },
+ {
+ "start": 4031.52,
+ "duration": 0.0,
+ "text": "you you are you can optimize the the size<01:07:11.920> of<01:07:12.040> P<01:07:12.400> and<01:07:12.760> your<01:07:12.960> residual<01:07:13.520> loss"
+ },
+ {
+ "start": 4034.31,
+ "duration": 0.0,
+ "text": "size of P and your residual loss"
+ },
+ {
+ "start": 4034.32,
+ "duration": 0.0,
+ "text": "size of P and your residual loss together.<01:07:15.280> So<01:07:15.880> so<01:07:16.160> I<01:07:16.320> just<01:07:16.520> feel<01:07:16.760> maybe<01:07:17.359> maybe"
+ },
+ {
+ "start": 4037.63,
+ "duration": 0.0,
+ "text": "together. So so I just feel maybe maybe"
+ },
+ {
+ "start": 4037.64,
+ "duration": 0.0,
+ "text": "together. So so I just feel maybe maybe the<01:07:17.800> the<01:07:17.920> method<01:07:18.280> can<01:07:18.480> directly<01:07:19.440> uh<01:07:19.800> combine"
+ },
+ {
+ "start": 4040.31,
+ "duration": 0.0,
+ "text": "the the method can directly uh combine"
+ },
+ {
+ "start": 4040.32,
+ "duration": 0.0,
+ "text": "the the method can directly uh combine into<01:07:20.680> your<01:07:20.840> method<01:07:21.240> and<01:07:21.720> you<01:07:21.920> don't<01:07:22.160> need<01:07:22.480> like"
+ },
+ {
+ "start": 4043.07,
+ "duration": 0.0,
+ "text": "into your method and you don't need like"
+ },
+ {
+ "start": 4043.08,
+ "duration": 0.0,
+ "text": "into your method and you don't need like uh"
+ },
+ {
+ "start": 4043.67,
+ "duration": 0.0,
+ "text": "uh"
+ },
+ {
+ "start": 4043.68,
+ "duration": 0.0,
+ "text": "uh something<01:07:24.240> like<01:07:25.040> uh<01:07:25.520> uh"
+ },
+ {
+ "start": 4046.349,
+ "duration": 0.0,
+ "text": "something like uh uh"
+ },
+ {
+ "start": 4046.359,
+ "duration": 0.0,
+ "text": "something like uh uh uh<01:07:26.840> you<01:07:26.920> don't<01:07:27.120> need<01:07:27.359> something<01:07:27.720> like<01:07:28.280> teacher"
+ },
+ {
+ "start": 4049.11,
+ "duration": 0.0,
+ "text": "uh you don't need something like teacher"
+ },
+ {
+ "start": 4049.12,
+ "duration": 0.0,
+ "text": "uh you don't need something like teacher student<01:07:29.760> way<01:07:30.040> to<01:07:30.240> to<01:07:30.359> measure<01:07:30.760> measure<01:07:31.240> that"
+ },
+ {
+ "start": 4051.47,
+ "duration": 0.0,
+ "text": "student way to to measure measure that"
+ },
+ {
+ "start": 4051.48,
+ "duration": 0.0,
+ "text": "student way to to measure measure that and<01:07:31.680> directly<01:07:32.080> optimize<01:07:32.560> the<01:07:32.680> model.<01:07:33.160> Yeah,"
+ },
+ {
+ "start": 4053.79,
+ "duration": 0.0,
+ "text": "and directly optimize the model. Yeah,"
+ },
+ {
+ "start": 4053.8,
+ "duration": 0.0,
+ "text": "and directly optimize the model. Yeah, that<01:07:34.040> that's<01:07:34.240> possible.<01:07:34.680> I<01:07:34.800> think<01:07:35.200> yeah,<01:07:35.320> it"
+ },
+ {
+ "start": 4055.349,
+ "duration": 0.0,
+ "text": "that that's possible. I think yeah, it"
+ },
+ {
+ "start": 4055.359,
+ "duration": 0.0,
+ "text": "that that's possible. I think yeah, it would<01:07:35.440> be<01:07:35.520> interesting<01:07:35.960> exploring<01:07:36.320> both"
+ },
+ {
+ "start": 4056.55,
+ "duration": 0.0,
+ "text": "would be interesting exploring both"
+ },
+ {
+ "start": 4056.56,
+ "duration": 0.0,
+ "text": "would be interesting exploring both different<01:07:36.840> coding<01:07:37.080> strategies<01:07:37.560> here.<01:07:38.359> Um"
+ },
+ {
+ "start": 4059.03,
+ "duration": 0.0,
+ "text": "different coding strategies here. Um"
+ },
+ {
+ "start": 4059.04,
+ "duration": 0.0,
+ "text": "different coding strategies here. Um and<01:07:39.240> then<01:07:39.440> so<01:07:39.560> both<01:07:39.840> both<01:07:40.040> versions,"
+ },
+ {
+ "start": 4060.39,
+ "duration": 0.0,
+ "text": "and then so both both versions,"
+ },
+ {
+ "start": 4060.4,
+ "duration": 0.0,
+ "text": "and then so both both versions, basically<01:07:41.120> both<01:07:41.440> take<01:07:41.640> our<01:07:41.760> sequential<01:07:42.160> code,"
+ },
+ {
+ "start": 4062.55,
+ "duration": 0.0,
+ "text": "basically both take our sequential code,"
+ },
+ {
+ "start": 4062.56,
+ "duration": 0.0,
+ "text": "basically both take our sequential code, maybe<01:07:42.760> test<01:07:43.000> it<01:07:43.120> out<01:07:43.359> in<01:07:43.760> in<01:07:43.880> that<01:07:44.040> setting,"
+ },
+ {
+ "start": 4064.43,
+ "duration": 0.0,
+ "text": "maybe test it out in in that setting,"
+ },
+ {
+ "start": 4064.44,
+ "duration": 0.0,
+ "text": "maybe test it out in in that setting, right?<01:07:45.080> Uh<01:07:45.240> and<01:07:45.440> then<01:07:45.600> take<01:07:45.840> the<01:07:45.920> codes<01:07:46.160> that"
+ },
+ {
+ "start": 4066.27,
+ "duration": 0.0,
+ "text": "right? Uh and then take the codes that"
+ },
+ {
+ "start": 4066.28,
+ "duration": 0.0,
+ "text": "right? Uh and then take the codes that they're<01:07:46.440> doing<01:07:46.800> and<01:07:46.960> then<01:07:47.080> use<01:07:47.240> it<01:07:47.359> here,<01:07:47.720> see"
+ },
+ {
+ "start": 4067.83,
+ "duration": 0.0,
+ "text": "they're doing and then use it here, see"
+ },
+ {
+ "start": 4067.84,
+ "duration": 0.0,
+ "text": "they're doing and then use it here, see if<01:07:47.960> we<01:07:48.040> get<01:07:48.160> better<01:07:48.359> codes.<01:07:48.960> I<01:07:49.040> think<01:07:49.240> both"
+ },
+ {
+ "start": 4069.59,
+ "duration": 0.0,
+ "text": "if we get better codes. I think both"
+ },
+ {
+ "start": 4069.6,
+ "duration": 0.0,
+ "text": "if we get better codes. I think both both<01:07:49.800> directions<01:07:50.120> would<01:07:50.200> be<01:07:50.280> good."
+ }
+ ],
+ "plain": "So,<00:00:01.560> I'm<00:00:01.720> Andrew<00:00:02.160> Wilson<00:00:02.680> and<00:00:03.080> I'm<00:00:03.200> going<00:00:03.320> to\nSo, I'm Andrew Wilson and I'm going to\nSo, I'm Andrew Wilson and I'm going to be<00:00:03.560> presenting<00:00:04.200> this<00:00:04.440> work<00:00:04.720> with<00:00:05.080> Mark<00:00:05.360> Finzi,\nbe presenting this work with Mark Finzi,\nbe presenting this work with Mark Finzi, who<00:00:06.280> led<00:00:06.520> the<00:00:06.640> work<00:00:06.960> along<00:00:07.280> with<00:00:07.520> Shikai<00:00:08.120> and\nwho led the work along with Shikai and\nwho led the work along with Shikai and Yiding,<00:00:09.120> and<00:00:09.400> we<00:00:09.520> also<00:00:09.920> collaborated<00:00:10.480> with\nYiding, and we also collaborated with\nYiding, and we also collaborated with Pavel<00:00:11.120> and<00:00:11.360> Zico.\nPavel and Zico.\nPavel and Zico. Uh<00:00:12.800> so,<00:00:13.200> let's<00:00:13.720> start<00:00:14.080> with<00:00:14.240> a<00:00:14.280> question.\nUh so, let's start with a question.\nUh so, let's start with a question. Does<00:00:15.960> this<00:00:16.280> image<00:00:16.960> to<00:00:17.080> you<00:00:17.320> look<00:00:17.600> like<00:00:17.920> noise\nDoes this image to you look like noise\nDoes this image to you look like noise or<00:00:19.000> signal?<00:00:19.920> I<00:00:20.040> imagine<00:00:20.760> it<00:00:21.000> looks<00:00:21.240> a<00:00:21.320> lot<00:00:21.560> like\nor signal? I imagine it looks a lot like\nor signal? I imagine it looks a lot like noise.<00:00:22.320> Perhaps<00:00:22.760> you<00:00:22.880> could<00:00:23.040> stare<00:00:23.280> at<00:00:23.440> it<00:00:23.560> for\nnoise. Perhaps you could stare at it for\nnoise. Perhaps you could stare at it for a<00:00:23.720> very<00:00:23.920> long<00:00:24.160> time<00:00:24.400> and<00:00:24.520> it<00:00:24.600> might<00:00:24.800> be<00:00:24.920> like<00:00:25.200> a\na very long time and it might be like a\na very long time and it might be like a modern<00:00:25.640> piece<00:00:25.920> of<00:00:26.160> artwork<00:00:26.640> where<00:00:26.760> a<00:00:26.840> face<00:00:27.160> or\nmodern piece of artwork where a face or\nmodern piece of artwork where a face or something<00:00:28.120> jumps<00:00:28.520> out<00:00:28.720> at<00:00:28.840> you.<00:00:29.200> In<00:00:29.440> fact,\nsomething jumps out at you. In fact,\nsomething jumps out at you. In fact, actually<00:00:30.160> there<00:00:30.400> is<00:00:30.640> structure.<00:00:31.920> Um<00:00:32.320> so,<00:00:32.960> uh\nactually there is structure. Um so, uh\nactually there is structure. Um so, uh you<00:00:33.280> might<00:00:33.480> have<00:00:33.640> to<00:00:33.760> stare<00:00:34.040> for<00:00:34.160> a<00:00:34.200> very,<00:00:34.440> very\nyou might have to stare for a very, very\nyou might have to stare for a very, very long<00:00:34.920> time,<00:00:35.440> but<00:00:36.040> if<00:00:36.400> you<00:00:36.600> have<00:00:36.800> good<00:00:36.960> vision,\nlong time, but if you have good vision,\nlong time, but if you have good vision, you'll<00:00:38.080> see<00:00:38.280> that<00:00:38.560> the<00:00:38.640> word<00:00:38.920> epiplexity<00:00:39.720> is\nyou'll see that the word epiplexity is\nyou'll see that the word epiplexity is sort<00:00:40.080> of<00:00:40.160> buried<00:00:40.560> amongst<00:00:41.040> the<00:00:41.360> the<00:00:41.480> white\nsort of buried amongst the the white\nsort of buried amongst the the white noise.<00:00:42.560> And<00:00:43.120> the<00:00:43.280> point<00:00:43.640> that<00:00:43.960> I'm<00:00:44.280> making\nnoise. And the point that I'm making\nnoise. And the point that I'm making with<00:00:44.920> this<00:00:45.080> example<00:00:45.640> is<00:00:45.800> that<00:00:45.960> whether<00:00:46.240> or<00:00:46.320> not\nwith this example is that whether or not\nwith this example is that whether or not something<00:00:47.080> appears<00:00:47.480> random<00:00:48.240> depends<00:00:48.640> on<00:00:48.920> on\nsomething appears random depends on on\nsomething appears random depends on on on<00:00:49.360> the<00:00:49.640> computation<00:00:50.240> available<00:00:50.680> to<00:00:50.840> us.<00:00:51.120> So,\non the computation available to us. So,\non the computation available to us. So, pseudorandom<00:00:51.920> numbers,<00:00:52.240> for<00:00:52.360> example,<00:00:52.960> are\npseudorandom numbers, for example, are\npseudorandom numbers, for example, are indistinguishable<00:00:54.040> from<00:00:54.400> actual<00:00:54.760> random\nindistinguishable from actual random\nindistinguishable from actual random numbers<00:00:55.440> if<00:00:55.600> we<00:00:55.760> have<00:00:56.400> only<00:00:56.640> polynomial<00:00:57.200> time\nnumbers if we have only polynomial time\nnumbers if we have only polynomial time computation<00:00:58.320> and<00:00:59.200> in<00:00:59.360> many<00:00:59.600> respects,<00:01:00.080> that's\ncomputation and in many respects, that's\ncomputation and in many respects, that's why<00:01:00.480> pseudorandom<00:01:01.360> numbers<00:01:01.480> are<00:01:01.800> ubiquitous\nwhy pseudorandom numbers are ubiquitous\nwhy pseudorandom numbers are ubiquitous and<00:01:03.040> useful<00:01:03.480> in<00:01:03.640> so<00:01:03.800> many<00:01:04.120> different\nand useful in so many different\nand useful in so many different settings.<00:01:05.720> And<00:01:05.960> so,\nsettings. And so,\nsettings. And so, accounting<00:01:07.880> for<00:01:08.000> computation<00:01:08.840> was<00:01:09.080> a<00:01:09.160> key\naccounting for computation was a key\naccounting for computation was a key consideration<00:01:10.360> in<00:01:10.560> reasoning<00:01:11.120> about<00:01:11.800> what\nconsideration in reasoning about what\nconsideration in reasoning about what Mark<00:01:12.240> is<00:01:12.360> going<00:01:12.560> to<00:01:12.680> introduce<00:01:13.120> in<00:01:13.200> a<00:01:13.280> moment,\nMark is going to introduce in a moment,\nMark is going to introduce in a moment, epiplexity,<00:01:14.560> this<00:01:14.760> new<00:01:14.920> measure<00:01:15.240> of\nepiplexity, this new measure of\nepiplexity, this new measure of information,<00:01:16.560> as<00:01:16.760> well<00:01:16.960> as<00:01:17.120> several\ninformation, as well as several\ninformation, as well as several paradoxes<00:01:18.520> which<00:01:19.000> um<00:01:19.560> can<00:01:19.760> partly<00:01:20.200> be\nparadoxes which um can partly be\nparadoxes which um can partly be explained<00:01:21.240> by<00:01:21.520> not<00:01:21.880> accounting<00:01:22.320> for\nexplained by not accounting for\nexplained by not accounting for computation.<00:01:23.560> So,\ncomputation. So,\ncomputation. So, uh<00:01:24.680> in<00:01:24.880> the<00:01:25.000> paper,<00:01:25.400> we<00:01:25.600> present<00:01:26.120> what<00:01:26.240> we<00:01:26.360> call\nuh in the paper, we present what we call\nuh in the paper, we present what we call three<00:01:26.760> apparent<00:01:27.160> paradoxes.<00:01:28.120> Uh<00:01:28.240> paradox<00:01:28.840> one\nthree apparent paradoxes. Uh paradox one\nthree apparent paradoxes. Uh paradox one is<00:01:29.440> that<00:01:29.600> information<00:01:30.240> can't<00:01:30.520> be<00:01:30.640> increased\nis that information can't be increased\nis that information can't be increased by<00:01:31.240> deterministic<00:01:32.360> processes.<00:01:33.560> Uh<00:01:33.800> yet,<00:01:34.280> as\nby deterministic processes. Uh yet, as\nby deterministic processes. Uh yet, as we<00:01:34.640> said,<00:01:34.960> pseudorandom<00:01:35.920> numbers<00:01:36.520> are\nwe said, pseudorandom numbers are\nwe said, pseudorandom numbers are everywhere<00:01:37.440> and<00:01:37.760> synthetic<00:01:38.200> data<00:01:38.560> is\neverywhere and synthetic data is\neverywhere and synthetic data is incredibly<00:01:39.200> useful<00:01:39.680> in<00:01:39.840> systems<00:01:40.240> like\nincredibly useful in systems like\nincredibly useful in systems like AlphaZero,<00:01:41.640> which<00:01:42.000> involve<00:01:42.400> a<00:01:42.440> bunch<00:01:42.680> of\nAlphaZero, which involve a bunch of\nAlphaZero, which involve a bunch of deterministic<00:01:43.360> processes,<00:01:44.040> learn\ndeterministic processes, learn\ndeterministic processes, learn sophisticated<00:01:45.000> strategies<00:01:45.640> from<00:01:46.240> games.<00:01:47.240> Uh\nsophisticated strategies from games. Uh\nsophisticated strategies from games. Uh paradox<00:01:48.040> two,<00:01:48.360> information<00:01:48.960> is<00:01:49.160> independent\nparadox two, information is independent\nparadox two, information is independent of<00:01:50.080> factorization<00:01:51.080> order.<00:01:51.440> So,<00:01:51.600> this<00:01:51.800> is\nof factorization order. So, this is\nof factorization order. So, this is given<00:01:52.240> by<00:01:52.800> Shannon<00:01:53.200> symmetry<00:01:53.680> of<00:01:53.800> information\ngiven by Shannon symmetry of information\ngiven by Shannon symmetry of information as<00:01:54.680> well<00:01:54.840> as<00:01:54.920> something<00:01:55.200> similar<00:01:55.600> for\nas well as something similar for\nas well as something similar for Kolmogorov<00:01:56.400> complexity<00:01:57.120> and<00:01:57.320> algorithmic\nKolmogorov complexity and algorithmic\nKolmogorov complexity and algorithmic information<00:01:58.840> theory.<00:01:59.560> Yet,<00:02:00.600> LLMs<00:02:01.080> are<00:02:01.160> going\ninformation theory. Yet, LLMs are going\ninformation theory. Yet, LLMs are going to<00:02:01.360> learn<00:02:01.680> a<00:02:01.760> lot<00:02:02.040> more<00:02:02.320> from<00:02:03.280> English<00:02:03.640> text\nto learn a lot more from English text\nto learn a lot more from English text ordered<00:02:04.360> from<00:02:04.760> left<00:02:04.960> to<00:02:05.080> right,<00:02:05.720> uh<00:02:05.920> picking\nordered from left to right, uh picking\nordered from left to right, uh picking out<00:02:06.360> an<00:02:06.520> arrow<00:02:06.800> of<00:02:06.920> time,<00:02:07.240> and<00:02:07.320> this<00:02:07.480> is<00:02:07.600> true\nout an arrow of time, and this is true\nout an arrow of time, and this is true of<00:02:08.080> all<00:02:08.240> sorts<00:02:08.520> of<00:02:08.640> different<00:02:09.360> problem\nof all sorts of different problem\nof all sorts of different problem settings.<00:02:10.600> And<00:02:10.880> paradox<00:02:11.280> three,<00:02:11.960> likelihood\nsettings. And paradox three, likelihood\nsettings. And paradox three, likelihood modeling<00:02:12.960> is<00:02:13.240> just<00:02:13.560> distribution<00:02:14.200> matching.\nmodeling is just distribution matching.\nmodeling is just distribution matching. So,<00:02:14.840> we<00:02:15.000> can't<00:02:15.280> hope<00:02:15.480> to<00:02:15.600> go<00:02:15.760> beyond<00:02:16.200> the\nSo, we can't hope to go beyond the\nSo, we can't hope to go beyond the generative<00:02:16.800> processes<00:02:17.640> that<00:02:18.160> created<00:02:18.520> the\ngenerative processes that created the\ngenerative processes that created the data<00:02:18.880> that<00:02:19.040> we're<00:02:19.160> training<00:02:19.520> on.<00:02:19.840> Yet,<00:02:20.040> we<00:02:20.200> see\ndata that we're training on. Yet, we see\ndata that we're training on. Yet, we see models<00:02:20.920> doing<00:02:21.240> precisely<00:02:21.800> that<00:02:22.160> in<00:02:22.320> all<00:02:22.480> sorts\nmodels doing precisely that in all sorts\nmodels doing precisely that in all sorts of<00:02:22.880> different<00:02:23.600> settings.<00:02:24.480> And<00:02:24.720> so,\nof different settings. And so,\nof different settings. And so, these<00:02:26.040> are<00:02:26.640> statements<00:02:27.280> which<00:02:27.520> can<00:02:27.720> be\nthese are statements which can be\nthese are statements which can be mathematically<00:02:28.920> justified<00:02:30.040> by<00:02:30.360> information\nmathematically justified by information\nmathematically justified by information theory,<00:02:31.320> but<00:02:32.080> um<00:02:32.320> really<00:02:32.600> don't<00:02:32.960> align<00:02:33.520> with\ntheory, but um really don't align with\ntheory, but um really don't align with our<00:02:34.120> intuitions<00:02:34.840> or<00:02:35.240> increasingly<00:02:36.000> what\nour intuitions or increasingly what\nour intuitions or increasingly what we're<00:02:36.360> seeing<00:02:36.840> in<00:02:37.240> practice.<00:02:38.000> And<00:02:38.520> it's<00:02:38.800> our\nwe're seeing in practice. And it's our\nwe're seeing in practice. And it's our contention<00:02:39.640> this<00:02:39.840> is<00:02:40.000> because\ncontention this is because\ncontention this is because quite<00:02:41.680> often<00:02:42.040> we're<00:02:42.360> assuming<00:02:43.000> unlimited\nquite often we're assuming unlimited\nquite often we're assuming unlimited computation<00:02:44.840> and<00:02:45.000> we're<00:02:45.120> not<00:02:45.400> targeting\ncomputation and we're not targeting\ncomputation and we're not targeting useful<00:02:46.520> information<00:02:47.080> content.\nuseful information content.\nuseful information content. So,<00:02:49.440> just<00:02:49.680> to<00:02:49.800> get<00:02:50.240> another<00:02:50.880> sort<00:02:51.080> of<00:02:51.600> sense<00:02:51.960> of\nSo, just to get another sort of sense of\nSo, just to get another sort of sense of some<00:02:52.400> of<00:02:52.480> these<00:02:52.720> points,<00:02:53.120> we<00:02:53.240> can<00:02:53.360> imagine<00:02:53.960> a\nsome of these points, we can imagine a\nsome of these points, we can imagine a system<00:02:54.600> like<00:02:55.400> AlphaZero<00:02:56.520> where<00:02:57.240> the\nsystem like AlphaZero where the\nsystem like AlphaZero where the description<00:02:57.960> length<00:02:58.200> of<00:02:58.320> the<00:02:58.400> whole<00:02:58.600> system\ndescription length of the whole system\ndescription length of the whole system is<00:02:59.200> actually<00:02:59.560> quite<00:02:59.960> small.<00:03:00.400> We<00:03:00.520> can<00:03:00.720> store\nis actually quite small. We can store\nis actually quite small. We can store the<00:03:01.040> rules<00:03:01.400> of<00:03:01.840> chess<00:03:02.200> using<00:03:02.520> a<00:03:02.560> small<00:03:02.800> number\nthe rules of chess using a small number\nthe rules of chess using a small number of<00:03:03.240> bytes.<00:03:03.600> The<00:03:03.680> training<00:03:04.080> algorithm\nof bytes. The training algorithm\nof bytes. The training algorithm shouldn't<00:03:05.480> take<00:03:05.720> much<00:03:05.960> more<00:03:06.120> than<00:03:06.240> about<00:03:06.520> 10\nshouldn't take much more than about 10\nshouldn't take much more than about 10 kilobytes.<00:03:07.720> Uh<00:03:07.800> random<00:03:08.160> seed,<00:03:08.680> also<00:03:08.960> very\nkilobytes. Uh random seed, also very\nkilobytes. Uh random seed, also very small.<00:03:10.080> Um<00:03:10.600> yet,<00:03:11.360> it<00:03:11.560> seems<00:03:11.960> like<00:03:12.280> we're\nsmall. Um yet, it seems like we're\nsmall. Um yet, it seems like we're learning<00:03:12.760> something<00:03:13.400> very<00:03:14.160> useful.<00:03:15.200> Um<00:03:15.520> and\nlearning something very useful. Um and\nlearning something very useful. Um and so,<00:03:16.520> since<00:03:16.960> information<00:03:17.640> can't<00:03:17.960> be<00:03:18.200> created,\nso, since information can't be created,\nso, since information can't be created, what<00:03:19.960> is<00:03:20.320> AlphaGo<00:03:21.040> actually<00:03:21.680> learning?<00:03:22.160> And\nwhat is AlphaGo actually learning? And\nwhat is AlphaGo actually learning? And this<00:03:22.960> is<00:03:23.200> exactly<00:03:23.760> the<00:03:23.880> kind<00:03:24.120> of<00:03:24.240> question\nthis is exactly the kind of question\nthis is exactly the kind of question that<00:03:24.800> motivated<00:03:25.560> our<00:03:25.720> work<00:03:26.040> on<00:03:26.440> epiplexity.\nthat motivated our work on epiplexity.\nthat motivated our work on epiplexity. Uh<00:03:29.000> we<00:03:29.160> have<00:03:29.480> one<00:03:29.680> more<00:03:29.840> example<00:03:30.280> here,<00:03:30.440> so<00:03:30.560> I'm\nUh we have one more example here, so I'm\nUh we have one more example here, so I'm just<00:03:30.760> going<00:03:30.880> to<00:03:30.960> play<00:03:31.120> a<00:03:31.160> bit<00:03:31.320> of<00:03:31.440> a<00:03:31.480> video<00:03:32.040> and\njust going to play a bit of a video and\njust going to play a bit of a video and uh<00:03:32.720> Mark<00:03:33.040> will<00:03:33.200> just<00:03:33.640> narrate<00:03:34.040> through<00:03:34.240> this\nuh Mark will just narrate through this\nuh Mark will just narrate through this example.\nexample.\nexample. Okay.<00:03:37.800> All<00:03:37.880> right.<00:03:38.200> So,<00:03:38.360> let's<00:03:38.560> see<00:03:38.640> if<00:03:38.760> we<00:03:38.840> can\nOkay. All right. So, let's see if we can\nOkay. All right. So, let's see if we can get<00:03:39.120> that<00:03:39.320> video.<00:03:40.120> Oh,<00:03:40.280> you<00:03:40.400> can<00:03:40.520> you<00:03:40.600> see<00:03:40.720> the\nget that video. Oh, you can you see the\nget that video. Oh, you can you see the video?\nvideo?\nvideo? Uh<00:03:42.760> it's<00:03:42.960> just<00:03:43.160> showing<00:03:43.320> the<00:03:43.400> presentation\nUh it's just showing the presentation\nUh it's just showing the presentation right<00:03:44.040> now.<00:03:44.440> Okay.<00:03:44.760> So,<00:03:44.840> I'll<00:03:44.920> just<00:03:45.120> change\nright now. Okay. So, I'll just change\nright now. Okay. So, I'll just change the<00:03:45.640> screen<00:03:46.000> sharing.\nthe screen sharing.\nthe screen sharing. Okay.\nOkay.\nOkay. All<00:03:49.440> right,<00:03:49.640> you<00:03:49.720> should<00:03:49.880> see<00:03:49.960> it<00:03:50.040> now.\nAll right, you should see it now.\nAll right, you should see it now. So,\nSo,\nSo, right.\nright.\nright. So,<00:03:53.800> we're<00:03:53.880> watching<00:03:54.120> this<00:03:54.240> video.<00:03:54.800> And\nSo, we're watching this video. And\nSo, we're watching this video. And again,<00:03:55.800> um\nagain, um\nagain, um is<00:03:57.320> this<00:03:57.720> structure<00:03:58.760> or<00:03:58.960> noise?\nis this structure or noise?\nis this structure or noise? I<00:04:01.120> think<00:04:01.360> I'll<00:04:01.480> play<00:04:01.560> it.<00:04:02.000> Mhm.\nI think I'll play it. Mhm.\nI think I'll play it. Mhm. So,<00:04:03.880> I<00:04:03.920> think<00:04:04.240> I<00:04:04.280> think<00:04:04.480> most<00:04:04.680> people<00:04:05.000> would\nSo, I think I think most people would\nSo, I think I think most people would agree<00:04:05.960> that<00:04:06.160> this<00:04:06.680> is<00:04:06.840> noise.\nagree that this is noise.\nagree that this is noise. But,<00:04:09.680> if<00:04:09.760> we<00:04:10.240> get<00:04:10.320> the<00:04:10.400> next<00:04:10.640> video,\nBut, if we get the next video,\nBut, if we get the next video, Mhm.\nMhm.\nMhm. One<00:04:13.400> moment.\nOne moment.\nOne moment. All<00:04:15.800> right.\nOkay.\nOkay.\nOkay. Most<00:04:25.400> people<00:04:25.520> would<00:04:25.640> agree<00:04:25.800> that<00:04:25.920> this<00:04:26.120> is\nMost people would agree that this is\nMost people would agree that this is noise.<00:04:27.720> But,<00:04:28.080> the<00:04:28.200> way<00:04:28.480> that<00:04:29.040> I<00:04:29.160> generated\nnoise. But, the way that I generated\nnoise. But, the way that I generated this<00:04:30.120> is<00:04:30.880> through<00:04:31.080> the<00:04:31.400> Wait,<00:04:31.640> wait.<00:04:32.520> Yes.<00:04:32.840> We\nthis is through the Wait, wait. Yes. We\nthis is through the Wait, wait. Yes. We don't<00:04:33.280> see<00:04:33.480> a<00:04:33.560> thing.\ndon't see a thing.\ndon't see a thing. At<00:04:35.800> least<00:04:36.040> I<00:04:36.120> don't.\nAt least I don't.\nAt least I don't. >> we<00:04:36.840> can<00:04:37.080> see<00:04:37.440> it.\n>> we can see it.\n>> we can see it. Let<00:04:39.960> me<00:04:40.040> know<00:04:40.240> if<00:04:40.360> you<00:04:40.480> see<00:04:40.600> it.\nLet me know if you see it.\nLet me know if you see it. >> able<00:04:40.920> to<00:04:41.000> see<00:04:41.280> it.<00:04:41.600> Uh\n>> able to see it. Uh\n>> able to see it. Uh Yeah,<00:04:42.760> I<00:04:42.800> see\nYeah, I see\nYeah, I see Yeah,<00:04:44.480> I<00:04:44.560> can<00:04:44.760> see<00:04:44.920> it<00:04:45.080> fine.<00:04:45.920> Yeah.<00:04:46.520> Me,<00:04:46.680> too.\nYeah, I can see it fine. Yeah. Me, too.\nYeah, I can see it fine. Yeah. Me, too. >> It's<00:04:47.120> only<00:04:47.320> my<00:04:47.520> problem,<00:04:47.960> probably.<00:04:48.520> Okay.\n>> It's only my problem, probably. Okay.\n>> It's only my problem, probably. Okay. Right.<00:04:49.760> So,<00:04:50.520> um<00:04:51.160> the<00:04:51.440> way<00:04:51.640> that<00:04:51.920> this<00:04:52.360> noise\nRight. So, um the way that this noise\nRight. So, um the way that this noise was<00:04:53.120> actually<00:04:53.440> generated<00:04:54.000> was<00:04:54.800> through<00:04:55.440> this\nwas actually generated was through this\nwas actually generated was through this game<00:04:56.320> of<00:04:56.440> life<00:04:56.680> cellular<00:04:56.960> automaton<00:04:57.880> and<00:04:58.120> a\ngame of life cellular automaton and a\ngame of life cellular automaton and a set<00:04:58.400> of<00:04:58.920> initial<00:04:59.240> conditions<00:04:59.840> which<00:05:00.040> I<00:05:00.120> then\nset of initial conditions which I then\nset of initial conditions which I then encrypted.\nencrypted.\nencrypted. So,\nSo,\nSo, uh\nuh\nuh somehow,<00:05:07.040> if\nsomehow, if\nsomehow, if for<00:05:08.640> somebody<00:05:09.000> with<00:05:09.440> infinite<00:05:09.800> compute,\nfor somebody with infinite compute,\nfor somebody with infinite compute, they<00:05:11.480> would<00:05:11.640> see<00:05:11.880> that<00:05:12.080> those<00:05:12.360> two<00:05:12.520> objects\nthey would see that those two objects\nthey would see that those two objects are<00:05:13.080> essentially<00:05:13.440> the<00:05:13.520> same.\nare essentially the same.\nare essentially the same. But,<00:05:15.080> it<00:05:15.880> is<00:05:16.080> kind<00:05:16.360> of<00:05:17.200> incredible<00:05:18.080> to<00:05:19.160> assert\nBut, it is kind of incredible to assert\nBut, it is kind of incredible to assert that<00:05:19.760> they<00:05:19.880> are<00:05:20.000> the<00:05:20.120> same<00:05:21.120> for<00:05:21.280> people<00:05:21.560> like\nthat they are the same for people like\nthat they are the same for people like us<00:05:22.240> with<00:05:22.360> limited<00:05:22.680> compute.<00:05:23.680> We<00:05:23.800> don't<00:05:23.960> have\nus with limited compute. We don't have\nus with limited compute. We don't have that<00:05:24.280> decryption<00:05:24.720> key.<00:05:25.240> We<00:05:25.360> can't<00:05:25.600> see<00:05:25.720> that\nthat decryption key. We can't see that\nthat decryption key. We can't see that structure.<00:05:26.680> If<00:05:26.760> we're<00:05:26.880> trying<00:05:27.080> to<00:05:27.120> train<00:05:27.360> on\nstructure. If we're trying to train on\nstructure. If we're trying to train on that<00:05:27.640> data,\nthat data,\nthat data, yeah,<00:05:29.320> and<00:05:29.680> we<00:05:29.800> don't<00:05:29.920> have<00:05:30.040> the<00:05:30.120> compute<00:05:30.520> to\nyeah, and we don't have the compute to\nyeah, and we don't have the compute to be<00:05:30.680> able<00:05:30.800> to<00:05:30.880> decrypt,<00:05:31.880> um<00:05:32.360> and<00:05:32.480> it's<00:05:32.600> just\nbe able to decrypt, um and it's just\nbe able to decrypt, um and it's just going<00:05:32.880> to<00:05:32.960> look<00:05:33.080> like<00:05:33.280> noise<00:05:33.560> to<00:05:33.680> us.\ngoing to look like noise to us.\ngoing to look like noise to us. And<00:05:34.960> again,<00:05:35.240> you<00:05:35.360> can<00:05:35.480> go<00:05:35.640> a<00:05:35.840> level<00:05:36.120> further.\nAnd again, you can go a level further.\nAnd again, you can go a level further. Um<00:05:38.040> so,<00:05:38.320> we<00:05:38.440> have<00:05:38.600> a<00:05:38.760> a<00:05:38.840> level<00:05:39.080> of<00:05:39.160> structure\nUm so, we have a a level of structure\nUm so, we have a a level of structure noise<00:05:39.840> that<00:05:39.920> we<00:05:40.000> see<00:05:40.480> on<00:05:40.600> the<00:05:40.680> left,<00:05:41.560> on<00:05:41.680> the\nnoise that we see on the left, on the\nnoise that we see on the left, on the middle,\nmiddle,\nmiddle, and<00:05:42.840> then<00:05:42.960> also<00:05:43.680> in<00:05:44.040> the<00:05:44.120> generating<00:05:44.520> process.\nand then also in the generating process.\nand then also in the generating process. And<00:05:46.120> my<00:05:46.840> right,<00:05:47.120> the<00:05:47.240> our<00:05:47.400> assertion<00:05:47.920> is<00:05:48.120> that\nAnd my right, the our assertion is that\nAnd my right, the our assertion is that um\num\num that<00:05:50.440> these<00:05:50.600> can<00:05:50.760> be<00:05:50.880> different\nthat these can be different\nthat these can be different um<00:05:52.840> because<00:05:53.400> of<00:05:53.520> the<00:05:53.600> compute<00:05:54.280> that<00:05:54.440> went<00:05:54.680> into\num because of the compute that went into\num because of the compute that went into the<00:05:55.240> computation<00:05:56.040> and<00:05:56.280> how<00:05:56.400> much<00:05:57.000> is<00:05:57.200> required\nthe computation and how much is required\nthe computation and how much is required to<00:05:57.720> actually<00:05:57.960> unravel<00:05:58.320> it.<00:05:58.840> Okay.<00:05:59.400> Yeah,<00:05:59.560> so\nto actually unravel it. Okay. Yeah, so\nto actually unravel it. Okay. Yeah, so that<00:05:59.880> that<00:06:00.120> that's<00:06:00.320> it.\nthat that that's it.\nthat that that's it. Okay.<00:06:02.080> And<00:06:02.240> also,<00:06:02.520> just<00:06:02.760> to<00:06:02.960> elaborate<00:06:03.520> a\nOkay. And also, just to elaborate a\nOkay. And also, just to elaborate a little<00:06:03.800> bit<00:06:03.920> more<00:06:04.320> on<00:06:04.640> the<00:06:04.760> difference\nlittle bit more on the difference\nlittle bit more on the difference between<00:06:06.240> structural<00:06:06.840> information<00:06:07.480> and\nbetween structural information and\nbetween structural information and random<00:06:08.120> information,<00:06:08.840> which<00:06:09.080> is<00:06:09.200> something<00:06:09.480> I\nrandom information, which is something I\nrandom information, which is something I alluded<00:06:09.960> to<00:06:10.160> when<00:06:10.360> I<00:06:10.440> said<00:06:10.880> that<00:06:11.720> we're<00:06:12.120> often\nalluded to when I said that we're often\nalluded to when I said that we're often not<00:06:12.640> targeting<00:06:13.080> useful<00:06:13.440> information<00:06:14.000> content\nnot targeting useful information content\nnot targeting useful information content and<00:06:14.720> that<00:06:14.920> can<00:06:15.720> um<00:06:15.920> lead<00:06:16.160> to<00:06:16.280> the<00:06:16.400> paradoxes\nand that can um lead to the paradoxes\nand that can um lead to the paradoxes that<00:06:17.360> we<00:06:17.480> presented.<00:06:18.560> Um\nthat we presented. Um\nthat we presented. Um we<00:06:19.800> can<00:06:19.920> imagine<00:06:20.360> in<00:06:20.440> this<00:06:20.640> first<00:06:20.960> row,<00:06:21.320> we\nwe can imagine in this first row, we\nwe can imagine in this first row, we have<00:06:22.040> just<00:06:22.240> a<00:06:22.320> simple<00:06:22.640> gradient<00:06:23.160> of<00:06:23.280> color.\nhave just a simple gradient of color.\nhave just a simple gradient of color. So,<00:06:23.960> this<00:06:24.240> has<00:06:24.400> got<00:06:24.680> very<00:06:24.920> simple<00:06:25.240> structure\nSo, this has got very simple structure\nSo, this has got very simple structure and<00:06:25.840> it's<00:06:26.000> not<00:06:26.200> very<00:06:26.440> noisy.<00:06:27.400> And<00:06:27.680> so,<00:06:27.920> this<00:06:28.120> is\nand it's not very noisy. And so, this is\nand it's not very noisy. And so, this is very<00:06:28.600> compressible.<00:06:29.800> Um\nvery compressible. Um\nvery compressible. Um and<00:06:31.800> uh\nand uh\nand uh in<00:06:32.520> the<00:06:32.600> middle<00:06:32.840> row,<00:06:33.160> we<00:06:33.440> have<00:06:33.720> natural\nin the middle row, we have natural\nin the middle row, we have natural images<00:06:34.920> and<00:06:35.240> some<00:06:35.640> structured<00:06:36.280> code.<00:06:37.200> Uh<00:06:37.440> so,\nimages and some structured code. Uh so,\nimages and some structured code. Uh so, this<00:06:37.880> data<00:06:38.840> is<00:06:39.080> going<00:06:39.320> to<00:06:39.440> be<00:06:39.880> very<00:06:40.400> useful<00:06:40.920> for\nthis data is going to be very useful for\nthis data is going to be very useful for training<00:06:41.600> a<00:06:41.680> model.<00:06:42.160> It<00:06:42.320> could<00:06:42.480> teach<00:06:42.800> our\ntraining a model. It could teach our\ntraining a model. It could teach our model<00:06:43.240> a<00:06:43.280> useful<00:06:43.640> representation<00:06:44.480> that<00:06:44.640> will\nmodel a useful representation that will\nmodel a useful representation that will make<00:06:45.520> um<00:06:45.760> predictions<00:06:46.520> on<00:06:46.840> downstream\nmake um predictions on downstream\nmake um predictions on downstream settings.<00:06:48.280> Um<00:06:48.640> it<00:06:49.000> has<00:06:49.840> uh<00:06:50.120> a<00:06:50.240> fair<00:06:50.480> amount<00:06:50.840> of\nsettings. Um it has uh a fair amount of\nsettings. Um it has uh a fair amount of structural<00:06:51.440> information<00:06:52.000> content<00:06:52.680> and<00:06:53.080> a\nstructural information content and a\nstructural information content and a little<00:06:53.360> bit<00:06:53.520> of<00:06:53.640> noise.<00:06:54.600> And<00:06:55.000> in<00:06:55.320> the<00:06:55.440> bottom\nlittle bit of noise. And in the bottom\nlittle bit of noise. And in the bottom row,<00:06:56.280> we<00:06:56.520> have<00:06:57.040> uh<00:06:57.280> just<00:06:57.600> white<00:06:57.920> noise,<00:06:58.440> which\nrow, we have uh just white noise, which\nrow, we have uh just white noise, which is<00:06:59.160> also<00:06:59.720> quite<00:07:00.080> incompressible,<00:07:01.280> but<00:07:01.480> it's\nis also quite incompressible, but it's\nis also quite incompressible, but it's not<00:07:01.840> going<00:07:01.960> to<00:07:02.040> teach<00:07:02.560> our<00:07:02.720> data<00:07:03.400> our<00:07:03.560> model\nnot going to teach our data our model\nnot going to teach our data our model anything<00:07:04.440> very<00:07:04.720> useful.<00:07:05.560> And<00:07:05.800> so,<00:07:05.960> this<00:07:06.160> has\nanything very useful. And so, this has\nanything very useful. And so, this has very<00:07:06.960> low<00:07:07.240> structural<00:07:07.760> information<00:07:08.360> content,\nvery low structural information content,\nvery low structural information content, um<00:07:09.880> but<00:07:10.480> uh<00:07:10.560> high<00:07:10.760> random<00:07:11.160> information\num but uh high random information\num but uh high random information content.<00:07:12.360> And<00:07:12.680> similarly,<00:07:13.200> in<00:07:13.320> this<00:07:13.480> code\ncontent. And similarly, in this code\ncontent. And similarly, in this code block,<00:07:14.080> we<00:07:14.160> just<00:07:14.400> have<00:07:14.560> sort<00:07:14.760> of<00:07:14.880> like<00:07:15.080> random\nblock, we just have sort of like random\nblock, we just have sort of like random hashes<00:07:15.840> and<00:07:15.960> things<00:07:16.160> like<00:07:16.360> this.<00:07:16.600> You\nhashes and things like this. You\nhashes and things like this. You basically<00:07:17.080> have<00:07:17.240> to<00:07:17.360> memorize<00:07:18.160> the<00:07:18.240> data.\nbasically have to memorize the data.\nbasically have to memorize the data. There<00:07:18.800> isn't<00:07:19.360> much<00:07:19.600> structure<00:07:20.040> that<00:07:20.200> we<00:07:20.320> can\nThere isn't much structure that we can\nThere isn't much structure that we can extract<00:07:20.960> from<00:07:21.120> that.<00:07:21.840> Um<00:07:22.200> Mark<00:07:22.520> is<00:07:22.640> going<00:07:22.760> to\nextract from that. Um Mark is going to\nextract from that. Um Mark is going to be<00:07:23.320> introducing<00:07:23.920> epiplexity<00:07:25.000> formally,<00:07:25.480> but\nbe introducing epiplexity formally, but\nbe introducing epiplexity formally, but just<00:07:26.000> as<00:07:26.320> like<00:07:26.640> a<00:07:26.720> teaser,<00:07:27.720> um<00:07:27.960> you<00:07:28.160> can\njust as like a teaser, um you can\njust as like a teaser, um you can heuristically<00:07:29.320> approximate<00:07:30.080> epiplexity<00:07:30.960> as\nheuristically approximate epiplexity as\nheuristically approximate epiplexity as the<00:07:31.320> area<00:07:31.760> under<00:07:32.040> the<00:07:32.760> uh<00:07:32.880> training<00:07:33.240> loss\nthe area under the uh training loss\nthe area under the uh training loss curve<00:07:33.840> above<00:07:34.200> the<00:07:34.320> final<00:07:34.680> value<00:07:35.200> of<00:07:35.400> the<00:07:35.520> loss.\ncurve above the final value of the loss.\ncurve above the final value of the loss. And<00:07:36.440> so,<00:07:36.560> we<00:07:36.680> can<00:07:36.840> see<00:07:36.960> this<00:07:37.120> first<00:07:37.320> system<00:07:37.600> is\nAnd so, we can see this first system is\nAnd so, we can see this first system is very<00:07:37.920> learnable,<00:07:38.520> but<00:07:38.680> there<00:07:38.800> isn't<00:07:39.040> very\nvery learnable, but there isn't very\nvery learnable, but there isn't very much<00:07:39.360> structure.<00:07:39.760> It<00:07:39.840> actually<00:07:40.080> has<00:07:40.240> low\nmuch structure. It actually has low\nmuch structure. It actually has low epiplexity<00:07:41.040> and<00:07:41.120> it<00:07:41.200> has<00:07:41.400> low<00:07:42.000> time-bounded\nepiplexity and it has low time-bounded\nepiplexity and it has low time-bounded entropy,<00:07:43.680> um<00:07:43.760> which<00:07:43.960> is<00:07:44.120> sort<00:07:44.280> of<00:07:44.440> what<00:07:44.760> is\nentropy, um which is sort of what is\nentropy, um which is sort of what is random<00:07:45.360> from<00:07:45.560> the<00:07:45.680> perspective<00:07:46.200> of<00:07:46.280> the\nrandom from the perspective of the\nrandom from the perspective of the model.<00:07:47.200> This<00:07:47.440> system<00:07:47.960> has<00:07:48.320> moderate\nmodel. This system has moderate\nmodel. This system has moderate epiplexity<00:07:49.720> and<00:07:50.280> relatively<00:07:50.800> low\nepiplexity and relatively low\nepiplexity and relatively low time-bounded<00:07:51.600> entropy.<00:07:52.400> And<00:07:52.520> this<00:07:52.680> bottom\ntime-bounded entropy. And this bottom\ntime-bounded entropy. And this bottom system<00:07:53.480> is<00:07:54.200> pretty<00:07:54.400> much<00:07:54.680> all<00:07:54.920> entropy<00:07:55.520> and<00:07:55.880> no\nsystem is pretty much all entropy and no\nsystem is pretty much all entropy and no epiplexity.\nepiplexity.\nepiplexity. Okay.<00:07:58.840> So,\nOkay. So,\nOkay. So, we<00:08:00.520> also<00:08:00.960> became<00:08:01.520> interested<00:08:02.320> in<00:08:02.560> some<00:08:02.800> of\nwe also became interested in some of\nwe also became interested in some of these<00:08:03.680> types<00:08:04.000> of<00:08:04.120> questions<00:08:04.760> because<00:08:05.880> in<00:08:06.040> our\nthese types of questions because in our\nthese types of questions because in our group,<00:08:06.760> we<00:08:06.960> had<00:08:07.160> observed<00:08:07.840> that<00:08:08.560> certain\ngroup, we had observed that certain\ngroup, we had observed that certain modalities<00:08:09.520> of<00:08:09.680> data<00:08:10.080> led<00:08:10.360> to\nmodalities of data led to\nmodalities of data led to representations<00:08:11.560> that<00:08:11.800> were<00:08:12.320> much<00:08:12.560> more\nrepresentations that were much more\nrepresentations that were much more transferable<00:08:13.440> than<00:08:13.680> others.<00:08:14.160> So,<00:08:14.840> uh<00:08:14.920> we<00:08:15.080> had\ntransferable than others. So, uh we had\ntransferable than others. So, uh we had this<00:08:15.480> paper<00:08:15.880> which<00:08:16.120> was<00:08:16.360> co-led<00:08:16.760> by<00:08:16.960> Mark\nthis paper which was co-led by Mark\nthis paper which was co-led by Mark called<00:08:17.960> LLM<00:08:18.400> time,<00:08:18.920> uh<00:08:19.000> large<00:08:19.280> language\ncalled LLM time, uh large language\ncalled LLM time, uh large language models<00:08:19.920> are<00:08:20.000> zero-shot<00:08:20.520> time<00:08:20.760> series\nmodels are zero-shot time series\nmodels are zero-shot time series forecasters.<00:08:22.320> Um<00:08:22.480> and<00:08:22.640> there<00:08:22.880> we<00:08:23.000> just<00:08:23.280> took\nforecasters. Um and there we just took\nforecasters. Um and there we just took an<00:08:24.200> LLM<00:08:24.640> that<00:08:24.840> had<00:08:24.960> been<00:08:25.200> pretrained<00:08:26.000> on<00:08:26.240> next\nan LLM that had been pretrained on next\nan LLM that had been pretrained on next word<00:08:26.600> prediction<00:08:27.160> off<00:08:27.400> the<00:08:27.480> shelf<00:08:28.000> and<00:08:28.160> then\nword prediction off the shelf and then\nword prediction off the shelf and then fed<00:08:28.600> it<00:08:29.080> string<00:08:29.400> token<00:08:30.000> Sorry,<00:08:30.280> uh<00:08:30.400> numbers<00:08:31.080> uh\nfed it string token Sorry, uh numbers uh\nfed it string token Sorry, uh numbers uh in<00:08:31.320> time<00:08:31.600> series<00:08:32.320> uh<00:08:32.440> naively<00:08:32.880> represented<00:08:33.479> as\nin time series uh naively represented as\nin time series uh naively represented as string<00:08:33.840> tokens<00:08:34.800> and<00:08:35.159> had<00:08:35.320> it<00:08:35.479> extrapolate\nstring tokens and had it extrapolate\nstring tokens and had it extrapolate like<00:08:36.320> the<00:08:36.400> next<00:08:36.599> sequence<00:08:37.000> of<00:08:37.080> string<00:08:37.320> tokens.\nlike the next sequence of string tokens.\nlike the next sequence of string tokens. And<00:08:38.479> in<00:08:38.640> some<00:08:38.800> cases,<00:08:39.280> this<00:08:39.479> could<00:08:39.680> work<00:08:40.039> as\nAnd in some cases, this could work as\nAnd in some cases, this could work as well<00:08:40.479> or<00:08:40.599> better<00:08:40.960> than<00:08:41.200> purpose-built<00:08:41.880> time\nwell or better than purpose-built time\nwell or better than purpose-built time series<00:08:42.479> models<00:08:42.840> that<00:08:43.000> had<00:08:43.120> specifically<00:08:44.120> been\nseries models that had specifically been\nseries models that had specifically been trained<00:08:44.760> on<00:08:45.000> this<00:08:45.120> time<00:08:45.360> series<00:08:45.680> data.<00:08:46.080> So,\ntrained on this time series data. So,\ntrained on this time series data. So, this<00:08:46.440> is<00:08:46.600> just<00:08:47.080> taking<00:08:47.400> a<00:08:47.440> next<00:08:47.680> word\nthis is just taking a next word\nthis is just taking a next word predictor,<00:08:48.280> completely<00:08:48.800> freezing<00:08:49.240> its\npredictor, completely freezing its\npredictor, completely freezing its representation,<00:08:50.120> and<00:08:50.240> having<00:08:50.560> it<00:08:51.040> make\nrepresentation, and having it make\nrepresentation, and having it make predictions<00:08:51.680> on<00:08:51.800> time<00:08:52.040> series<00:08:52.320> in<00:08:52.440> a\npredictions on time series in a\npredictions on time series in a zero-shot<00:08:52.960> setting.<00:08:53.200> It<00:08:53.320> can<00:08:53.400> do<00:08:53.480> that<00:08:53.600> quite\nzero-shot setting. It can do that quite\nzero-shot setting. It can do that quite well.<00:08:54.320> This<00:08:54.480> was<00:08:54.640> very<00:08:54.840> surprising.<00:08:55.920> Uh<00:08:56.120> we\nwell. This was very surprising. Uh we\nwell. This was very surprising. Uh we had<00:08:56.440> a<00:08:56.480> similar<00:08:56.880> result<00:08:57.360> in<00:08:57.520> a<00:08:57.600> different\nhad a similar result in a different\nhad a similar result in a different paper<00:08:58.440> on<00:08:58.640> generating<00:08:59.160> stable<00:08:59.600> inorganic\npaper on generating stable inorganic\npaper on generating stable inorganic crystals,<00:09:01.240> where<00:09:01.560> text-based<00:09:02.120> pretraining\ncrystals, where text-based pretraining\ncrystals, where text-based pretraining again<00:09:03.120> seemed<00:09:03.360> to<00:09:03.480> be<00:09:03.720> an<00:09:03.920> indispensable<00:09:04.720> part\nagain seemed to be an indispensable part\nagain seemed to be an indispensable part of<00:09:05.200> the<00:09:05.360> pipeline.<00:09:06.360> And<00:09:07.240> um<00:09:07.480> this<00:09:07.680> was<00:09:07.840> also\nof the pipeline. And um this was also\nof the pipeline. And um this was also kind<00:09:08.440> of<00:09:08.720> surprising.<00:09:09.800> Um<00:09:10.000> and<00:09:10.120> then<00:09:10.240> there\nkind of surprising. Um and then there\nkind of surprising. Um and then there are<00:09:10.640> neural<00:09:11.000> cellular<00:09:11.560> automata,<00:09:12.360> and<00:09:12.560> we'll\nare neural cellular automata, and we'll\nare neural cellular automata, and we'll be<00:09:12.800> talking<00:09:13.160> about<00:09:13.440> this<00:09:13.680> a<00:09:13.760> fair<00:09:13.920> bit<00:09:14.080> more<00:09:14.280> in\nbe talking about this a fair bit more in\nbe talking about this a fair bit more in a<00:09:14.440> moment,<00:09:15.240> um<00:09:15.600> which<00:09:16.440> uh<00:09:16.800> tend<00:09:17.040> to<00:09:17.120> be<00:09:17.280> useful\na moment, um which uh tend to be useful\na moment, um which uh tend to be useful for<00:09:17.880> quite<00:09:18.200> a<00:09:18.280> wide<00:09:18.600> array<00:09:19.040> of<00:09:19.440> understanding\nfor quite a wide array of understanding\nfor quite a wide array of understanding different<00:09:20.480> modalities<00:09:21.040> of<00:09:21.160> data<00:09:21.480> and\ndifferent modalities of data and\ndifferent modalities of data and different<00:09:21.840> types<00:09:22.120> of<00:09:22.240> problems.<00:09:22.880> And<00:09:23.080> so,\ndifferent types of problems. And so,\ndifferent types of problems. And so, there's<00:09:23.800> this<00:09:24.000> question<00:09:24.400> of<00:09:24.560> why<00:09:24.760> language\nthere's this question of why language\nthere's this question of why language data<00:09:25.520> and<00:09:25.680> other<00:09:25.880> types<00:09:26.160> of<00:09:26.320> data<00:09:27.280> can<00:09:27.440> be\ndata and other types of data can be\ndata and other types of data can be particularly<00:09:28.160> transferable,<00:09:28.960> whereas<00:09:29.400> like\nparticularly transferable, whereas like\nparticularly transferable, whereas like some<00:09:29.760> modalities<00:09:30.360> of<00:09:30.480> data<00:09:30.960> are<00:09:31.280> not<00:09:31.520> nearly\nsome modalities of data are not nearly\nsome modalities of data are not nearly as<00:09:32.160> transferable.<00:09:33.360> And<00:09:33.600> so,<00:09:34.000> what<00:09:34.240> is<00:09:34.400> it\nas transferable. And so, what is it\nas transferable. And so, what is it about<00:09:34.840> that<00:09:35.120> data<00:09:35.840> that<00:09:36.040> leads<00:09:36.280> the<00:09:36.360> model<00:09:36.760> to\nabout that data that leads the model to\nabout that data that leads the model to have<00:09:37.160> a<00:09:37.240> relatively<00:09:37.920> general\nhave a relatively general\nhave a relatively general representation?<00:09:39.600> And<00:09:39.760> how<00:09:39.920> should<00:09:40.120> we<00:09:40.240> be\nrepresentation? And how should we be\nrepresentation? And how should we be thinking<00:09:40.840> about<00:09:41.360> OOD<00:09:42.080> generalization<00:09:43.000> and\nthinking about OOD generalization and\nthinking about OOD generalization and data<00:09:43.480> selection<00:09:44.000> towards<00:09:44.680> OOD\ndata selection towards OOD\ndata selection towards OOD generalization?<00:09:46.480> And<00:09:46.640> so,<00:09:47.040> just<00:09:47.240> to<00:09:47.360> step\ngeneralization? And so, just to step\ngeneralization? And so, just to step back<00:09:47.840> a<00:09:47.880> little<00:09:48.120> bit,<00:09:48.640> uh<00:09:48.760> as<00:09:48.920> a<00:09:48.960> bit<00:09:49.080> of\nback a little bit, uh as a bit of\nback a little bit, uh as a bit of background,<00:09:50.200> there<00:09:50.480> are<00:09:50.880> many<00:09:51.120> different\nbackground, there are many different\nbackground, there are many different measures<00:09:52.360> of<00:09:52.640> information<00:09:53.320> and<00:09:53.480> theories<00:09:53.840> of\nmeasures of information and theories of\nmeasures of information and theories of information.<00:09:54.640> So,<00:09:54.800> there's<00:09:55.040> classical\ninformation. So, there's classical\ninformation. So, there's classical Shannon<00:09:55.840> information<00:09:56.400> theory<00:09:56.720> where\nShannon information theory where\nShannon information theory where information<00:09:57.360> is<00:09:57.520> the<00:09:57.640> surprisal<00:09:58.240> in<00:09:58.360> seeing\ninformation is the surprisal in seeing\ninformation is the surprisal in seeing the<00:09:58.680> value<00:09:59.000> of<00:09:59.080> a<00:09:59.120> random<00:09:59.440> variable.<00:10:00.320> There's\nthe value of a random variable. There's\nthe value of a random variable. There's also<00:10:00.880> algorithmic<00:10:01.440> information<00:10:02.000> theory,\nalso algorithmic information theory,\nalso algorithmic information theory, which<00:10:02.560> applies<00:10:02.960> to<00:10:03.120> non-random<00:10:03.680> variables\nwhich applies to non-random variables\nwhich applies to non-random variables and<00:10:04.800> often<00:10:05.040> measures<00:10:05.400> incompressibility<00:10:06.400> of\nand often measures incompressibility of\nand often measures incompressibility of data<00:10:07.240> through<00:10:07.480> things<00:10:07.720> like<00:10:07.920> Kolmogorov\ndata through things like Kolmogorov\ndata through things like Kolmogorov complexity.\ncomplexity.\ncomplexity. Uh<00:10:09.800> intuitively,<00:10:10.760> uh<00:10:10.960> useful<00:10:11.280> information\nUh intuitively, uh useful information\nUh intuitively, uh useful information ought<00:10:12.520> to<00:10:12.600> reduce<00:10:12.960> uncertainty<00:10:13.720> in<00:10:13.920> our\nought to reduce uncertainty in our\nought to reduce uncertainty in our predictions.\npredictions.\npredictions. So,<00:10:16.680> just<00:10:16.880> to<00:10:17.000> expand<00:10:17.360> a<00:10:17.400> little<00:10:17.560> bit<00:10:17.720> more,<00:10:18.280> so\nSo, just to expand a little bit more, so\nSo, just to expand a little bit more, so Shannon<00:10:18.800> information<00:10:19.960> is<00:10:20.240> represented<00:10:21.160> as\nShannon information is represented as\nShannon information is represented as log<00:10:21.880> base<00:10:22.240> two<00:10:22.760> of<00:10:23.000> one<00:10:23.200> over<00:10:23.760> the<00:10:23.880> probability\nlog base two of one over the probability\nlog base two of one over the probability distribution<00:10:25.440> associated<00:10:26.000> with<00:10:26.120> the<00:10:26.200> random\ndistribution associated with the random\ndistribution associated with the random variable<00:10:26.960> that<00:10:27.120> we're<00:10:27.240> considering.<00:10:28.040> This<00:10:28.200> is\nvariable that we're considering. This is\nvariable that we're considering. This is considered<00:10:28.800> the<00:10:28.920> surprisal<00:10:29.600> in<00:10:29.760> observing<00:10:30.800> uh\nconsidered the surprisal in observing uh\nconsidered the surprisal in observing uh the<00:10:31.600> value<00:10:31.920> of<00:10:32.000> this<00:10:32.160> random<00:10:32.440> variable<00:10:32.920> X.<00:10:33.680> The\nthe value of this random variable X. The\nthe value of this random variable X. The Shannon<00:10:34.280> entropy<00:10:34.720> is<00:10:34.920> the<00:10:35.120> average\nShannon entropy is the average\nShannon entropy is the average information<00:10:36.000> content<00:10:36.560> in<00:10:36.840> X,<00:10:37.600> and<00:10:37.840> the<00:10:37.920> mutual\ninformation content in X, and the mutual\ninformation content in X, and the mutual information<00:10:39.000> is<00:10:39.760> our<00:10:40.160> uncertainty<00:10:41.080> in<00:10:41.360> X\ninformation is our uncertainty in X\ninformation is our uncertainty in X after<00:10:42.080> our<00:10:42.600> the<00:10:42.680> reduction<00:10:43.160> in<00:10:43.240> our\nafter our the reduction in our\nafter our the reduction in our uncertainty<00:10:43.840> in<00:10:43.960> X<00:10:44.120> after<00:10:44.360> we<00:10:44.480> observe<00:10:45.040> Y.\nuncertainty in X after we observe Y.\nuncertainty in X after we observe Y. So,<00:10:46.760> Shannon<00:10:47.120> information<00:10:47.720> has<00:10:47.920> several\nSo, Shannon information has several\nSo, Shannon information has several really<00:10:48.560> key<00:10:48.840> properties.<00:10:49.480> Symmetry<00:10:49.920> of\nreally key properties. Symmetry of\nreally key properties. Symmetry of information,<00:10:50.760> so<00:10:50.880> this<00:10:51.040> is<00:10:51.200> related<00:10:51.600> to<00:10:51.680> that\ninformation, so this is related to that\ninformation, so this is related to that second<00:10:52.200> paradox<00:10:52.720> I<00:10:52.800> mentioned.<00:10:53.520> The\nsecond paradox I mentioned. The\nsecond paradox I mentioned. The information<00:10:54.080> that<00:10:54.200> we<00:10:54.320> get<00:10:54.640> in<00:10:55.120> predicting<00:10:55.520> X\ninformation that we get in predicting X\ninformation that we get in predicting X from<00:10:56.040> from<00:10:56.240> Y<00:10:56.520> is<00:10:56.680> the<00:10:56.760> same<00:10:56.960> as<00:10:57.080> predicting<00:10:57.440> Y\nfrom from Y is the same as predicting Y\nfrom from Y is the same as predicting Y from<00:10:58.320> X.<00:10:58.880> Um<00:10:59.400> deterministic<00:11:00.040> transformations\nfrom X. Um deterministic transformations\nfrom X. Um deterministic transformations don't<00:11:01.120> add<00:11:01.360> information,<00:11:01.920> so<00:11:02.080> if<00:11:02.200> we<00:11:02.320> have<00:11:02.880> a\ndon't add information, so if we have a\ndon't add information, so if we have a deterministic<00:11:03.560> transformation<00:11:04.240> F<00:11:04.520> operating\ndeterministic transformation F operating\ndeterministic transformation F operating on<00:11:05.160> X<00:11:05.400> to<00:11:05.480> give<00:11:05.640> us<00:11:05.800> Y,<00:11:06.360> the<00:11:06.480> entropy<00:11:06.880> of<00:11:07.000> Y\non X to give us Y, the entropy of Y\non X to give us Y, the entropy of Y given<00:11:07.480> X<00:11:07.680> is<00:11:08.000> zero,<00:11:08.560> and<00:11:08.920> as<00:11:09.080> a<00:11:09.120> corollary,<00:11:09.640> the\ngiven X is zero, and as a corollary, the\ngiven X is zero, and as a corollary, the entropy<00:11:10.560> of<00:11:10.680> f<00:11:10.800> of<00:11:10.920> X<00:11:11.160> is<00:11:11.400> always<00:11:11.680> less<00:11:11.839> than<00:11:11.960> or\nentropy of f of X is always less than or\nentropy of f of X is always less than or equal<00:11:12.400> to<00:11:12.680> the<00:11:12.760> entropy<00:11:13.120> of<00:11:13.280> X.<00:11:13.920> And<00:11:14.080> related\nequal to the entropy of X. And related\nequal to the entropy of X. And related to<00:11:14.560> that,<00:11:14.839> we<00:11:14.960> have<00:11:15.120> something<00:11:15.440> called<00:11:15.640> the\nto that, we have something called the\nto that, we have something called the data<00:11:16.080> processing<00:11:16.640> inequality.<00:11:17.520> If<00:11:17.720> Y<00:11:17.920> is\ndata processing inequality. If Y is\ndata processing inequality. If Y is obtained<00:11:18.520> from<00:11:18.760> X<00:11:18.960> through<00:11:19.160> some<00:11:19.400> processing,\nobtained from X through some processing,\nobtained from X through some processing, like<00:11:21.000> a<00:11:21.040> deterministic<00:11:21.600> transformation,<00:11:22.240> but\nlike a deterministic transformation, but\nlike a deterministic transformation, but not<00:11:22.560> necessarily,<00:11:23.600> and<00:11:23.760> similarly,<00:11:24.360> Z\nnot necessarily, and similarly, Z\nnot necessarily, and similarly, Z through<00:11:24.920> Y,<00:11:25.560> then<00:11:25.760> the<00:11:25.839> mutual<00:11:26.200> information\nthrough Y, then the mutual information\nthrough Y, then the mutual information between<00:11:27.200> X<00:11:27.440> and<00:11:27.560> Z<00:11:27.800> is<00:11:28.000> less<00:11:28.200> than<00:11:28.320> or<00:11:28.400> equal<00:11:28.800> to\nbetween X and Z is less than or equal to\nbetween X and Z is less than or equal to the<00:11:29.120> mutual<00:11:29.400> information<00:11:29.880> between<00:11:30.400> X<00:11:30.760> and<00:11:31.160> Y.\nthe mutual information between X and Y.\nthe mutual information between X and Y. Uh<00:11:32.400> objects<00:11:32.800> which<00:11:33.120> aren't<00:11:33.400> random<00:11:34.320> um<00:11:34.600> don't\nUh objects which aren't random um don't\nUh objects which aren't random um don't have<00:11:35.120> information<00:11:35.760> from<00:11:36.400> uh<00:11:36.560> the<00:11:36.680> perspective\nhave information from uh the perspective\nhave information from uh the perspective of<00:11:37.480> classical<00:11:37.960> Shannon<00:11:38.240> information<00:11:38.760> theory.\nof classical Shannon information theory.\nof classical Shannon information theory. This<00:11:39.560> is<00:11:39.680> different<00:11:40.040> than<00:11:40.360> algorithmic\nThis is different than algorithmic\nThis is different than algorithmic information<00:11:41.480> theory,<00:11:41.839> which<00:11:42.640> studies<00:11:43.120> the\ninformation theory, which studies the\ninformation theory, which studies the information<00:11:43.920> content<00:11:44.520> of<00:11:44.800> any<00:11:45.080> object,\ninformation content of any object,\ninformation content of any object, doesn't<00:11:45.839> have<00:11:46.000> to<00:11:46.080> be<00:11:46.200> random.\ndoesn't have to be random.\ndoesn't have to be random. In<00:11:47.839> algorithmic<00:11:48.280> information<00:11:48.800> theory,<00:11:49.120> the\nIn algorithmic information theory, the\nIn algorithmic information theory, the prefix<00:11:49.880> Kolmogorov<00:11:50.360> complexity<00:11:51.200> of<00:11:51.480> some\nprefix Kolmogorov complexity of some\nprefix Kolmogorov complexity of some object<00:11:52.120> X<00:11:52.839> is<00:11:53.160> the<00:11:53.280> shortest<00:11:53.920> self-delimiting\nobject X is the shortest self-delimiting\nobject X is the shortest self-delimiting program<00:11:55.360> that<00:11:55.560> outputs<00:11:56.040> X<00:11:56.360> and<00:11:56.560> then<00:11:56.920> halts.\nprogram that outputs X and then halts.\nprogram that outputs X and then halts. There's<00:11:58.240> also<00:11:58.520> a<00:11:58.600> similar<00:11:59.240> symmetry<00:11:59.680> of\nThere's also a similar symmetry of\nThere's also a similar symmetry of information<00:12:00.560> in\ninformation in\ninformation in algorithmic<00:12:02.680> information<00:12:03.240> theory<00:12:03.600> and<00:12:03.760> also\nalgorithmic information theory and also\nalgorithmic information theory and also an<00:12:04.120> information<00:12:05.040> non-increase<00:12:05.880> property\nan information non-increase property\nan information non-increase property through<00:12:06.680> deterministic<00:12:07.360> transformations<00:12:08.120> F.\nthrough deterministic transformations F.\nthrough deterministic transformations F. Like<00:12:09.400> Shannon<00:12:09.760> information,\nLike Shannon information,\nLike Shannon information, Kolmogorov<00:12:12.240> complexity<00:12:12.920> is<00:12:13.120> an<00:12:13.280> absolute\nKolmogorov complexity is an absolute\nKolmogorov complexity is an absolute measure<00:12:14.000> of<00:12:14.200> information<00:12:15.240> and<00:12:15.600> doesn't\nmeasure of information and doesn't\nmeasure of information and doesn't separate<00:12:17.120> useful<00:12:17.600> structure<00:12:18.080> from\nseparate useful structure from\nseparate useful structure from unpredictable<00:12:19.040> structure,<00:12:19.480> like<00:12:19.640> we<00:12:19.760> were\nunpredictable structure, like we were\nunpredictable structure, like we were considering<00:12:20.440> with<00:12:20.560> some<00:12:20.720> of<00:12:20.800> those<00:12:21.000> examples\nconsidering with some of those examples\nconsidering with some of those examples earlier<00:12:21.880> with<00:12:22.040> the<00:12:22.120> natural<00:12:22.520> images<00:12:23.040> and<00:12:23.280> and\nearlier with the natural images and and\nearlier with the natural images and and white<00:12:23.640> noise.<00:12:24.480> It's<00:12:24.640> incomputable.<00:12:25.839> Uh<00:12:26.000> we\nwhite noise. It's incomputable. Uh we\nwhite noise. It's incomputable. Uh we don't<00:12:26.320> know<00:12:26.440> what<00:12:26.600> the<00:12:26.680> shortest<00:12:27.040> program<00:12:27.440> is,\ndon't know what the shortest program is,\ndon't know what the shortest program is, but<00:12:28.320> it<00:12:28.440> can<00:12:28.560> be<00:12:28.680> upper<00:12:28.880> bounded<00:12:29.320> and<00:12:29.400> it<00:12:29.480> can\nbut it can be upper bounded and it can\nbut it can be upper bounded and it can still<00:12:29.760> be<00:12:29.880> very<00:12:30.120> useful.<00:12:30.480> And<00:12:30.600> so,<00:12:30.760> we<00:12:30.920> found\nstill be very useful. And so, we found\nstill be very useful. And so, we found Kolmogorov<00:12:31.600> complexity<00:12:32.600> very<00:12:33.120> useful<00:12:33.520> as<00:12:33.680> a\nKolmogorov complexity very useful as a\nKolmogorov complexity very useful as a concept<00:12:34.480> in<00:12:34.640> formulating<00:12:35.320> generalization\nconcept in formulating generalization\nconcept in formulating generalization bounds<00:12:36.400> for<00:12:36.520> large<00:12:36.920> neural<00:12:37.120> networks.\nThere's<00:12:40.320> um<00:12:40.760> a<00:12:41.120> a<00:12:41.200> a<00:12:41.240> slightly<00:12:41.920> less\nThere's um a a a slightly less\nThere's um a a a slightly less well-known<00:12:42.760> concept<00:12:43.240> called<00:12:43.480> sophistication\nwell-known concept called sophistication\nwell-known concept called sophistication in<00:12:44.600> algorithmic<00:12:45.280> information<00:12:45.839> theory,<00:12:46.120> which\nin algorithmic information theory, which\nin algorithmic information theory, which is<00:12:46.600> the<00:12:46.800> smallest<00:12:47.320> Kolmogorov<00:12:47.800> complexity<00:12:48.440> of\nis the smallest Kolmogorov complexity of\nis the smallest Kolmogorov complexity of a<00:12:48.640> set<00:12:49.000> S<00:12:49.240> such<00:12:49.480> that<00:12:49.640> X<00:12:49.839> is<00:12:50.000> a<00:12:50.040> random<00:12:50.400> element\na set S such that X is a random element\na set S such that X is a random element from<00:12:50.920> that<00:12:51.120> set.<00:12:51.680> This<00:12:51.880> does<00:12:52.080> try<00:12:52.320> to<00:12:52.440> carve\nfrom that set. This does try to carve\nfrom that set. This does try to carve out<00:12:53.520> uh<00:12:54.040> structural<00:12:54.680> information<00:12:55.280> content\nout uh structural information content\nout uh structural information content from<00:12:56.040> random<00:12:56.360> information,<00:12:57.320> but<00:12:57.640> it's\nfrom random information, but it's\nfrom random information, but it's difficult<00:12:58.280> to<00:12:58.400> find<00:12:59.080> high<00:12:59.280> sophistication\ndifficult to find high sophistication\ndifficult to find high sophistication objects<00:13:01.120> due<00:13:01.320> to<00:13:01.680> Shannon's<00:13:02.120> incompleteness\nobjects due to Shannon's incompleteness\nobjects due to Shannon's incompleteness theorem.\ntheorem.\ntheorem. And\nAnd\nAnd since<00:13:05.680> it<00:13:06.000> is<00:13:06.200> not<00:13:06.480> considering<00:13:06.960> computation,\nsince it is not considering computation,\nsince it is not considering computation, typically<00:13:08.440> complex<00:13:08.960> objects<00:13:09.480> often<00:13:09.800> appear\ntypically complex objects often appear\ntypically complex objects often appear to<00:13:10.400> lose<00:13:10.680> their<00:13:10.960> complexity<00:13:11.560> when<00:13:11.720> measured\nto lose their complexity when measured\nto lose their complexity when measured by<00:13:12.360> sophistication,<00:13:13.600> and<00:13:13.800> it's<00:13:13.960> actually<00:13:14.520> not\nby sophistication, and it's actually not\nby sophistication, and it's actually not trivial<00:13:15.280> to<00:13:15.720> make<00:13:15.960> sophistication\ntrivial to make sophistication\ntrivial to make sophistication time-bounded.<00:13:17.680> So,<00:13:17.839> in<00:13:17.920> the<00:13:18.040> paper,<00:13:18.360> we<00:13:18.480> show\ntime-bounded. So, in the paper, we show\ntime-bounded. So, in the paper, we show that<00:13:18.839> it<00:13:19.080> becomes<00:13:19.440> essentially<00:13:19.920> constant<00:13:20.320> for\nthat it becomes essentially constant for\nthat it becomes essentially constant for all<00:13:20.640> strings<00:13:21.400> when<00:13:21.560> you<00:13:21.640> try<00:13:21.800> to<00:13:21.960> do<00:13:22.120> that.\nall strings when you try to do that.\nall strings when you try to do that. Uh<00:13:23.280> so,<00:13:23.480> it's<00:13:24.200> our<00:13:24.360> belief<00:13:24.760> that<00:13:25.240> really\nUh so, it's our belief that really\nUh so, it's our belief that really understanding<00:13:26.040> the<00:13:26.120> role<00:13:26.280> of<00:13:26.360> computation<00:13:27.040> is\nunderstanding the role of computation is\nunderstanding the role of computation is central<00:13:27.760> to<00:13:28.120> understanding<00:13:29.080> these<00:13:29.280> phenomena\ncentral to understanding these phenomena\ncentral to understanding these phenomena like<00:13:30.360> emergence<00:13:31.080> and<00:13:31.440> induction,<00:13:32.240> chaos,\nlike emergence and induction, chaos,\nlike emergence and induction, chaos, cryptography.\ncryptography.\ncryptography. And<00:13:34.880> I<00:13:34.920> thought<00:13:35.280> I<00:13:35.480> had<00:13:35.800> to<00:13:35.880> mention<00:13:36.440> Levin\nAnd I thought I had to mention Levin\nAnd I thought I had to mention Levin complexity<00:13:37.400> because<00:13:37.880> this<00:13:38.080> is<00:13:38.200> the<00:13:38.320> Levin\ncomplexity because this is the Levin\ncomplexity because this is the Levin group<00:13:39.000> that<00:13:39.560> introduced<00:13:40.120> Levin<00:13:40.400> complexity.\ngroup that introduced Levin complexity.\ngroup that introduced Levin complexity. I'm<00:13:41.440> just<00:13:41.600> kidding,<00:13:41.920> I<00:13:42.080> I<00:13:42.200> don't<00:13:42.440> think<00:13:42.600> that.\nI'm just kidding, I I don't think that.\nI'm just kidding, I I don't think that. Um\nUm\nUm uh<00:13:44.400> so,<00:13:44.520> Levin<00:13:44.800> complexity<00:13:45.320> is<00:13:45.520> a\nuh so, Levin complexity is a\nuh so, Levin complexity is a compute-limited<00:13:46.320> notion<00:13:46.640> of<00:13:46.760> Kolmogorov\ncompute-limited notion of Kolmogorov\ncompute-limited notion of Kolmogorov complexity.<00:13:48.320> It's<00:13:48.520> concerned<00:13:49.080> with<00:13:49.560> how\ncomplexity. It's concerned with how\ncomplexity. It's concerned with how compactly<00:13:50.560> you<00:13:50.680> can<00:13:50.839> generate<00:13:51.240> one<00:13:51.400> specific\ncompactly you can generate one specific\ncompactly you can generate one specific output,<00:13:52.880> rather<00:13:53.120> than<00:13:53.320> what<00:13:53.440> can<00:13:53.560> be\noutput, rather than what can be\noutput, rather than what can be extracted<00:13:54.080> from<00:13:54.200> a<00:13:54.240> distribution.<00:13:55.440> Um<00:13:55.839> but<00:13:56.160> it\nextracted from a distribution. Um but it\nextracted from a distribution. Um but it really<00:13:56.600> doesn't<00:13:56.960> do<00:13:57.240> what<00:13:57.600> we're<00:13:57.800> looking<00:13:58.200> for\nreally doesn't do what we're looking for\nreally doesn't do what we're looking for in<00:13:59.040> appiplexity.<00:14:00.160> Um<00:14:00.400> for<00:14:00.520> example,\nin appiplexity. Um for example,\nin appiplexity. Um for example, pseudo-random<00:14:01.800> numbers<00:14:02.280> would<00:14:02.440> be<00:14:02.560> treated\npseudo-random numbers would be treated\npseudo-random numbers would be treated as<00:14:03.200> simple<00:14:03.680> by<00:14:04.040> Levin<00:14:04.320> complexity<00:14:04.880> because\nas simple by Levin complexity because\nas simple by Levin complexity because there<00:14:05.520> is<00:14:05.760> a<00:14:05.800> short<00:14:06.080> program<00:14:06.560> that<00:14:06.800> can\nthere is a short program that can\nthere is a short program that can generate<00:14:07.440> them.<00:14:07.640> You<00:14:07.720> just<00:14:08.000> run<00:14:08.520> your\ngenerate them. You just run your\ngenerate them. You just run your generator<00:14:09.240> on<00:14:09.480> some<00:14:09.680> seed,<00:14:10.480> um<00:14:10.839> and<00:14:11.360> uh<00:14:11.720> that\ngenerator on some seed, um and uh that\ngenerator on some seed, um and uh that can<00:14:12.040> be<00:14:12.120> done<00:14:12.320> in<00:14:12.440> a<00:14:12.480> very<00:14:12.640> short<00:14:12.880> amount<00:14:13.079> of\ncan be done in a very short amount of\ncan be done in a very short amount of time.<00:14:14.000> Um<00:14:14.760> and<00:14:15.440> uh\ntime. Um and uh\ntime. Um and uh this<00:14:16.720> is<00:14:16.880> really,<00:14:17.280> you<00:14:17.400> know,<00:14:17.640> a<00:14:17.680> distinction\nthis is really, you know, a distinction\nthis is really, you know, a distinction that<00:14:18.400> we're<00:14:18.880> focused<00:14:19.320> on<00:14:19.680> in<00:14:19.880> this<00:14:20.160> this<00:14:20.360> work.\nthat we're focused on in this this work.\nthat we're focused on in this this work. Okay,<00:14:21.959> and<00:14:22.280> finally,<00:14:22.920> uh\nOkay, and finally, uh\nOkay, and finally, uh uh<00:14:24.079> we<00:14:24.240> can<00:14:24.400> sort<00:14:24.600> of<00:14:25.240> consider<00:14:25.680> what<00:14:25.880> it\nuh we can sort of consider what it\nuh we can sort of consider what it actually<00:14:26.320> means<00:14:26.560> to<00:14:26.680> be<00:14:26.920> random.<00:14:27.360> This<00:14:27.560> has\nactually means to be random. This has\nactually means to be random. This has been<00:14:28.280> uh\nbeen uh\nbeen uh something<00:14:29.440> a<00:14:29.520> discussion<00:14:30.040> of<00:14:30.240> of<00:14:30.400> great\nsomething a discussion of of great\nsomething a discussion of of great interest<00:14:31.040> to<00:14:31.240> mathematicians<00:14:32.160> throughout\ninterest to mathematicians throughout\ninterest to mathematicians throughout the<00:14:32.560> 20th<00:14:32.920> century.<00:14:33.720> Uh<00:14:33.959> so,<00:14:34.240> a<00:14:34.320> random\nthe 20th century. Uh so, a random\nthe 20th century. Uh so, a random variable<00:14:34.959> is<00:14:35.040> defined<00:14:35.440> as<00:14:35.560> a<00:14:35.600> map<00:14:35.920> from<00:14:36.320> a\nvariable is defined as a map from a\nvariable is defined as a map from a measurable<00:14:36.800> probability<00:14:37.320> space<00:14:37.600> to\nmeasurable probability space to\nmeasurable probability space to different<00:14:38.000> outcomes<00:14:39.079> with<00:14:39.240> probabilities\ndifferent outcomes with probabilities\ndifferent outcomes with probabilities corresponding<00:14:40.240> to<00:14:40.320> the<00:14:40.400> measure<00:14:40.720> of<00:14:40.800> that\ncorresponding to the measure of that\ncorresponding to the measure of that space<00:14:41.280> that<00:14:41.440> lead<00:14:41.600> to<00:14:41.680> a<00:14:41.760> certain<00:14:42.040> outcome.<00:14:43.079> In\nspace that lead to a certain outcome. In\nspace that lead to a certain outcome. In uh<00:14:43.760> the<00:14:43.839> mid-20th<00:14:44.400> century,<00:14:44.800> there<00:14:45.000> was\nuh the mid-20th century, there was\nuh the mid-20th century, there was interest<00:14:45.880> in<00:14:46.480> precisely<00:14:46.959> formalizing<00:14:47.680> what\ninterest in precisely formalizing what\ninterest in precisely formalizing what it<00:14:47.920> means<00:14:48.160> for<00:14:48.280> a<00:14:48.320> sample<00:14:48.680> to<00:14:48.839> be<00:14:49.280> a<00:14:49.440> random\nit means for a sample to be a random\nit means for a sample to be a random draw<00:14:50.040> from<00:14:50.240> a<00:14:50.280> distribution,<00:14:51.440> and\ndraw from a distribution, and\ndraw from a distribution, and central<00:14:53.040> to<00:14:53.160> their<00:14:53.360> considerations<00:14:54.560> um<00:14:55.000> was\ncentral to their considerations um was\ncentral to their considerations um was uh\nuh\nuh uh<00:14:56.480> sort<00:14:56.640> of<00:14:56.760> having\nuh sort of having\nuh sort of having uh<00:14:58.120> large<00:14:59.120> uh<00:14:59.400> uniform<00:15:00.400> sequences<00:15:01.280> uh<00:15:01.600> uh<00:15:01.839> for\nuh large uh uniform sequences uh uh for\nuh large uh uniform sequences uh uh for for<00:15:02.240> binary<00:15:02.560> numbers<00:15:03.440> uh<00:15:03.640> from<00:15:03.800> which<00:15:03.959> we<00:15:04.040> can\nfor binary numbers uh from which we can\nfor binary numbers uh from which we can construct<00:15:04.720> other<00:15:05.040> distributions.<00:15:06.280> And<00:15:06.640> if<00:15:06.760> we\nconstruct other distributions. And if we\nconstruct other distributions. And if we think<00:15:07.040> about<00:15:07.280> these<00:15:07.480> sequences,<00:15:08.079> we<00:15:08.280> could\nthink about these sequences, we could\nthink about these sequences, we could ask<00:15:09.720> um<00:15:10.440> whether<00:15:11.200> all<00:15:11.400> of<00:15:11.440> these<00:15:11.600> sequences\nask um whether all of these sequences\nask um whether all of these sequences are<00:15:12.200> equally<00:15:12.520> random<00:15:12.880> since<00:15:13.079> they're<00:15:13.240> equally\nare equally random since they're equally\nare equally random since they're equally likely.<00:15:14.040> So,<00:15:14.160> we<00:15:14.280> could<00:15:14.440> have<00:15:14.560> a<00:15:14.640> sequence<00:15:15.079> of\nlikely. So, we could have a sequence of\nlikely. So, we could have a sequence of just<00:15:15.440> repeating<00:15:15.880> ones,<00:15:16.120> for<00:15:16.240> example,<00:15:17.040> versus\njust repeating ones, for example, versus\njust repeating ones, for example, versus a<00:15:17.560> sequence<00:15:18.040> that<00:15:18.280> looks<00:15:18.920> much<00:15:19.120> more\na sequence that looks much more\na sequence that looks much more unpredictable,<00:15:20.120> like<00:15:20.360> 1001110\nunpredictable, like 1001110\nunpredictable, like 1001110 and<00:15:22.079> so<00:15:22.200> on.<00:15:22.920> Um<00:15:23.360> and<00:15:23.640> so,<00:15:24.440> uh<00:15:24.600> these<00:15:24.760> two\nand so on. Um and so, uh these two\nand so on. Um and so, uh these two sequences<00:15:25.640> have<00:15:25.920> the<00:15:26.040> same<00:15:26.360> probability\nsequences have the same probability\nsequences have the same probability mass,<00:15:28.000> um<00:15:28.480> and<00:15:28.680> so,<00:15:28.839> in<00:15:28.959> some<00:15:29.200> sense,<00:15:29.760> it<00:15:29.959> might\nmass, um and so, in some sense, it might\nmass, um and so, in some sense, it might seem<00:15:30.440> like<00:15:30.680> they're<00:15:30.920> equally<00:15:31.400> random,<00:15:32.160> but\nseem like they're equally random, but\nseem like they're equally random, but intuitively,<00:15:33.200> the<00:15:33.360> first<00:15:33.640> sequence<00:15:34.320> doesn't\nintuitively, the first sequence doesn't\nintuitively, the first sequence doesn't seem<00:15:35.040> as<00:15:35.240> random<00:15:35.720> as<00:15:36.040> the<00:15:36.160> second.<00:15:36.959> And<00:15:37.200> so,<00:15:37.640> to\nseem as random as the second. And so, to\nseem as random as the second. And so, to get<00:15:37.959> some<00:15:38.120> intuition<00:15:38.560> about<00:15:38.839> this,<00:15:39.040> we<00:15:39.160> could\nget some intuition about this, we could\nget some intuition about this, we could start<00:15:39.640> to<00:15:39.720> compute<00:15:40.480> statistics<00:15:41.079> of<00:15:41.200> these\nstart to compute statistics of these\nstart to compute statistics of these sequences,<00:15:42.160> look<00:15:42.360> at<00:15:42.480> things<00:15:42.720> like<00:15:42.920> the<00:15:43.000> law\nsequences, look at things like the law\nsequences, look at things like the law of<00:15:43.440> large<00:15:43.720> numbers,<00:15:44.440> which<00:15:44.640> would<00:15:44.800> say<00:15:44.959> that\nof large numbers, which would say that\nof large numbers, which would say that the<00:15:45.400> average<00:15:45.760> entry<00:15:46.480> of<00:15:46.640> this<00:15:46.800> sequence\nthe average entry of this sequence\nthe average entry of this sequence should<00:15:47.440> be<00:15:47.760> a<00:15:47.880> half,<00:15:48.320> which<00:15:48.880> would<00:15:49.560> clearly\nshould be a half, which would clearly\nshould be a half, which would clearly not<00:15:50.040> apply<00:15:50.360> to<00:15:50.520> the<00:15:50.640> first<00:15:50.880> sequence.<00:15:51.760> And\nnot apply to the first sequence. And\nnot apply to the first sequence. And Martin-Löf<00:15:52.760> randomness<00:15:53.440> uh<00:15:53.560> formalizes<00:15:54.240> this\nMartin-Löf randomness uh formalizes this\nMartin-Löf randomness uh formalizes this idea<00:15:55.440> that<00:15:55.720> a<00:15:55.800> sequence<00:15:56.360> ought<00:15:56.600> to<00:15:56.720> pass<00:15:57.240> all\nidea that a sequence ought to pass all\nidea that a sequence ought to pass all computable<00:15:58.320> tests,<00:15:59.200> but<00:15:59.520> this<00:15:59.720> doesn't\ncomputable tests, but this doesn't\ncomputable tests, but this doesn't account<00:16:00.839> also<00:16:01.240> for<00:16:01.720> computation.<00:16:02.839> There's\naccount also for computation. There's\naccount also for computation. There's also<00:16:03.360> a<00:16:03.400> notion<00:16:03.760> of<00:16:03.880> cryptographic\nalso a notion of cryptographic\nalso a notion of cryptographic randomness<00:16:05.440> um<00:16:05.640> where<00:16:05.800> sequences<00:16:06.360> must<00:16:06.640> pass\nrandomness um where sequences must pass\nrandomness um where sequences must pass polynomial-time<00:16:08.520> randomness<00:16:09.000> tests.<00:16:09.480> And<00:16:09.600> I\npolynomial-time randomness tests. And I\npolynomial-time randomness tests. And I think<00:16:09.880> Mark<00:16:10.079> might<00:16:10.240> have<00:16:10.360> a<00:16:10.400> few<00:16:10.680> few<00:16:10.839> thoughts\nthink Mark might have a few few thoughts\nthink Mark might have a few few thoughts on<00:16:11.200> this<00:16:11.360> as<00:16:11.520> well.\non this as well.\non this as well. Yeah,<00:16:12.760> and<00:16:13.160> just<00:16:13.440> to<00:16:13.520> motivate<00:16:14.120> why\nYeah, and just to motivate why\nYeah, and just to motivate why we<00:16:15.680> want<00:16:15.839> to<00:16:15.880> make<00:16:16.079> this<00:16:16.240> change<00:16:16.600> from<00:16:17.120> uh<00:16:17.240> you\nwe want to make this change from uh you\nwe want to make this change from uh you know,<00:16:17.560> why<00:16:18.079> it's<00:16:18.320> a<00:16:18.360> useful<00:16:19.000> uh<00:16:19.079> change<00:16:19.280> to<00:16:19.400> go\nknow, why it's a useful uh change to go\nknow, why it's a useful uh change to go from<00:16:19.680> this<00:16:19.920> Martin-Löf<00:16:20.320> randomness,<00:16:20.839> which\nfrom this Martin-Löf randomness, which\nfrom this Martin-Löf randomness, which is<00:16:21.160> this<00:16:21.720> this<00:16:21.839> more<00:16:22.000> accepted<00:16:22.680> uh<00:16:23.120> definition\nis this this more accepted uh definition\nis this this more accepted uh definition of<00:16:23.821> [clears throat]<00:16:23.839> randomness,<00:16:24.280> to<00:16:24.400> the\nof [clears throat] randomness, to the\nof [clears throat] randomness, to the one<00:16:24.720> that<00:16:25.000> cryptographers<00:16:25.640> use.\none that cryptographers use.\none that cryptographers use. Um\nUm\nUm take,<00:16:28.120> for<00:16:28.240> example,\ntake, for example,\ntake, for example, uh<00:16:30.360> rock,<00:16:30.520> paper,<00:16:30.760> scissors,<00:16:31.240> all<00:16:31.320> right,\nuh rock, paper, scissors, all right,\nuh rock, paper, scissors, all right, game,<00:16:32.000> where<00:16:32.839> we<00:16:32.959> all<00:16:33.079> know<00:16:33.360> what<00:16:33.640> the<00:16:34.079> Nash\ngame, where we all know what the Nash\ngame, where we all know what the Nash equilibrium<00:16:34.800> strategy<00:16:35.200> is<00:16:35.640> of<00:16:36.520> uh\nequilibrium strategy is of uh\nequilibrium strategy is of uh predicting<00:16:38.040> rock,<00:16:38.280> paper,<00:16:38.480> and<00:16:38.600> scissors\npredicting rock, paper, and scissors\npredicting rock, paper, and scissors with<00:16:39.520> probability<00:16:40.040> each<00:16:40.320> 1/3.\nwith probability each 1/3.\nwith probability each 1/3. But<00:16:41.880> how<00:16:41.959> do<00:16:42.040> we<00:16:42.120> actually<00:16:42.360> implement<00:16:42.760> that\nBut how do we actually implement that\nBut how do we actually implement that strategy,<00:16:43.839> whether<00:16:44.040> it's<00:16:44.160> on<00:16:44.280> a<00:16:44.320> computer<00:16:45.040> or\nstrategy, whether it's on a computer or\nstrategy, whether it's on a computer or on<00:16:45.200> a<00:16:45.240> human?\non a human?\non a human? In<00:16:46.520> fact,<00:16:47.400> the<00:16:47.520> Martin-Löf<00:16:47.959> random\nIn fact, the Martin-Löf random\nIn fact, the Martin-Löf random sequences,<00:16:48.760> they're<00:16:49.000> all<00:16:49.320> incomputable.\nsequences, they're all incomputable.\nsequences, they're all incomputable. So,<00:16:51.280> there<00:16:51.440> must<00:16:51.640> be<00:16:51.760> no<00:16:52.040> computer<00:16:52.400> program\nSo, there must be no computer program\nSo, there must be no computer program that<00:16:53.560> outputs<00:16:54.120> a<00:16:54.200> Martin-Löf<00:16:54.600> random\nthat outputs a Martin-Löf random\nthat outputs a Martin-Löf random sequence.<00:16:55.680> So,<00:16:55.800> how<00:16:55.880> do<00:16:55.959> we<00:16:56.040> do<00:16:56.200> it?\nsequence. So, how do we do it?\nsequence. So, how do we do it? Of<00:16:57.720> course,\nOf course,\nOf course, uh\nuh\nuh turns<00:17:00.800> out<00:17:00.959> you<00:17:01.040> don't<00:17:01.240> need<00:17:02.120> a<00:17:02.320> truly\nturns out you don't need a truly\nturns out you don't need a truly Martin-Löf<00:17:03.600> random<00:17:03.839> sequence.\nMartin-Löf random sequence.\nMartin-Löf random sequence. You<00:17:05.079> just<00:17:05.240> need<00:17:05.400> something<00:17:05.760> that<00:17:05.920> will<00:17:06.079> fool\nYou just need something that will fool\nYou just need something that will fool your<00:17:06.679> adversary.\nyour adversary.\nyour adversary. And<00:17:08.199> then<00:17:08.360> this<00:17:08.640> also<00:17:08.959> becomes<00:17:09.320> relevant<00:17:09.839> in\nAnd then this also becomes relevant in\nAnd then this also becomes relevant in the<00:17:10.240> actual<00:17:10.560> playing<00:17:11.040> of\nthe actual playing of\nthe actual playing of say<00:17:12.240> rock,<00:17:12.439> paper,<00:17:12.679> scissors<00:17:13.199> in<00:17:13.480> the\nsay rock, paper, scissors in the\nsay rock, paper, scissors in the competitions,<00:17:14.720> where<00:17:15.199> people<00:17:15.439> try<00:17:15.640> very<00:17:15.839> hard\ncompetitions, where people try very hard\ncompetitions, where people try very hard to<00:17:16.600> be<00:17:16.760> random,<00:17:17.280> and<00:17:17.400> it's<00:17:17.520> a<00:17:17.560> difficult<00:17:17.920> thing\nto be random, and it's a difficult thing\nto be random, and it's a difficult thing to<00:17:18.560> be<00:17:18.679> random,<00:17:19.040> but<00:17:19.240> they<00:17:19.360> just<00:17:19.600> need<00:17:19.839> to<00:17:19.959> fool\nto be random, but they just need to fool\nto be random, but they just need to fool their<00:17:20.760> opponents.\ntheir opponents.\ntheir opponents. And<00:17:22.839> from<00:17:23.079> the<00:17:23.199> game<00:17:23.480> setting,<00:17:24.079> you<00:17:24.199> know,<00:17:24.280> in\nAnd from the game setting, you know, in\nAnd from the game setting, you know, in this<00:17:24.520> kind<00:17:24.679> of<00:17:24.839> algorithmic<00:17:25.280> game<00:17:25.439> setting,\nthis kind of algorithmic game setting,\nthis kind of algorithmic game setting, okay,<00:17:26.040> that<00:17:26.720> that's<00:17:27.400> that's<00:17:27.600> one<00:17:27.760> frame.\nokay, that that's that's one frame.\nokay, that that's that's one frame. But<00:17:28.880> also,<00:17:29.640> even<00:17:30.000> for<00:17:30.679> um<00:17:31.520> our<00:17:31.679> use<00:17:32.040> of\nBut also, even for um our use of\nBut also, even for um our use of randomness,<00:17:32.800> say<00:17:33.040> in<00:17:33.160> randomized\nrandomness, say in randomized\nrandomness, say in randomized algorithms,<00:17:34.640> so,<00:17:35.120> you<00:17:35.240> might<00:17:35.480> consider<00:17:35.880> an\nalgorithms, so, you might consider an\nalgorithms, so, you might consider an algorithm<00:17:36.320> like<00:17:37.080> MCMC\nalgorithm like MCMC\nalgorithm like MCMC or<00:17:38.840> quicksort,<00:17:39.640> some<00:17:39.800> other<00:17:39.960> randomized\nor quicksort, some other randomized\nor quicksort, some other randomized algorithm.\nalgorithm.\nalgorithm. Well,\nhow<00:17:44.880> does<00:17:45.240> your<00:17:45.440> algorithm<00:17:46.120> know?<00:17:46.560> I<00:17:46.600> mean,\nhow does your algorithm know? I mean,\nhow does your algorithm know? I mean, so,\nso,\nso, in<00:17:48.480> order\nin order\nin order for<00:17:50.000> your<00:17:50.240> algorithm<00:17:50.920> to<00:17:51.040> behave<00:17:51.440> differently\nfor your algorithm to behave differently\nfor your algorithm to behave differently on<00:17:52.960> truly<00:17:53.400> random<00:17:53.800> sequences<00:17:55.040> or\non truly random sequences or\non truly random sequences or cryptographically<00:17:56.080> random<00:17:56.360> sequences,<00:17:57.000> it\ncryptographically random sequences, it\ncryptographically random sequences, it would<00:17:57.280> need<00:17:57.640> to<00:17:57.760> actually<00:17:58.760> distinguish\nwould need to actually distinguish\nwould need to actually distinguish between<00:17:59.640> the<00:17:59.720> two.\nbetween the two.\nbetween the two. If<00:18:01.160> somehow<00:18:01.560> it's<00:18:01.720> just<00:18:01.880> going<00:18:02.200> to<00:18:03.080> obviously\nIf somehow it's just going to obviously\nIf somehow it's just going to obviously fail<00:18:04.600> with<00:18:05.600> your<00:18:05.720> cryptographic<00:18:06.520> random\nfail with your cryptographic random\nfail with your cryptographic random sequence\nsequence\nsequence versus<00:18:08.240> your<00:18:08.360> truly<00:18:08.600> random<00:18:08.840> sequence,<00:18:09.280> then\nversus your truly random sequence, then\nversus your truly random sequence, then your<00:18:10.040> random<00:18:10.720> your<00:18:11.240> your<00:18:11.480> your<00:18:11.679> cryptographic\nyour random your your your cryptographic\nyour random your your your cryptographic random<00:18:12.440> sequence<00:18:12.800> is<00:18:12.880> not<00:18:13.440> um\nrandom sequence is not um\nrandom sequence is not um actually<00:18:14.679> indistinguishable\nactually indistinguishable\nactually indistinguishable computationally<00:18:15.720> indistinguishable.<00:18:16.320> So,\ncomputationally indistinguishable. So,\ncomputationally indistinguishable. So, in<00:18:17.840> these<00:18:18.080> different<00:18:18.360> ways,\nin these different ways,\nin these different ways, um\num\num the\nthe\nthe the<00:18:21.880> the<00:18:22.040> weaker<00:18:22.320> notion<00:18:22.679> of<00:18:22.800> cryptographic\nthe the weaker notion of cryptographic\nthe the weaker notion of cryptographic randomness<00:18:23.760> is<00:18:23.840> essentially<00:18:24.160> the<00:18:24.280> one<00:18:24.440> that\nrandomness is essentially the one that\nrandomness is essentially the one that is\nis\nis uh<00:18:25.640> more<00:18:25.840> relevant<00:18:26.760> um<00:18:26.880> to<00:18:27.080> us.<00:18:27.360> And<00:18:27.640> there<00:18:27.800> are\nuh more relevant um to us. And there are\nuh more relevant um to us. And there are some<00:18:28.840> uh<00:18:29.200> some<00:18:29.360> important<00:18:29.919> ties<00:18:30.320> to<00:18:30.840> say\nsome uh some important ties to say\nsome uh some important ties to say complexity<00:18:31.640> theory.<00:18:32.400> Say<00:18:32.720> uh\ncomplexity theory. Say uh\ncomplexity theory. Say uh the<00:18:33.679> um<00:18:34.159> you<00:18:34.240> know,<00:18:34.360> conjectured<00:18:35.040> equivalence\nthe um you know, conjectured equivalence\nthe um you know, conjectured equivalence of\nof\nof uh<00:18:36.480> bounded<00:18:36.840> error<00:18:37.400> polynomial<00:18:37.840> time<00:18:38.800> uh\nuh bounded error polynomial time uh\nuh bounded error polynomial time uh and<00:18:40.080> just<00:18:40.320> ordinary\nand just ordinary\nand just ordinary polynomial<00:18:41.840> time.<00:18:42.640> Um<00:18:43.159> so,<00:18:43.440> anyways,<00:18:43.760> just<00:18:44.000> a\npolynomial time. Um so, anyways, just a\npolynomial time. Um so, anyways, just a a<00:18:44.200> few<00:18:44.560> notes<00:18:44.800> there<00:18:45.000> that<00:18:45.200> actually<00:18:45.520> this\na few notes there that actually this\na few notes there that actually this though<00:18:47.159> less\nthough less\nthough less uh\nuh\nuh uh\nuh\nuh you<00:18:50.679> know,<00:18:51.080> thought<00:18:51.280> about\nyou know, thought about\nyou know, thought about with<00:18:52.520> yeah,<00:18:53.080> less<00:18:53.480> obviously<00:18:53.960> the\nwith yeah, less obviously the\nwith yeah, less obviously the theoretical<00:18:54.600> notion,<00:18:55.040> there<00:18:55.320> are<00:18:55.400> some<00:18:55.560> good\ntheoretical notion, there are some good\ntheoretical notion, there are some good reasons<00:18:56.080> to<00:18:56.200> think<00:18:56.440> that<00:18:56.679> this<00:18:56.880> cryptographic\nreasons to think that this cryptographic\nreasons to think that this cryptographic randomness<00:18:58.000> is<00:18:58.800> um\nrandomness is um\nrandomness is um the<00:19:00.040> the<00:19:00.159> more<00:19:00.320> relevant<00:19:00.640> notion<00:19:00.880> to<00:19:01.040> us.\nRight.<00:19:04.440> And<00:19:04.720> so,<00:19:05.120> following<00:19:05.560> on<00:19:05.919> on<00:19:06.080> this<00:19:06.400> and\nRight. And so, following on on this and\nRight. And so, following on on this and the<00:19:07.080> importance<00:19:07.600> of<00:19:07.720> computation,<00:19:08.480> we<00:19:08.679> can\nthe importance of computation, we can\nthe importance of computation, we can further<00:19:09.679> consider<00:19:10.600> cryptographically\nfurther consider cryptographically\nfurther consider cryptographically secure<00:19:11.880> pseudo-random<00:19:12.919> number<00:19:13.240> generators.\nsecure pseudo-random number generators.\nsecure pseudo-random number generators. Uh<00:19:14.320> so,<00:19:14.480> the<00:19:14.679> outputs<00:19:15.280> of<00:19:15.800> these<00:19:16.440> um\nUh so, the outputs of these um\nUh so, the outputs of these um generators<00:19:17.600> are<00:19:17.760> going<00:19:18.040> to<00:19:18.159> be<00:19:18.320> statistically\ngenerators are going to be statistically\ngenerators are going to be statistically indistinguishable<00:19:19.919> from<00:19:20.800> actual<00:19:21.159> random\nindistinguishable from actual random\nindistinguishable from actual random numbers<00:19:21.960> if<00:19:22.200> we<00:19:22.360> only<00:19:22.640> have<00:19:23.440> polynomial-time\nnumbers if we only have polynomial-time\nnumbers if we only have polynomial-time computation.<00:19:25.960> Um<00:19:26.480> there's<00:19:26.720> a<00:19:26.760> closely\ncomputation. Um there's a closely\ncomputation. Um there's a closely related<00:19:27.520> concept<00:19:28.000> that<00:19:28.120> we<00:19:28.240> make<00:19:28.480> use<00:19:28.720> of\nrelated concept that we make use of\nrelated concept that we make use of throughout<00:19:29.520> the<00:19:29.640> paper<00:19:30.640> um<00:19:30.880> called<00:19:31.360> a<00:19:31.440> one-way\nthroughout the paper um called a one-way\nthroughout the paper um called a one-way function,<00:19:32.520> um<00:19:32.800> which<00:19:33.120> is<00:19:33.560> uh\nfunction, um which is uh\nfunction, um which is uh very<00:19:34.480> important<00:19:35.000> in<00:19:35.400> cryptography.<00:19:36.679> Uh<00:19:36.880> these\nvery important in cryptography. Uh these\nvery important in cryptography. Uh these one-way<00:19:37.440> functions<00:19:38.080> are<00:19:38.720> easy<00:19:39.200> or\none-way functions are easy or\none-way functions are easy or computationally<00:19:40.440> inexpensive<00:19:41.080> to<00:19:41.200> evaluate\ncomputationally inexpensive to evaluate\ncomputationally inexpensive to evaluate in<00:19:41.880> one<00:19:42.040> direction,<00:19:42.480> but<00:19:42.679> very\nin one direction, but very\nin one direction, but very computationally<00:19:43.720> expensive<00:19:44.360> to<00:19:45.200> invert.<00:19:45.880> And\ncomputationally expensive to invert. And\ncomputationally expensive to invert. And so,<00:19:46.720> cryptography<00:19:47.679> is<00:19:47.880> an<00:19:48.080> area<00:19:48.480> which<00:19:48.800> has<00:19:49.400> um\nso, cryptography is an area which has um\nso, cryptography is an area which has um really<00:19:49.960> considered<00:19:50.520> computational\nreally considered computational\nreally considered computational constraints<00:19:52.200> quite<00:19:52.480> extensively,<00:19:53.440> but<00:19:53.960> this\nconstraints quite extensively, but this\nconstraints quite extensively, but this is<00:19:54.240> something<00:19:54.520> that<00:19:54.640> has<00:19:54.880> not<00:19:55.200> been\nis something that has not been\nis something that has not been considered<00:19:55.960> as<00:19:56.120> much<00:19:56.440> in<00:19:56.600> learning<00:19:56.880> theory<00:19:57.360> or\nconsidered as much in learning theory or\nconsidered as much in learning theory or information<00:19:58.160> theory.<00:19:59.000> And<00:19:59.360> this<00:19:59.600> can<00:19:59.720> be\ninformation theory. And this can be\ninformation theory. And this can be quite<00:20:00.200> important<00:20:00.720> for<00:20:01.160> explaining<00:20:01.880> um\nquite important for explaining um\nquite important for explaining um behavior<00:20:02.760> of<00:20:03.040> AI<00:20:03.240> systems.<00:20:04.120> So,<00:20:04.400> we<00:20:04.600> can,<00:20:04.760> for\nbehavior of AI systems. So, we can, for\nbehavior of AI systems. So, we can, for example,<00:20:05.760> look<00:20:06.160> at<00:20:06.360> the<00:20:06.440> Shannon<00:20:06.840> information\nexample, look at the Shannon information\nexample, look at the Shannon information associated<00:20:08.320> with<00:20:09.120> uh<00:20:09.560> the<00:20:09.760> output<00:20:10.080> of<00:20:10.240> a\nassociated with uh the output of a\nassociated with uh the output of a random<00:20:10.600> number<00:20:10.840> generator.<00:20:11.520> Uh<00:20:11.880> so,<00:20:12.560> uh<00:20:12.880> these\nrandom number generator. Uh so, uh these\nrandom number generator. Uh so, uh these are<00:20:13.160> just<00:20:13.360> deterministic<00:20:13.960> transformations\nare just deterministic transformations\nare just deterministic transformations um\num\num due<00:20:15.840> to<00:20:15.960> the<00:20:16.160> data<00:20:16.400> processing<00:20:17.000> inequality,\ndue to the data processing inequality,\ndue to the data processing inequality, we're<00:20:18.000> not<00:20:18.360> actually<00:20:18.880> increasing<00:20:19.440> the\nwe're not actually increasing the\nwe're not actually increasing the information<00:20:20.480> content<00:20:21.400> um\ninformation content um\ninformation content um uh<00:20:22.200> according<00:20:22.560> to<00:20:22.680> Shannon<00:20:22.920> information,<00:20:23.880> and\nuh according to Shannon information, and\nuh according to Shannon information, and we<00:20:24.200> can<00:20:24.520> get<00:20:24.720> a<00:20:24.760> similar<00:20:25.320> result<00:20:25.840> from\nwe can get a similar result from\nwe can get a similar result from algorithmic<00:20:27.000> information<00:20:27.560> theory<00:20:27.840> with\nalgorithmic information theory with\nalgorithmic information theory with Kolmogorov<00:20:28.760> complexity.<00:20:30.000> And<00:20:30.280> so,<00:20:31.080> uh<00:20:31.960> this\nKolmogorov complexity. And so, uh this\nKolmogorov complexity. And so, uh this leads<00:20:32.840> to<00:20:32.920> this<00:20:33.080> question<00:20:33.480> of<00:20:33.880> like<00:20:34.360> um\nleads to this question of like um\nleads to this question of like um you<00:20:35.960> know,<00:20:36.080> how<00:20:36.280> can<00:20:36.440> pseudo<00:20:36.680> random<00:20:36.960> numbers\nyou know, how can pseudo random numbers\nyou know, how can pseudo random numbers then<00:20:37.560> actually<00:20:37.920> be\nthen actually be\nthen actually be uh<00:20:39.640> uh\nuh uh\nuh uh useful?<00:20:41.000> Uh\nuseful? Uh\nuseful? Uh uh<00:20:42.320> they're<00:20:42.760> indistinguishable<00:20:43.600> from<00:20:43.800> actual\nuh they're indistinguishable from actual\nuh they're indistinguishable from actual random<00:20:44.440> numbers,<00:20:45.080> um<00:20:45.760> uh<00:20:46.120> but<00:20:46.680> they<00:20:46.920> don't\nrandom numbers, um uh but they don't\nrandom numbers, um uh but they don't seem<00:20:47.520> to<00:20:47.640> add<00:20:47.840> information.<00:20:48.960> Um<00:20:49.160> and<00:20:49.320> so,<00:20:49.800> how\nseem to add information. Um and so, how\nseem to add information. Um and so, how can<00:20:50.160> we<00:20:50.560> really<00:20:50.840> accommodate<00:20:51.400> this<00:20:51.720> in\ncan we really accommodate this in\ncan we really accommodate this in rethinking<00:20:52.680> how<00:20:52.840> we<00:20:52.960> measure<00:20:53.320> information?\nrethinking how we measure information?\nrethinking how we measure information? Um<00:20:55.320> we've<00:20:55.560> also<00:20:56.480> made<00:20:56.800> use<00:20:57.160> of<00:20:57.640> elementary\nUm we've also made use of elementary\nUm we've also made use of elementary cellular<00:20:58.720> automata<00:20:59.760> as<00:20:59.960> a<00:21:00.040> mechanism<00:21:00.720> for\ncellular automata as a mechanism for\ncellular automata as a mechanism for reasoning<00:21:02.000> about<00:21:02.240> the<00:21:02.360> role<00:21:02.600> of<00:21:02.680> computation\nreasoning about the role of computation\nreasoning about the role of computation and<00:21:04.000> emergent<00:21:04.480> structure<00:21:04.960> and<00:21:05.120> deterministic\nand emergent structure and deterministic\nand emergent structure and deterministic transformations.<00:21:06.640> So,<00:21:06.800> just<00:21:07.040> as<00:21:07.160> a<00:21:07.200> little\ntransformations. So, just as a little\ntransformations. So, just as a little bit<00:21:07.480> of<00:21:07.600> background,<00:21:08.680> um<00:21:09.080> ECA<00:21:09.720> are<00:21:10.280> uh<00:21:10.600> 1D\nbit of background, um ECA are uh 1D\nbit of background, um ECA are uh 1D array<00:21:11.520> of<00:21:11.760> binary<00:21:12.200> cells.\narray of binary cells.\narray of binary cells. Each<00:21:14.280> cell's<00:21:15.120> next<00:21:15.480> value<00:21:16.080> at<00:21:16.280> the<00:21:16.360> next\nEach cell's next value at the next\nEach cell's next value at the next iteration<00:21:17.240> depends<00:21:17.760> only<00:21:18.120> on<00:21:18.560> its<00:21:19.240> own<00:21:19.480> value\niteration depends only on its own value\niteration depends only on its own value plus<00:21:20.720> the<00:21:20.840> value<00:21:21.320> of<00:21:21.520> its<00:21:21.800> two<00:21:22.000> neighbors.\nplus the value of its two neighbors.\nplus the value of its two neighbors. And<00:21:23.480> so,<00:21:23.600> this<00:21:23.800> means<00:21:24.000> there<00:21:24.160> going<00:21:24.360> to<00:21:24.520> be\nAnd so, this means there going to be\nAnd so, this means there going to be eight<00:21:25.360> possible<00:21:25.920> local<00:21:26.520> neighborhoods<00:21:27.120> that\neight possible local neighborhoods that\neight possible local neighborhoods that will<00:21:28.080> determine<00:21:28.640> the<00:21:28.760> state<00:21:29.080> of<00:21:29.280> a<00:21:29.560> cell<00:21:29.800> at\nwill determine the state of a cell at\nwill determine the state of a cell at the<00:21:30.000> next<00:21:30.280> time<00:21:30.480> step.<00:21:31.320> And<00:21:31.880> each<00:21:32.120> of<00:21:32.200> these\nthe next time step. And each of these\nthe next time step. And each of these local<00:21:32.680> neighborhoods<00:21:33.280> can<00:21:33.520> have<00:21:33.960> a<00:21:34.040> rule\nlocal neighborhoods can have a rule\nlocal neighborhoods can have a rule associated<00:21:34.920> with<00:21:35.080> them.<00:21:35.360> So,<00:21:35.520> that<00:21:35.760> means\nassociated with them. So, that means\nassociated with them. So, that means that<00:21:36.200> there<00:21:36.520> are<00:21:36.920> two<00:21:37.080> to<00:21:37.160> the<00:21:37.320> eight<00:21:37.560> or<00:21:37.680> 256\nthat there are two to the eight or 256\nthat there are two to the eight or 256 different<00:21:39.440> possible<00:21:40.160> ECA<00:21:40.800> rules.\ndifferent possible ECA rules.\ndifferent possible ECA rules. And<00:21:42.240> these<00:21:42.520> rules<00:21:43.040> give<00:21:43.320> rise<00:21:43.680> to<00:21:44.160> very\nAnd these rules give rise to very\nAnd these rules give rise to very different<00:21:44.760> complexities<00:21:45.680> and<00:21:46.440> structures.\ndifferent complexities and structures.\ndifferent complexities and structures. And<00:21:47.680> so,<00:21:48.080> in<00:21:48.240> these<00:21:48.520> figures,<00:21:49.640> we<00:21:49.840> have<00:21:50.240> time\nAnd so, in these figures, we have time\nAnd so, in these figures, we have time running<00:21:51.240> from<00:21:51.600> top<00:21:51.920> to<00:21:52.040> bottom<00:21:52.600> in<00:21:52.800> the\nrunning from top to bottom in the\nrunning from top to bottom in the evolution<00:21:53.480> of<00:21:53.760> data<00:21:54.400> um\nevolution of data um\nevolution of data um which<00:21:55.960> is<00:21:56.080> generated<00:21:56.560> from<00:21:56.720> these<00:21:56.960> rules.<00:21:57.880> In\nwhich is generated from these rules. In\nwhich is generated from these rules. In the<00:21:58.120> left<00:21:58.400> panel<00:21:58.679> here,<00:21:58.920> we<00:21:59.040> have<00:21:59.160> an<00:21:59.280> example\nthe left panel here, we have an example\nthe left panel here, we have an example of<00:22:00.520> rule<00:22:00.840> 30.<00:22:01.400> So,<00:22:01.679> 111<00:22:02.280> here<00:22:02.520> maps<00:22:02.760> to<00:22:02.880> zero,\nof rule 30. So, 111 here maps to zero,\nof rule 30. So, 111 here maps to zero, 110<00:22:03.800> to<00:22:03.920> zero,<00:22:04.240> and<00:22:04.400> so<00:22:04.560> on.\n110 to zero, and so on.\n110 to zero, and so on. Um\nUm\nUm we<00:22:06.920> can\nwe can\nwe can see<00:22:08.960> that<00:22:09.480> for<00:22:09.640> certain<00:22:09.960> rules,<00:22:10.320> there<00:22:10.560> are\nsee that for certain rules, there are\nsee that for certain rules, there are very<00:22:11.400> simple<00:22:11.800> structures<00:22:12.360> that<00:22:12.480> arise,<00:22:12.960> like\nvery simple structures that arise, like\nvery simple structures that arise, like rule<00:22:13.520> 15.<00:22:14.600> Um<00:22:14.760> for<00:22:15.000> others,<00:22:15.360> like<00:22:15.600> rule<00:22:15.880> 30,<00:22:16.360> we\nrule 15. Um for others, like rule 30, we\nrule 15. Um for others, like rule 30, we effectively<00:22:17.679> have<00:22:18.240> random<00:22:18.600> structure.<00:22:19.160> And\neffectively have random structure. And\neffectively have random structure. And then,<00:22:19.520> rule<00:22:19.720> 54<00:22:20.320> is<00:22:20.440> kind<00:22:20.720> of<00:22:21.240> in<00:22:21.400> between.<00:22:21.880> It\nthen, rule 54 is kind of in between. It\nthen, rule 54 is kind of in between. It seems<00:22:22.280> to<00:22:22.400> have<00:22:22.760> structural<00:22:23.280> complexity,<00:22:24.520> um\nseems to have structural complexity, um\nseems to have structural complexity, um but<00:22:25.280> it's<00:22:25.679> still<00:22:25.960> relatively<00:22:26.880> predictable<00:22:27.920> as\nbut it's still relatively predictable as\nbut it's still relatively predictable as long<00:22:28.240> as<00:22:28.360> you<00:22:28.480> have<00:22:28.640> enough<00:22:28.840> computation.<00:22:30.120> Uh\nlong as you have enough computation. Uh\nlong as you have enough computation. Uh superimposed<00:22:31.080> on<00:22:31.200> these<00:22:31.400> images,<00:22:31.960> we<00:22:32.200> have<00:22:32.679> uh\nsuperimposed on these images, we have uh\nsuperimposed on these images, we have uh figures<00:22:33.360> of<00:22:34.040> uh<00:22:34.200> coffee<00:22:34.600> mixing<00:22:34.960> with<00:22:35.160> cream.\nfigures of uh coffee mixing with cream.\nfigures of uh coffee mixing with cream. And<00:22:35.800> so,<00:22:36.000> this<00:22:36.240> is<00:22:36.440> inspired<00:22:36.960> by<00:22:37.360> a<00:22:37.440> blog<00:22:37.720> post\nAnd so, this is inspired by a blog post\nAnd so, this is inspired by a blog post from<00:22:38.880> Scott<00:22:39.200> Aaronson<00:22:39.920> uh<00:22:40.440> around<00:22:40.760> 2010,\nfrom Scott Aaronson uh around 2010,\nfrom Scott Aaronson uh around 2010, where<00:22:42.360> he's<00:22:42.600> imagining<00:22:43.080> that<00:22:43.240> you<00:22:43.600> initially\nwhere he's imagining that you initially\nwhere he's imagining that you initially have<00:22:44.280> this<00:22:44.440> system<00:22:44.800> of<00:22:44.920> separated<00:22:45.440> coffee<00:22:45.760> and\nhave this system of separated coffee and\nhave this system of separated coffee and cream,<00:22:46.240> and<00:22:46.360> you<00:22:46.440> start<00:22:46.760> mixing<00:22:47.080> them\ncream, and you start mixing them\ncream, and you start mixing them together.<00:22:48.080> And<00:22:48.200> as<00:22:48.360> you<00:22:48.480> do<00:22:48.679> this,<00:22:48.880> the\ntogether. And as you do this, the\ntogether. And as you do this, the entropy<00:22:49.440> of<00:22:49.560> the<00:22:49.640> system<00:22:50.160> continues<00:22:50.640> to\nentropy of the system continues to\nentropy of the system continues to increase,<00:22:51.480> but<00:22:51.720> intuitively,<00:22:53.080> the\nincrease, but intuitively, the\nincrease, but intuitively, the sophistication<00:22:54.120> of<00:22:54.200> the<00:22:54.320> system<00:22:54.720> is\nsophistication of the system is\nsophistication of the system is non-monotonic.<00:22:56.000> So,<00:22:56.600> uh<00:22:56.840> at<00:22:56.960> the<00:22:57.040> beginning,\nnon-monotonic. So, uh at the beginning,\nnon-monotonic. So, uh at the beginning, you<00:22:57.880> don't<00:22:58.120> really<00:22:58.360> have<00:22:58.600> much<00:22:58.920> intuitive\nyou don't really have much intuitive\nyou don't really have much intuitive complexity.<00:23:00.600> In<00:23:01.000> the<00:23:01.120> middle,<00:23:01.520> you<00:23:01.720> have<00:23:02.080> some\ncomplexity. In the middle, you have some\ncomplexity. In the middle, you have some maximum<00:23:02.840> of<00:23:02.960> complexity,<00:23:03.640> and<00:23:03.760> then<00:23:03.880> at<00:23:03.960> the\nmaximum of complexity, and then at the\nmaximum of complexity, and then at the end,<00:23:04.679> you<00:23:04.840> actually<00:23:05.080> don't<00:23:05.240> have<00:23:05.400> any\nend, you actually don't have any\nend, you actually don't have any interesting<00:23:06.000> complexity<00:23:06.640> anymore.<00:23:07.480> And<00:23:07.679> so,\ninteresting complexity anymore. And so,\ninteresting complexity anymore. And so, this<00:23:08.280> is<00:23:08.440> exactly<00:23:09.000> what<00:23:09.240> we're<00:23:09.880> intending<00:23:10.360> to\nthis is exactly what we're intending to\nthis is exactly what we're intending to capture<00:23:11.000> with<00:23:11.720> appiplexity.\ncapture with appiplexity.\ncapture with appiplexity. These<00:23:14.880> ECA<00:23:15.400> systems<00:23:16.000> are<00:23:16.200> also<00:23:17.320> really\nThese ECA systems are also really\nThese ECA systems are also really interesting<00:23:18.280> because<00:23:18.760> they<00:23:19.040> allow<00:23:19.400> us<00:23:19.560> to\ninteresting because they allow us to\ninteresting because they allow us to study<00:23:20.040> the<00:23:20.120> emergent<00:23:20.560> phenomena.<00:23:21.520> Like,<00:23:21.679> if\nstudy the emergent phenomena. Like, if\nstudy the emergent phenomena. Like, if you<00:23:22.320> could<00:23:22.440> just<00:23:22.679> reverse<00:23:23.080> engineer<00:23:23.640> the\nyou could just reverse engineer the\nyou could just reverse engineer the rules<00:23:24.280> behind<00:23:25.120> the<00:23:25.240> data,<00:23:25.760> then<00:23:26.000> you<00:23:26.120> could\nrules behind the data, then you could\nrules behind the data, then you could predict<00:23:26.679> ahead<00:23:27.040> very<00:23:27.440> easily,<00:23:27.840> and<00:23:27.960> this\npredict ahead very easily, and this\npredict ahead very easily, and this would<00:23:28.240> have<00:23:28.360> a<00:23:28.440> very<00:23:28.640> short<00:23:29.000> description\nwould have a very short description\nwould have a very short description length,<00:23:29.800> and<00:23:30.280> actually<00:23:30.600> wouldn't\nlength, and actually wouldn't\nlength, and actually wouldn't necessarily<00:23:31.360> be<00:23:31.480> very<00:23:31.800> interesting<00:23:32.360> from<00:23:32.560> the\nnecessarily be very interesting from the\nnecessarily be very interesting from the perspective<00:23:33.200> of<00:23:33.320> downstream\nperspective of downstream\nperspective of downstream generalization.<00:23:35.360> But<00:23:35.520> because<00:23:35.960> it's<00:23:36.440> very,\ngeneralization. But because it's very,\ngeneralization. But because it's very, very<00:23:36.920> difficult<00:23:37.480> for<00:23:37.600> a<00:23:37.679> model<00:23:38.000> to<00:23:38.160> do<00:23:38.440> that,\nvery difficult for a model to do that,\nvery difficult for a model to do that, it<00:23:39.280> instead<00:23:39.800> learns<00:23:40.160> emergent<00:23:40.640> structures<00:23:41.600> of\nit instead learns emergent structures of\nit instead learns emergent structures of floaters<00:23:42.240> and<00:23:42.360> things<00:23:42.600> like<00:23:42.800> this<00:23:43.040> that<00:23:43.160> it\nfloaters and things like this that it\nfloaters and things like this that it can<00:23:43.440> use<00:23:43.679> to<00:23:43.760> predict<00:23:44.200> the<00:23:44.280> next<00:23:44.520> state.<00:23:44.840> So,\ncan use to predict the next state. So,\ncan use to predict the next state. So, in<00:23:45.080> some<00:23:45.280> sense,<00:23:45.520> it's<00:23:45.720> actually<00:23:46.040> going\nin some sense, it's actually going\nin some sense, it's actually going beyond<00:23:47.120> the<00:23:47.200> data<00:23:47.480> generating<00:23:48.360> process.<00:23:49.120> And\nbeyond the data generating process. And\nbeyond the data generating process. And this<00:23:49.800> is<00:23:49.960> something<00:23:50.280> that<00:23:50.400> we<00:23:50.560> can<00:23:51.000> capture\nthis is something that we can capture\nthis is something that we can capture with<00:23:51.560> appiplexity.<00:23:52.280> So,<00:23:52.800> now<00:23:52.960> Mark's<00:23:53.280> going\nwith appiplexity. So, now Mark's going\nwith appiplexity. So, now Mark's going to<00:23:53.720> properly<00:23:54.120> introduce<00:23:54.560> appiplexity<00:23:55.360> and<00:23:55.600> go\nto properly introduce appiplexity and go\nto properly introduce appiplexity and go through<00:23:56.480> how<00:23:56.679> it<00:23:56.880> can<00:23:57.240> help<00:23:57.520> resolve<00:23:57.880> these\nthrough how it can help resolve these\nthrough how it can help resolve these paradoxes<00:23:58.720> that<00:23:58.800> we've<00:23:59.000> introduced.\nAll<00:24:03.720> right.\nSo,<00:24:12.480> with<00:24:12.640> that<00:24:13.040> intuition<00:24:14.000> um<00:24:14.160> setting<00:24:14.480> the\nSo, with that intuition um setting the\nSo, with that intuition um setting the stage,\nstage,\nstage, I<00:24:15.760> hope<00:24:15.960> everyone<00:24:16.240> can<00:24:16.520> see<00:24:17.040> all<00:24:17.280> right.\nI hope everyone can see all right.\nI hope everyone can see all right. Let<00:24:18.400> me<00:24:18.520> just<00:24:18.800> move<00:24:19.080> this.\nLet me just move this.\nLet me just move this. Looks<00:24:20.720> good.\nLooks good.\nLooks good. Uh\nUh\nUh yeah,<00:24:24.840> so<00:24:24.960> with<00:24:25.080> that<00:24:25.560> intuition<00:24:26.080> setting<00:24:26.360> the\nyeah, so with that intuition setting the\nyeah, so with that intuition setting the stage,<00:24:27.080> now<00:24:27.280> we'll<00:24:27.480> actually<00:24:28.480> define<00:24:29.760> our\nstage, now we'll actually define our\nstage, now we'll actually define our appiplexity.<00:24:31.720> So,<00:24:31.880> the<00:24:31.960> starting<00:24:32.320> point,<00:24:33.200> as\nappiplexity. So, the starting point, as\nappiplexity. So, the starting point, as Andrew's<00:24:34.160> been<00:24:34.320> alluding<00:24:34.679> to,<00:24:35.160> is\nAndrew's been alluding to, is\nAndrew's been alluding to, is restricting<00:24:36.679> the<00:24:36.800> computation<00:24:37.600> available<00:24:38.400> to\nrestricting the computation available to\nrestricting the computation available to the<00:24:38.600> model.\nthe model.\nthe model. And<00:24:40.240> here,<00:24:40.840> what<00:24:40.960> we<00:24:41.080> mean<00:24:41.280> by<00:24:41.440> model<00:24:42.160> is<00:24:42.720> a\nAnd here, what we mean by model is a\nAnd here, what we mean by model is a probabilistic<00:24:43.400> model.<00:24:44.240> It's<00:24:44.400> going<00:24:44.520> to<00:24:44.600> be\nprobabilistic model. It's going to be\nprobabilistic model. It's going to be taking<00:24:45.160> the<00:24:45.240> place<00:24:45.560> of<00:24:45.720> our<00:24:46.040> machine<00:24:46.280> learning\ntaking the place of our machine learning\ntaking the place of our machine learning model<00:24:46.840> that<00:24:47.000> is<00:24:47.120> looking<00:24:47.360> at<00:24:47.440> this<00:24:47.560> data,\nmodel that is looking at this data,\nmodel that is looking at this data, trying<00:24:48.480> to<00:24:48.560> understand<00:24:48.960> it.\ntrying to understand it.\ntrying to understand it. Trying<00:24:50.360> to<00:24:51.400> provide<00:24:51.720> a<00:24:51.760> short<00:24:52.000> code<00:24:52.679> to\nTrying to provide a short code to\nTrying to provide a short code to produce<00:24:53.000> that<00:24:53.120> model.\nproduce that model.\nproduce that model. So,<00:24:54.400> we<00:24:54.880> write<00:24:55.800> PT<00:24:56.560> as<00:24:57.200> set<00:24:57.480> of<00:24:57.560> programs<00:24:58.240> that\nSo, we write PT as set of programs that\nSo, we write PT as set of programs that implement<00:24:59.160> normalized<00:24:59.640> probability\nimplement normalized probability\nimplement normalized probability distributions<00:25:01.120> on<00:25:01.320> just<00:25:02.160> a<00:25:02.240> binary<00:25:02.600> string<00:25:03.120> of\ndistributions on just a binary string of\ndistributions on just a binary string of length<00:25:03.480> n,\nlength n,\nlength n, where<00:25:05.240> both<00:25:06.120> sampling<00:25:07.200> and<00:25:07.480> probability\nwhere both sampling and probability\nwhere both sampling and probability estimation<00:25:08.600> can<00:25:08.760> be<00:25:08.840> done<00:25:09.280> in<00:25:09.400> time<00:25:09.760> T<00:25:10.000> of<00:25:10.120> n.\nestimation can be done in time T of n.\nestimation can be done in time T of n. So,<00:25:10.600> T<00:25:10.720> is<00:25:10.840> going<00:25:10.960> to<00:25:11.000> be<00:25:11.080> a<00:25:11.120> function.<00:25:11.920> Could\nSo, T is going to be a function. Could\nSo, T is going to be a function. Could be<00:25:12.200> n<00:25:12.320> squared,<00:25:13.120> could<00:25:13.280> be,<00:25:13.440> you<00:25:13.520> know,<00:25:13.640> some\nbe n squared, could be, you know, some\nbe n squared, could be, you know, some constant,<00:25:14.160> you<00:25:14.240> know,<00:25:14.400> some<00:25:14.520> linear\nconstant, you know, some linear\nconstant, you know, some linear function,\nfunction,\nfunction, and<00:25:16.000> whatnot.\nand whatnot.\nand whatnot. And<00:25:17.800> that's<00:25:18.000> how<00:25:18.120> we're<00:25:18.200> going<00:25:18.320> to<00:25:18.400> restrict\nAnd that's how we're going to restrict\nAnd that's how we're going to restrict the<00:25:19.160> computation.\nthe computation.\nthe computation. So,<00:25:22.040> yeah,<00:25:22.400> m-<00:25:22.640> note<00:25:22.840> here,<00:25:23.280> this<00:25:23.480> is<00:25:23.600> just<00:25:24.040> for\nSo, yeah, m- note here, this is just for\nSo, yeah, m- note here, this is just for discrete<00:25:24.720> data.\ndiscrete data.\ndiscrete data. So,<00:25:25.760> with<00:25:25.880> that<00:25:26.120> in<00:25:26.280> mind,<00:25:26.960> we<00:25:27.440> define\nSo, with that in mind, we define\nSo, with that in mind, we define appiplexity<00:25:29.280> and<00:25:29.400> time-bounded<00:25:29.840> entropy<00:25:30.560> in\nappiplexity and time-bounded entropy in\nappiplexity and time-bounded entropy in terms<00:25:31.280> of<00:25:31.520> this\nterms of this\nterms of this uh<00:25:33.000> you<00:25:33.080> know,<00:25:33.160> related<00:25:33.440> to<00:25:33.520> this<00:25:33.679> minimum\nuh you know, related to this minimum\nuh you know, related to this minimum description<00:25:34.520> length<00:25:34.720> principle.\ndescription length principle.\ndescription length principle. So,<00:25:36.640> we<00:25:36.880> consider<00:25:37.280> this<00:25:37.440> quantity,<00:25:37.960> which<00:25:38.200> is\nSo, we consider this quantity, which is\nSo, we consider this quantity, which is the<00:25:38.400> sum<00:25:39.080> of<00:25:39.360> the<00:25:39.480> program<00:25:39.840> size,<00:25:40.880> measured<00:25:41.160> in\nthe sum of the program size, measured in\nthe sum of the program size, measured in bits,\nbits,\nbits, and<00:25:42.560> then<00:25:43.120> this<00:25:44.040> um\nand then this um\nand then this um uh<00:25:45.560> negative<00:25:45.920> log<00:25:46.080> likelihood,<00:25:46.600> expected\nuh negative log likelihood, expected\nuh negative log likelihood, expected negative<00:25:47.240> log<00:25:47.360> likelihood,<00:25:48.160> of<00:25:48.600> the<00:25:48.679> data\nnegative log likelihood, of the data\nnegative log likelihood, of the data under<00:25:50.080> the<00:25:50.160> probability<00:25:50.440> distribution\nunder the probability distribution\nunder the probability distribution determined<00:25:51.800> by<00:25:51.920> that<00:25:52.080> program.\ndetermined by that program.\ndetermined by that program. Um<00:25:54.480> we<00:25:54.600> can<00:25:54.720> think<00:25:54.920> of<00:25:55.040> this<00:25:55.280> whole<00:25:55.520> quantity\nUm we can think of this whole quantity\nUm we can think of this whole quantity as<00:25:56.520> within<00:25:56.840> a<00:25:56.880> constant<00:25:58.000> to<00:25:59.000> the<00:25:59.960> uh\nas within a constant to the uh\nas within a constant to the uh the<00:26:01.600> code<00:26:01.920> length<00:26:02.560> of<00:26:02.679> the<00:26:02.760> data<00:26:03.520> using<00:26:03.880> the\nthe code length of the data using the\nthe code length of the data using the model<00:26:04.520> as<00:26:04.720> the<00:26:04.800> compressor.\nmodel as the compressor.\nmodel as the compressor. So,<00:26:07.120> thinking<00:26:07.440> about<00:26:08.240> this\nSo, thinking about this\nSo, thinking about this uh<00:26:10.120> search<00:26:11.200> over\nuh search over\nuh search over different<00:26:12.760> models,\ndifferent models,\ndifferent models, consider<00:26:14.480> these<00:26:14.640> different,<00:26:15.360> you<00:26:15.440> know,<00:26:15.600> the\nconsider these different, you know, the\nconsider these different, you know, the this<00:26:15.960> different<00:26:16.480> uh<00:26:16.880> description<00:26:17.360> length,\nthis different uh description length,\nthis different uh description length, and<00:26:18.360> we<00:26:18.520> want<00:26:18.760> to<00:26:18.840> take<00:26:19.080> the<00:26:19.200> one<00:26:19.520> that\nand we want to take the one that\nand we want to take the one that minimizes<00:26:20.240> it,<00:26:20.520> so<00:26:20.679> with<00:26:20.800> the<00:26:20.880> shortest\nminimizes it, so with the shortest\nminimizes it, so with the shortest description<00:26:21.600> length\ndescription length\ndescription length in<00:26:22.800> this<00:26:23.040> set<00:26:23.440> of<00:26:23.560> time-bounded<00:26:24.040> probability\nin this set of time-bounded probability\nin this set of time-bounded probability distributions.<00:26:25.480> Call<00:26:25.600> that<00:26:25.760> P<00:26:25.880> star.\ndistributions. Call that P star.\ndistributions. Call that P star. Then,<00:26:27.800> we<00:26:27.920> have<00:26:28.080> these<00:26:28.320> two<00:26:28.520> quantities.<00:26:29.480> This\nThen, we have these two quantities. This\nThen, we have these two quantities. This is<00:26:29.760> how<00:26:29.880> we're<00:26:29.960> going<00:26:30.080> to<00:26:30.160> separate<00:26:30.600> out<00:26:30.800> the\nis how we're going to separate out the\nis how we're going to separate out the structure<00:26:31.800> and<00:26:31.920> the<00:26:32.000> randomness.<00:26:32.760> The\nstructure and the randomness. The\nstructure and the randomness. The structure<00:26:33.880> is<00:26:34.240> just<00:26:34.600> the<00:26:34.720> size<00:26:35.240> of<00:26:35.320> this\nstructure is just the size of this\nstructure is just the size of this program<00:26:35.800> P<00:26:35.960> star.\nprogram P star.\nprogram P star. And<00:26:37.800> the<00:26:37.920> randomness,<00:26:39.040> the<00:26:39.160> time-bounded,\nAnd the randomness, the time-bounded,\nAnd the randomness, the time-bounded, what<00:26:39.800> we<00:26:39.880> call<00:26:40.120> time-bounded<00:26:40.640> entropy,\nwhat we call time-bounded entropy,\nwhat we call time-bounded entropy, is<00:26:42.000> going<00:26:42.160> to<00:26:42.240> be<00:26:42.720> this\nis going to be this\nis going to be this uh<00:26:44.560> cross<00:26:44.800> entropy.<00:26:45.760> Um<00:26:45.960> just<00:26:46.240> the<00:26:46.280> expected\nuh cross entropy. Um just the expected\nuh cross entropy. Um just the expected uh<00:26:48.000> right,<00:26:48.440> uh<00:26:48.880> log<00:26:49.840> uh<00:26:50.320> negative<00:26:50.640> log\nuh right, uh log uh negative log\nuh right, uh log uh negative log likelihood<00:26:51.640> of<00:26:52.280> that<00:26:52.440> data.\nlikelihood of that data.\nlikelihood of that data. We<00:26:53.920> should<00:26:54.120> think<00:26:54.360> of<00:26:54.520> this<00:26:54.760> data<00:26:55.040> this<00:26:55.400> X<00:26:56.080> as\nWe should think of this data this X as\nWe should think of this data this X as not,<00:26:56.720> say,<00:26:57.000> an<00:26:57.120> individual<00:26:57.600> example,<00:26:58.000> but<00:26:58.160> the\nnot, say, an individual example, but the\nnot, say, an individual example, but the entire<00:26:58.520> data<00:26:58.760> set<00:26:59.200> that<00:26:59.360> we're<00:26:59.760> considering\nentire data set that we're considering\nentire data set that we're considering uh<00:27:01.120> training<00:27:01.440> on.<00:27:01.960> And<00:27:02.080> this<00:27:02.280> P<00:27:03.280> um<00:27:03.760> could\nuh training on. And this P um could\nuh training on. And this P um could involve<00:27:04.640> a<00:27:04.679> very<00:27:04.880> complex<00:27:05.320> procedure<00:27:06.560> for\ninvolve a very complex procedure for\ninvolve a very complex procedure for running<00:27:06.960> it,<00:27:07.200> where<00:27:07.440> maybe<00:27:07.840> actually<00:27:08.200> this<00:27:08.400> is\nrunning it, where maybe actually this is\nrunning it, where maybe actually this is very<00:27:08.760> complex<00:27:09.400> compressed,<00:27:10.080> and<00:27:10.240> we<00:27:10.880> are\nvery complex compressed, and we are\nvery complex compressed, and we are going<00:27:11.400> to<00:27:11.760> use<00:27:12.120> some<00:27:12.280> of<00:27:12.400> the<00:27:12.480> compute<00:27:13.160> in<00:27:13.560> a\ngoing to use some of the compute in a\ngoing to use some of the compute in a lot<00:27:13.880> of<00:27:13.960> to<00:27:14.080> us<00:27:14.240> in<00:27:14.320> this<00:27:14.480> time<00:27:14.720> bound<00:27:15.360> to<00:27:15.520> do\nlot of to us in this time bound to do\nlot of to us in this time bound to do decompression<00:27:16.840> as<00:27:17.000> well<00:27:17.240> as<00:27:17.880> inference.\ndecompression as well as inference.\ndecompression as well as inference. Right.<00:27:20.138> [clears throat]<00:27:20.200> So,<00:27:20.720> that's<00:27:20.960> where\nRight. [clears throat] So, that's where\nRight. [clears throat] So, that's where this<00:27:21.240> time<00:27:21.480> bound<00:27:21.679> comes<00:27:21.920> in,<00:27:22.280> S<00:27:23.080> for\nthis time bound comes in, S for\nthis time bound comes in, S for structure.<00:27:24.360> Um<00:27:24.800> so,<00:27:24.960> this<00:27:25.120> is<00:27:25.240> the\nstructure. Um so, this is the\nstructure. Um so, this is the appiplexity<00:27:26.000> of<00:27:26.200> X<00:27:26.679> given<00:27:26.960> time<00:27:27.160> bound<00:27:27.360> T.<00:27:28.120> And\nappiplexity of X given time bound T. And\nappiplexity of X given time bound T. And this<00:27:28.480> would<00:27:28.600> be<00:27:29.160> the<00:27:29.240> time-bounded<00:27:29.640> entropy\nthis would be the time-bounded entropy\nthis would be the time-bounded entropy of<00:27:30.679> X<00:27:31.600> um<00:27:32.200> given<00:27:32.440> time<00:27:32.600> bound<00:27:32.800> T.<00:27:33.560> And<00:27:33.880> again,\nof X um given time bound T. And again,\nof X um given time bound T. And again, it's<00:27:34.640> defined<00:27:35.000> on<00:27:35.160> random<00:27:35.440> variables,<00:27:36.080> unlike\nit's defined on random variables, unlike\nit's defined on random variables, unlike um<00:27:37.000> yeah,<00:27:37.200> so<00:27:37.800> uh<00:27:37.880> not<00:27:38.120> not<00:27:38.400> like<00:27:38.760> uh\num yeah, so uh not not like uh\num yeah, so uh not not like uh Kolmogorov<00:27:39.120> complexity.<00:27:40.080> Okay.\nSo,<00:27:42.960> going<00:27:43.280> through<00:27:43.920> this<00:27:44.120> picture,\nSo, going through this picture,\nSo, going through this picture, um<00:27:45.920> which\num which\num which uh<00:27:48.280> Andrew<00:27:49.040> um\nuh Andrew um\nuh Andrew um uh<00:27:50.160> walked<00:27:50.400> you<00:27:50.480> through<00:27:50.560> earlier,<00:27:51.160> now<00:27:51.440> we'll\nuh walked you through earlier, now we'll\nuh walked you through earlier, now we'll just\njust\njust go<00:27:52.840> through<00:27:53.160> how<00:27:54.120> actually<00:27:55.040> uh<00:27:55.560> the\ngo through how actually uh the\ngo through how actually uh the appiplexity<00:27:56.480> and<00:27:56.560> time-bounded<00:27:56.920> entropy\nappiplexity and time-bounded entropy\nappiplexity and time-bounded entropy looks<00:27:57.560> for<00:27:57.720> each<00:27:57.880> of<00:27:57.920> these.\nlooks for each of these.\nlooks for each of these. So,<00:27:59.760> for<00:27:59.880> this<00:28:00.040> very<00:28:00.200> repetitive<00:28:00.679> code,\nSo, for this very repetitive code,\nSo, for this very repetitive code, we<00:28:02.240> can<00:28:02.360> have<00:28:02.480> a<00:28:02.520> very<00:28:02.760> simple<00:28:03.120> pro-<00:28:03.360> like,\nwe can have a very simple pro- like,\nwe can have a very simple pro- like, imagine<00:28:04.080> we<00:28:04.200> have<00:28:04.320> an<00:28:04.360> entire<00:28:04.640> data<00:28:04.880> set\nimagine we have an entire data set\nimagine we have an entire data set filled<00:28:06.520> with<00:28:06.720> just<00:28:07.320> boilerplate<00:28:08.160> super\nfilled with just boilerplate super\nfilled with just boilerplate super repetitive<00:28:09.240> code.\nrepetitive code.\nrepetitive code. An<00:28:11.800> LLM\nAn LLM\nAn LLM can<00:28:14.560> we<00:28:14.720> can,<00:28:15.000> with<00:28:15.160> a<00:28:15.200> very<00:28:15.400> small<00:28:15.760> LLM,\ncan we can, with a very small LLM,\ncan we can, with a very small LLM, do<00:28:17.160> a<00:28:17.200> very<00:28:17.400> good<00:28:17.600> job<00:28:18.120> at<00:28:18.280> predicting\ndo a very good job at predicting\ndo a very good job at predicting the<00:28:20.000> code<00:28:20.480> here.<00:28:21.120> We<00:28:21.240> don't<00:28:21.520> need<00:28:22.040> a<00:28:22.120> large<00:28:22.440> LLM\nthe code here. We don't need a large LLM\nthe code here. We don't need a large LLM to<00:28:23.240> do<00:28:23.600> those<00:28:23.800> good<00:28:23.960> predictions.\nto do those good predictions.\nto do those good predictions. And<00:28:25.360> because<00:28:25.679> we<00:28:25.800> pay<00:28:26.000> for<00:28:26.120> the<00:28:26.200> cost<00:28:26.800> of<00:28:26.919> the\nAnd because we pay for the cost of the\nAnd because we pay for the cost of the LLM<00:28:27.679> in<00:28:27.919> the<00:28:28.040> total<00:28:28.240> description<00:28:28.679> length,\nLLM in the total description length,\nLLM in the total description length, then<00:28:30.120> we<00:28:30.280> are<00:28:30.320> incentivized<00:28:31.120> in<00:28:31.240> the<00:28:31.360> search\nthen we are incentivized in the search\nthen we are incentivized in the search to<00:28:32.120> use<00:28:32.280> a<00:28:32.360> small<00:28:32.679> LLM\nto use a small LLM\nto use a small LLM or<00:28:33.880> other<00:28:34.120> probabilistic<00:28:34.679> model.\nor other probabilistic model.\nor other probabilistic model. And<00:28:36.440> so,<00:28:36.800> we<00:28:37.040> would<00:28:37.240> find<00:28:37.880> low<00:28:38.360> appiplexity,\nAnd so, we would find low appiplexity,\nAnd so, we would find low appiplexity, um<00:28:40.200> and<00:28:40.360> also<00:28:40.679> low<00:28:40.840> time-bounded<00:28:41.280> entropy,\num and also low time-bounded entropy,\num and also low time-bounded entropy, because<00:28:42.360> the<00:28:42.480> loss<00:28:43.000> would<00:28:43.120> be<00:28:43.200> small.<00:28:43.960> And<00:28:44.040> the\nbecause the loss would be small. And the\nbecause the loss would be small. And the same<00:28:44.320> thing<00:28:44.560> for,<00:28:44.760> say,<00:28:44.880> this<00:28:45.080> image<00:28:45.320> data.\nsame thing for, say, this image data.\nsame thing for, say, this image data. And<00:28:46.240> you<00:28:46.320> can<00:28:46.480> see<00:28:46.679> it<00:28:47.440> to<00:28:47.520> some<00:28:47.720> extent<00:28:48.159> in<00:28:48.280> the\nAnd you can see it to some extent in the\nAnd you can see it to some extent in the loss.\nloss.\nloss. Um\nUm\nUm in<00:28:50.960> that\nin that\nin that in<00:28:52.560> for<00:28:53.120> this<00:28:53.600> low<00:28:54.080> appiplexity<00:28:54.640> data,<00:28:55.000> the\nin for this low appiplexity data, the\nin for this low appiplexity data, the loss<00:28:55.600> decays<00:28:55.880> very<00:28:56.080> quickly\nloss decays very quickly\nloss decays very quickly with<00:28:57.919> the<00:28:58.440> the<00:28:58.880> the<00:28:59.000> steps,<00:28:59.640> um<00:28:59.960> and<00:29:00.159> with<00:29:00.280> the\nwith the the the steps, um and with the\nwith the the the steps, um and with the compute.<00:29:01.360> And<00:29:01.480> so,<00:29:01.520> spending<00:29:01.840> additional\ncompute. And so, spending additional\ncompute. And so, spending additional compute,<00:29:03.120> um<00:29:03.600> making<00:29:04.040> a<00:29:04.120> larger<00:29:04.440> model,<00:29:05.320> is\ncompute, um making a larger model, is\ncompute, um making a larger model, is not<00:29:06.000> going<00:29:06.159> to<00:29:06.240> benefit<00:29:06.560> us.\nnot going to benefit us.\nnot going to benefit us. On<00:29:07.440> the<00:29:07.520> other<00:29:07.679> hand,<00:29:08.159> for<00:29:08.679> random<00:29:08.960> noise\nOn the other hand, for random noise\nOn the other hand, for random noise data,<00:29:09.679> or<00:29:09.760> for<00:29:09.880> data<00:29:10.080> that<00:29:10.240> is<00:29:10.360> fundamentally\ndata, or for data that is fundamentally\ndata, or for data that is fundamentally unpredictable,\nunpredictable,\nunpredictable, um<00:29:13.159> or<00:29:13.320> at<00:29:13.400> least<00:29:13.640> unpredictable<00:29:14.200> given<00:29:14.400> a\num or at least unpredictable given a\num or at least unpredictable given a certain<00:29:14.640> amount<00:29:14.800> of<00:29:14.840> compute,<00:29:15.400> say,<00:29:16.320> you\ncertain amount of compute, say, you\ncertain amount of compute, say, you know,<00:29:17.080> what<00:29:17.600> uh<00:29:18.120> the<00:29:18.200> hash<00:29:18.560> of<00:29:18.679> our<00:29:19.240> uh<00:29:19.679> of<00:29:19.880> our\nknow, what uh the hash of our uh of our\nknow, what uh the hash of our uh of our API<00:29:20.600> key<00:29:20.760> is,\nAPI key is,\nAPI key is, that<00:29:22.400> also<00:29:23.520> the<00:29:23.679> optimal<00:29:24.080> model<00:29:24.320> size<00:29:24.720> will<00:29:24.880> be\nthat also the optimal model size will be\nthat also the optimal model size will be small.<00:29:25.720> And<00:29:25.840> by<00:29:25.919> the<00:29:26.000> way,<00:29:26.520> feel<00:29:26.720> free<00:29:27.040> to\nsmall. And by the way, feel free to\nsmall. And by the way, feel free to interrupt<00:29:27.560> me<00:29:27.720> with<00:29:27.880> questions.<00:29:29.080> Um<00:29:29.520> that's,\ninterrupt me with questions. Um that's,\ninterrupt me with questions. Um that's, you<00:29:30.000> know,\nyou know,\nyou know, that's<00:29:31.040> that's<00:29:31.320> a<00:29:31.880> real<00:29:32.040> part<00:29:32.159> of<00:29:32.240> this<00:29:32.320> talk.\nthat's that's a real part of this talk.\nthat's that's a real part of this talk. Happy<00:29:32.840> to<00:29:33.159> uh<00:29:33.520> happy<00:29:33.640> to<00:29:33.720> take<00:29:33.880> them.\nHappy to uh happy to take them.\nHappy to uh happy to take them. So,\nSo,\nSo, with<00:29:35.960> the<00:29:36.040> random<00:29:36.320> noise,<00:29:37.240> the<00:29:37.320> trouble<00:29:37.679> is<00:29:37.960> we\nwith the random noise, the trouble is we\nwith the random noise, the trouble is we can't<00:29:38.480> do<00:29:39.080> much<00:29:39.400> better\ncan't do much better\ncan't do much better than<00:29:41.159> well,<00:29:41.440> if<00:29:41.720> it's<00:29:41.840> purely<00:29:42.080> random<00:29:42.280> noise,\nthan well, if it's purely random noise,\nthan well, if it's purely random noise, we<00:29:42.560> can't<00:29:42.800> do<00:29:43.080> any<00:29:43.280> better<00:29:43.800> than<00:29:43.919> just<00:29:44.120> random\nwe can't do any better than just random\nwe can't do any better than just random predictions.\npredictions.\npredictions. And<00:29:45.760> you<00:29:45.840> can<00:29:45.960> make<00:29:46.200> random<00:29:46.480> predictions<00:29:47.240> a\nAnd you can make random predictions a\nAnd you can make random predictions a very<00:29:47.520> tiny<00:29:47.840> model.\nvery tiny model.\nvery tiny model. So<00:29:49.760> again,<00:29:50.040> thinking<00:29:50.320> about<00:29:50.480> this<00:29:50.640> two-part\nSo again, thinking about this two-part\nSo again, thinking about this two-part code<00:29:51.280> length,\ncode length,\ncode length, then<00:29:52.520> we<00:29:52.640> are<00:29:52.680> incentivized<00:29:53.480> to<00:29:53.640> use<00:29:54.040> a<00:29:54.120> very\nthen we are incentivized to use a very\nthen we are incentivized to use a very tiny<00:29:54.560> model.\nTrying<00:29:57.360> to<00:29:57.480> minimize<00:29:57.960> this<00:29:58.280> this<00:29:58.480> two-part\nTrying to minimize this this two-part\nTrying to minimize this this two-part code<00:29:59.000> length<00:29:59.520> on<00:29:59.720> this<00:29:59.840> noise<00:30:00.120> data,<00:30:00.400> we<00:30:00.560> will\ncode length on this noise data, we will\ncode length on this noise data, we will end<00:30:00.920> up<00:30:01.320> with<00:30:01.720> a<00:30:01.800> tiny<00:30:02.080> model,\nend up with a tiny model,\nend up with a tiny model, and<00:30:03.160> therefore<00:30:03.680> also<00:30:04.200> a<00:30:04.280> tiny<00:30:04.840> epi-plexity.\nand therefore also a tiny epi-plexity.\nand therefore also a tiny epi-plexity. And<00:30:06.400> that's<00:30:06.720> going<00:30:06.880> to<00:30:06.920> be<00:30:07.000> the<00:30:07.080> same<00:30:07.720> even<00:30:08.040> as\nAnd that's going to be the same even as\nAnd that's going to be the same even as we<00:30:08.360> increase<00:30:08.800> the<00:30:08.880> compute<00:30:09.240> bound.\nwe increase the compute bound.\nwe increase the compute bound. Um<00:30:10.600> whereas<00:30:11.120> the<00:30:11.280> time-bounded<00:30:11.720> entropy<00:30:12.240> is\nUm whereas the time-bounded entropy is\nUm whereas the time-bounded entropy is high.\nhigh.\nhigh. So<00:30:13.480> that<00:30:13.720> way<00:30:14.080> time-bounded<00:30:14.440> entropy\nSo that way time-bounded entropy\nSo that way time-bounded entropy captures<00:30:15.120> the<00:30:15.200> fact<00:30:15.520> that<00:30:16.240> we<00:30:16.360> have<00:30:16.560> this\ncaptures the fact that we have this\ncaptures the fact that we have this random<00:30:17.520> structure<00:30:17.880> this<00:30:18.160> randomness<00:30:18.520> here,\nrandom structure this randomness here,\nrandom structure this randomness here, um\num\num and<00:30:20.600> very<00:30:20.800> little<00:30:21.000> structure.<00:30:21.960> And<00:30:22.080> then<00:30:22.920> more\nand very little structure. And then more\nand very little structure. And then more interesting<00:30:23.520> data,<00:30:23.960> the<00:30:24.040> kind<00:30:24.560> that<00:30:24.840> we<00:30:25.000> think\ninteresting data, the kind that we think\ninteresting data, the kind that we think provides<00:30:26.240> useful<00:30:26.680> signal<00:30:27.080> to<00:30:27.200> train<00:30:27.480> on,\nprovides useful signal to train on,\nprovides useful signal to train on, is\nis\nis uh<00:30:31.880> in\nuh in\nuh in we<00:30:32.640> find,<00:30:33.200> right,<00:30:33.640> that\nwe find, right, that\nwe find, right, that we<00:30:35.280> get<00:30:35.680> large<00:30:36.000> models<00:30:36.800> on<00:30:36.920> this<00:30:37.040> data.<00:30:37.760> Why<00:30:37.880> is\nwe get large models on this data. Why is\nwe get large models on this data. Why is it<00:30:38.120> that<00:30:38.680> that<00:30:39.080> uh<00:30:39.440> we<00:30:39.560> have<00:30:39.720> such<00:30:39.960> large\nit that that uh we have such large\nit that that uh we have such large models\nmodels\nmodels for\nfor\nfor uh<00:30:43.400> doing<00:30:43.640> generative<00:30:43.960> modeling<00:30:44.320> of<00:30:44.440> images\nuh doing generative modeling of images\nuh doing generative modeling of images or<00:30:45.360> for<00:30:45.480> language<00:30:45.800> models<00:30:46.280> on<00:30:46.760> text<00:30:47.280> and<00:30:47.400> code?\nor for language models on text and code?\nor for language models on text and code? It's<00:30:48.440> because<00:30:48.680> there's<00:30:48.800> a<00:30:48.880> lot<00:30:49.080> to<00:30:49.200> learn.<00:30:50.120> And\nIt's because there's a lot to learn. And\nIt's because there's a lot to learn. And actually<00:30:50.680> even<00:30:51.160> from<00:30:51.520> this<00:30:51.720> MDL<00:30:52.000> perspective,\nactually even from this MDL perspective,\nactually even from this MDL perspective, we<00:30:53.360> are<00:30:53.520> incentivized<00:30:54.160> to<00:30:54.240> learn<00:30:54.400> a<00:30:54.440> lot\nwe are incentivized to learn a lot\nwe are incentivized to learn a lot because<00:30:55.000> incorporating<00:30:55.560> the<00:30:55.640> structure<00:30:55.920> into\nbecause incorporating the structure into\nbecause incorporating the structure into the<00:30:56.120> model<00:30:56.360> still<00:30:56.800> leads<00:30:57.200> to<00:30:57.600> reductions<00:30:58.560> in\nthe model still leads to reductions in\nthe model still leads to reductions in the<00:30:59.320> total<00:30:59.720> description<00:31:00.200> length.\nthe total description length.\nthe total description length. Right?<00:31:01.920> So<00:31:02.080> with<00:31:02.160> this<00:31:02.320> interesting,<00:31:03.040> you\nRight? So with this interesting, you\nRight? So with this interesting, you know,<00:31:03.360> complex,<00:31:04.280> partially<00:31:04.680> predictable,\nknow, complex, partially predictable,\nknow, complex, partially predictable, partially<00:31:05.560> unpredictable<00:31:06.880> uh<00:31:06.960> code,<00:31:07.760> as<00:31:07.960> we\npartially unpredictable uh code, as we\npartially unpredictable uh code, as we spend<00:31:08.560> additional<00:31:09.000> computation,<00:31:10.160> our\nspend additional computation, our\nspend additional computation, our predictions<00:31:10.720> get<00:31:10.880> better,\npredictions get better,\npredictions get better, and<00:31:12.520> the<00:31:12.640> optimal<00:31:12.920> model<00:31:13.160> size<00:31:13.760> gets<00:31:13.920> bigger.\nand the optimal model size gets bigger.\nand the optimal model size gets bigger. This<00:31:15.640> high<00:31:15.800> epi-plexity<00:31:16.880> and<00:31:17.640> yeah.\nNow,<00:31:21.080> in<00:31:21.200> the<00:31:21.280> paper<00:31:21.600> we<00:31:21.680> have<00:31:21.800> a<00:31:21.840> couple<00:31:22.120> ways\nNow, in the paper we have a couple ways\nNow, in the paper we have a couple ways of<00:31:22.800> estimating<00:31:23.240> epi-plexity.\nof estimating epi-plexity.\nof estimating epi-plexity. The<00:31:25.400> one<00:31:25.600> that<00:31:25.720> we<00:31:25.840> use<00:31:26.320> for<00:31:26.480> most<00:31:26.760> of\nThe one that we use for most of\nThe one that we use for most of experiments<00:31:27.720> is<00:31:27.960> with<00:31:28.120> this<00:31:28.360> particular\nexperiments is with this particular\nexperiments is with this particular coding<00:31:29.120> scheme.\ncoding scheme.\ncoding scheme. The<00:31:30.760> thought<00:31:31.040> is,<00:31:31.760> okay,<00:31:32.000> we<00:31:32.160> have<00:31:32.360> this\nThe thought is, okay, we have this\nThe thought is, okay, we have this general<00:31:33.080> model<00:31:33.320> class,<00:31:34.040> all<00:31:34.240> of<00:31:34.320> these\ngeneral model class, all of these\ngeneral model class, all of these time-bounded<00:31:35.200> programs<00:31:36.040> that<00:31:36.320> admit\ntime-bounded programs that admit\ntime-bounded programs that admit probability<00:31:37.000> distributions,<00:31:38.240> that<00:31:38.320> we're\nprobability distributions, that we're\nprobability distributions, that we're going<00:31:38.600> to<00:31:38.720> use<00:31:39.040> but<00:31:39.160> instead<00:31:39.440> we're<00:31:39.520> going<00:31:39.640> to\ngoing to use but instead we're going to\ngoing to use but instead we're going to use<00:31:40.280> um<00:31:40.640> neural<00:31:40.800> networks<00:31:41.160> for<00:31:41.240> this.\nuse um neural networks for this.\nuse um neural networks for this. And<00:31:42.440> in<00:31:42.520> the<00:31:42.600> paper,<00:31:43.200> even<00:31:43.400> more\nAnd in the paper, even more\nAnd in the paper, even more specifically,<00:31:44.800> uh<00:31:45.120> auto-regressive\nspecifically, uh auto-regressive\nspecifically, uh auto-regressive transformers.\ntransformers.\ntransformers. So<00:31:47.880> the<00:31:47.960> question<00:31:48.320> then<00:31:48.680> is\nSo the question then is\nSo the question then is how<00:31:51.120> do<00:31:51.360> we\nhow do we\nhow do we uh<00:31:53.400> create<00:31:53.760> short<00:31:54.040> codes<00:31:54.880> for<00:31:55.120> those<00:31:55.480> models?\nuh create short codes for those models?\nuh create short codes for those models? And<00:31:58.000> just<00:31:58.760> counting<00:31:59.040> the<00:31:59.120> parameters<00:31:59.840> doesn't\nAnd just counting the parameters doesn't\nAnd just counting the parameters doesn't work<00:32:00.280> very<00:32:00.440> well\nwork very well\nwork very well because<00:32:02.200> you<00:32:02.320> can<00:32:02.440> have\nbecause you can have\nbecause you can have let's<00:32:04.000> say<00:32:04.160> we<00:32:04.280> have<00:32:04.440> a<00:32:04.480> massive<00:32:04.960> model\nlet's say we have a massive model\nlet's say we have a massive model and<00:32:06.280> we<00:32:06.360> train<00:32:06.640> it<00:32:06.920> on<00:32:07.760> random<00:32:08.000> noise,\nand we train it on random noise,\nand we train it on random noise, there's<00:32:09.360> very<00:32:09.560> little<00:32:09.760> information<00:32:10.240> in<00:32:10.320> that\nthere's very little information in that\nthere's very little information in that model.<00:32:11.000> You<00:32:11.120> could<00:32:11.240> have<00:32:11.320> used<00:32:11.440> a<00:32:11.480> much\nmodel. You could have used a much\nmodel. You could have used a much smaller<00:32:11.840> model.\nsmaller model.\nsmaller model. Um<00:32:13.920> but<00:32:14.360> if<00:32:14.480> you're<00:32:14.560> just<00:32:14.720> counting<00:32:14.960> the\nUm but if you're just counting the\nUm but if you're just counting the parameters,<00:32:15.640> you<00:32:15.880> would<00:32:16.000> think<00:32:16.240> that<00:32:16.480> you\nparameters, you would think that you\nparameters, you would think that you have<00:32:16.679> a<00:32:16.720> large<00:32:16.960> number.<00:32:17.440> So<00:32:17.560> we<00:32:17.600> need<00:32:17.800> a<00:32:17.920> uh\nhave a large number. So we need a uh\nhave a large number. So we need a uh slightly<00:32:18.520> more\nslightly more\nslightly more uh<00:32:20.120> sophisticated<00:32:20.679> code.\nuh sophisticated code.\nuh sophisticated code. And<00:32:21.720> that's<00:32:22.120> where<00:32:22.400> this<00:32:22.679> re-quential<00:32:23.160> coding\nAnd that's where this re-quential coding\nAnd that's where this re-quential coding comes<00:32:23.720> in.<00:32:24.320> Now,<00:32:24.440> I'm<00:32:24.520> not<00:32:24.640> going<00:32:24.760> to<00:32:24.800> go<00:32:24.960> into\ncomes in. Now, I'm not going to go into\ncomes in. Now, I'm not going to go into this<00:32:25.440> in<00:32:25.920> great<00:32:26.160> detail.\nthis in great detail.\nthis in great detail. Definitely<00:32:27.800> uh<00:32:27.960> first<00:32:28.160> to<00:32:28.200> the<00:32:28.280> paper<00:32:28.480> for\nDefinitely uh first to the paper for\nDefinitely uh first to the paper for that,<00:32:28.720> but<00:32:28.800> it's<00:32:28.920> a<00:32:28.960> really<00:32:29.120> cool<00:32:29.320> coding\nthat, but it's a really cool coding\nthat, but it's a really cool coding technique<00:32:30.080> that<00:32:30.240> we<00:32:30.320> came<00:32:30.520> up<00:32:30.679> with\ntechnique that we came up with\ntechnique that we came up with where<00:32:32.720> um\nwhere um\nwhere um we<00:32:34.080> try<00:32:34.640> to\nwe try to\nwe try to make<00:32:35.920> an<00:32:36.000> explicit<00:32:36.600> code<00:32:37.160> that<00:32:37.400> separates<00:32:37.960> out\nmake an explicit code that separates out\nmake an explicit code that separates out the<00:32:39.920> this<00:32:40.240> structural<00:32:41.280> the<00:32:41.400> amount<00:32:41.720> that<00:32:41.920> is\nthe this structural the amount that is\nthe this structural the amount that is needed<00:32:42.240> to<00:32:42.320> code<00:32:42.760> the\nneeded to code the\nneeded to code the you<00:32:43.600> know,<00:32:43.760> the<00:32:44.400> all<00:32:44.520> the<00:32:44.600> structure<00:32:44.960> in<00:32:45.040> the\nyou know, the all the structure in the\nyou know, the all the structure in the model<00:32:45.400> that<00:32:45.520> it<00:32:45.640> uses<00:32:45.920> for<00:32:46.040> predictions,\nmodel that it uses for predictions,\nmodel that it uses for predictions, um\num\num uh<00:32:49.120> also<00:32:49.400> not<00:32:49.600> paying<00:32:50.040> the<00:32:50.320> the<00:32:50.400> cost<00:32:50.760> for<00:32:50.960> the\nuh also not paying the the cost for the\nuh also not paying the the cost for the the<00:32:51.560> the<00:32:51.679> data,<00:32:52.679> um<00:32:53.040> but<00:32:53.560> that<00:32:54.480> is<00:32:54.720> somewhat\nthe the data, um but that is somewhat\nthe the data, um but that is somewhat decoupled<00:32:55.520> from<00:32:55.640> the<00:32:55.720> number<00:32:55.920> of<00:32:56.000> parameters.\ndecoupled from the number of parameters.\ndecoupled from the number of parameters. And<00:32:57.440> the<00:32:57.520> way<00:32:57.679> it<00:32:57.800> works<00:32:58.480> is<00:32:58.800> that<00:32:58.960> we<00:32:59.080> have\nAnd the way it works is that we have\nAnd the way it works is that we have really<00:32:59.880> two<00:33:00.120> models.\nreally two models.\nreally two models. We<00:33:01.200> have<00:33:01.320> a<00:33:01.400> student<00:33:01.840> model<00:33:02.280> and<00:33:02.360> a<00:33:02.400> teacher\nWe have a student model and a teacher\nWe have a student model and a teacher model.\nmodel.\nmodel. And<00:33:04.720> we<00:33:04.840> somehow<00:33:05.600> use<00:33:05.960> the<00:33:06.080> teacher<00:33:06.960> to\nAnd we somehow use the teacher to\nAnd we somehow use the teacher to uh<00:33:08.360> we<00:33:08.520> code<00:33:09.720> data\nuh we code data\nuh we code data from<00:33:12.040> the<00:33:12.160> teacher's<00:33:12.679> distribution\nfrom the teacher's distribution\nfrom the teacher's distribution um<00:33:14.840> using<00:33:15.520> the<00:33:15.640> student\num using the student\num using the student and<00:33:17.679> then<00:33:18.120> train<00:33:18.440> the<00:33:18.520> student<00:33:18.840> on<00:33:18.920> that<00:33:19.080> data\nand then train the student on that data\nand then train the student on that data and<00:33:19.920> then<00:33:20.080> repeat.\nand then repeat.\nand then repeat. And<00:33:22.679> yeah,<00:33:22.840> so<00:33:23.000> it's<00:33:23.160> it's<00:33:23.320> a<00:33:23.360> little<00:33:23.600> bit<00:33:23.720> of<00:33:23.800> a\nAnd yeah, so it's it's a little bit of a\nAnd yeah, so it's it's a little bit of a tricky<00:33:24.160> thing,<00:33:24.560> um<00:33:24.840> but<00:33:25.160> at<00:33:25.240> the<00:33:25.360> end<00:33:25.480> of<00:33:25.560> the\ntricky thing, um but at the end of the\ntricky thing, um but at the end of the day,<00:33:26.280> what<00:33:26.400> we<00:33:26.560> get<00:33:27.480> is<00:33:27.600> a<00:33:27.679> code<00:33:28.000> length<00:33:28.280> for<00:33:28.400> a\nday, what we get is a code length for a\nday, what we get is a code length for a model<00:33:29.440> which<00:33:29.640> is<00:33:30.480> essentially<00:33:31.040> the<00:33:31.160> area\nmodel which is essentially the area\nmodel which is essentially the area between<00:33:32.200> these<00:33:32.440> two<00:33:32.600> curves,<00:33:33.240> between<00:33:33.760> the\nbetween these two curves, between the\nbetween these two curves, between the loss<00:33:34.480> of<00:33:34.679> the<00:33:34.800> teacher<00:33:35.120> model\nloss of the teacher model\nloss of the teacher model in<00:33:36.480> blue,<00:33:36.880> and<00:33:37.000> then<00:33:37.080> the<00:33:37.160> loss<00:33:37.440> of<00:33:37.520> the\nin blue, and then the loss of the\nin blue, and then the loss of the student<00:33:37.880> model<00:33:38.400> trained<00:33:39.240> on<00:33:39.480> the<00:33:39.560> data\nstudent model trained on the data\nstudent model trained on the data produced<00:33:40.160> by<00:33:40.240> that<00:33:40.440> teacher.<00:33:41.120> The<00:33:41.240> area\nproduced by that teacher. The area\nproduced by that teacher. The area between<00:33:41.920> those<00:33:42.120> two<00:33:42.280> curves\nbetween those two curves\nbetween those two curves essentially<00:33:44.360> gives<00:33:44.720> you<00:33:45.240> I<00:33:45.280> mean,<00:33:45.600> we<00:33:45.720> have<00:33:45.880> a\nessentially gives you I mean, we have a\nessentially gives you I mean, we have a uh<00:33:46.400> a<00:33:46.440> very,<00:33:46.800> you<00:33:46.880> know,<00:33:47.160> um<00:33:47.400> precise<00:33:47.840> code,\nuh a very, you know, um precise code,\nuh a very, you know, um precise code, but<00:33:48.760> um<00:33:49.160> I'm<00:33:49.320> just<00:33:49.960> uh<00:33:50.080> laying<00:33:50.280> it<00:33:50.360> out<00:33:50.440> in\nbut um I'm just uh laying it out in\nbut um I'm just uh laying it out in high-level<00:33:50.840> terms<00:33:51.040> here,<00:33:51.640> um<00:33:51.960> gives<00:33:52.240> you<00:33:52.440> a\nhigh-level terms here, um gives you a\nhigh-level terms here, um gives you a code<00:33:53.240> for<00:33:53.880> this<00:33:54.440> final<00:33:55.120> student<00:33:55.480> model.<00:33:56.240> And\ncode for this final student model. And\ncode for this final student model. And this<00:33:56.520> code<00:33:57.600> is<00:33:57.800> going<00:33:58.120> to<00:33:58.560> vary<00:33:59.040> even<00:33:59.280> with<00:33:59.440> a\nthis code is going to vary even with a\nthis code is going to vary even with a large<00:33:59.920> this<00:34:00.080> code<00:34:00.320> can<00:34:00.440> be<00:34:00.560> small<00:34:01.040> even<00:34:01.240> with<00:34:01.400> a\nlarge this code can be small even with a\nlarge this code can be small even with a large<00:34:01.720> model<00:34:02.040> with<00:34:02.120> lots<00:34:02.360> of<00:34:02.440> parameters,\nlarge model with lots of parameters,\nlarge model with lots of parameters, um<00:34:04.120> and<00:34:04.400> so<00:34:04.800> we<00:34:04.960> can<00:34:05.080> actually<00:34:05.360> be<00:34:05.679> and<00:34:05.840> and\num and so we can actually be and and\num and so we can actually be and and it's<00:34:06.080> actually<00:34:06.320> quite<00:34:06.520> competitive<00:34:07.280> just\nit's actually quite competitive just\nit's actually quite competitive just thinking<00:34:07.679> about<00:34:07.880> the<00:34:07.960> best<00:34:08.679> compression<00:34:09.240> that\nthinking about the best compression that\nthinking about the best compression that you<00:34:09.440> can<00:34:09.640> do<00:34:10.399> for\nyou can do for\nyou can do for an<00:34:11.919> auto-regressive<00:34:12.399> transformer.\nan auto-regressive transformer.\nan auto-regressive transformer. So<00:34:15.440> then<00:34:15.800> we<00:34:15.919> just<00:34:16.120> train<00:34:16.600> many<00:34:16.840> different\nSo then we just train many different\nSo then we just train many different networks<00:34:17.640> with<00:34:17.720> different<00:34:17.919> parameters<00:34:18.280> to\nnetworks with different parameters to\nnetworks with different parameters to compute\ncompute\ncompute compute<00:34:19.560> the<00:34:19.640> total<00:34:19.919> code<00:34:20.120> length<00:34:20.960> um\ncompute the total code length um\ncompute the total code length um before<00:34:22.640> again<00:34:23.000> taking<00:34:23.399> this<00:34:23.640> code<00:34:24.080> for<00:34:24.240> the\nbefore again taking this code for the\nbefore again taking this code for the neural<00:34:24.520> network<00:34:25.280> and<00:34:25.440> then<00:34:25.600> also<00:34:26.120> taking<00:34:26.399> the\nneural network and then also taking the\nneural network and then also taking the code<00:34:26.960> for<00:34:27.040> the<00:34:27.159> data<00:34:27.640> given<00:34:27.840> that<00:34:27.960> network.<00:34:28.879> Um\ncode for the data given that network. Um\ncode for the data given that network. Um and<00:34:29.240> then<00:34:29.359> we<00:34:29.440> just<00:34:29.640> evaluate\nand then we just evaluate\nand then we just evaluate among<00:34:31.280> all<00:34:31.399> these<00:34:31.600> different<00:34:32.040> candidates,\namong all these different candidates,\namong all these different candidates, all<00:34:33.120> the<00:34:33.240> you<00:34:33.320> know,<00:34:33.399> we<00:34:33.560> lay<00:34:33.800> them<00:34:33.960> all<00:34:34.159> out<00:34:34.359> on\nall the you know, we lay them all out on\nall the you know, we lay them all out on the<00:34:34.520> same<00:34:34.760> curve<00:34:35.480> that<00:34:35.640> has<00:34:35.960> compute<00:34:36.359> on<00:34:36.480> the\nthe same curve that has compute on the\nthe same curve that has compute on the x-axis<00:34:37.600> and<00:34:38.080> this<00:34:38.919> total<00:34:39.159> description<00:34:39.560> length\nx-axis and this total description length\nx-axis and this total description length on<00:34:39.879> the<00:34:39.960> y-axis,\non the y-axis,\non the y-axis, and<00:34:41.240> we<00:34:41.359> just<00:34:41.560> take<00:34:41.760> the<00:34:41.840> ones<00:34:42.280> on<00:34:42.480> this\nand we just take the ones on this\nand we just take the ones on this frontier\nfrontier\nfrontier and<00:34:44.159> take<00:34:44.800> well,<00:34:45.359> take<00:34:45.720> the<00:34:46.080> uh\nand take well, take the uh\nand take well, take the uh the<00:34:47.640> the<00:34:47.720> code<00:34:47.919> length<00:34:48.240> for<00:34:48.359> the<00:34:48.440> models<00:34:48.760> on\nthe the code length for the models on\nthe the code length for the models on that<00:34:49.000> frontier,<00:34:49.480> right?<00:34:49.640> So<00:34:49.760> here<00:34:50.000> is\nthat frontier, right? So here is\nthat frontier, right? So here is example,<00:34:51.120> you<00:34:51.200> have<00:34:51.320> many<00:34:51.520> different<00:34:52.320> uh\nexample, you have many different uh\nexample, you have many different uh uh<00:34:53.080> models<00:34:53.320> with<00:34:53.399> different<00:34:53.600> number<00:34:53.720> of\nuh models with different number of\nuh models with different number of parameters,<00:34:54.760> they<00:34:55.280> each<00:34:55.879> have<00:34:56.000> this<00:34:56.200> little\nparameters, they each have this little\nparameters, they each have this little U-shaped<00:34:56.840> curve,<00:34:57.120> we<00:34:57.240> overlay<00:34:57.640> them,<00:34:58.440> um<00:34:58.760> and\nU-shaped curve, we overlay them, um and\nU-shaped curve, we overlay them, um and then<00:34:59.080> this\nthen this\nthen this time-bounded<00:35:00.440> entropy<00:35:01.000> is<00:35:01.320> is<00:35:01.440> going<00:35:01.680> down<00:35:02.080> as\ntime-bounded entropy is is going down as\ntime-bounded entropy is is going down as we<00:35:02.440> increase<00:35:02.800> the<00:35:02.880> amount<00:35:03.040> of<00:35:03.120> compute<00:35:03.359> that\nwe increase the amount of compute that\nwe increase the amount of compute that we<00:35:03.520> have<00:35:03.800> by<00:35:04.200> increasing<00:35:04.560> the<00:35:04.640> number<00:35:04.760> of\nwe have by increasing the number of\nwe have by increasing the number of parameters,<00:35:05.720> um<00:35:06.359> and<00:35:06.520> also<00:35:06.720> increasing<00:35:07.120> the\nparameters, um and also increasing the\nparameters, um and also increasing the number<00:35:07.480> of<00:35:07.880> uh\nnumber of uh\nnumber of uh uh<00:35:08.720> data<00:35:08.840> points<00:35:09.040> that<00:35:09.120> we<00:35:09.160> train<00:35:09.359> on,<00:35:10.000> um<00:35:10.320> and\nuh data points that we train on, um and\nuh data points that we train on, um and then<00:35:11.080> uh\nthen uh\nthen uh right,<00:35:12.040> and<00:35:12.120> then<00:35:12.240> here\nSo\nSo\nSo circling<00:35:17.280> back<00:35:17.720> to\ncircling back to\ncircling back to Andrew's<00:35:20.640> uh<00:35:20.800> right,<00:35:21.000> I<00:35:21.040> mean,<00:35:21.160> this<00:35:21.320> framing\nAndrew's uh right, I mean, this framing\nAndrew's uh right, I mean, this framing that<00:35:21.680> we<00:35:21.760> have,<00:35:22.359> um\nthat we have, um\nthat we have, um three<00:35:23.760> paradoxes<00:35:24.480> of<00:35:24.600> information,<00:35:25.160> right?\nthree paradoxes of information, right?\nthree paradoxes of information, right? Uh<00:35:25.960> or<00:35:26.080> apparent<00:35:26.400> paradoxes.<00:35:27.359> So\nUh or apparent paradoxes. So\nUh or apparent paradoxes. So we'll<00:35:29.120> now<00:35:29.440> go<00:35:29.600> through<00:35:29.800> them<00:35:30.280> and<00:35:30.840> see<00:35:31.440> if<00:35:31.600> we\nwe'll now go through them and see if we\nwe'll now go through them and see if we can<00:35:32.600> reinterpret<00:35:33.120> them<00:35:33.640> with<00:35:33.800> the<00:35:33.880> help<00:35:34.320> of\ncan reinterpret them with the help of\ncan reinterpret them with the help of these<00:35:34.960> theoretical<00:35:35.320> tools<00:35:36.120> like\nthese theoretical tools like\nthese theoretical tools like epi-plexity.\nepi-plexity.\nepi-plexity. So<00:35:37.560> the<00:35:37.640> first<00:35:37.840> one,<00:35:38.160> information<00:35:38.600> cannot<00:35:38.800> be\nSo the first one, information cannot be\nSo the first one, information cannot be increased<00:35:39.359> by<00:35:39.480> deterministic<00:35:40.000> processes,\nincreased by deterministic processes,\nincreased by deterministic processes, right?<00:35:41.680> In<00:35:41.760> fact,<00:35:42.000> we<00:35:42.040> will<00:35:42.160> find<00:35:42.400> that\nright? In fact, we will find that\nright? In fact, we will find that time-bounded<00:35:43.320> entropy<00:35:43.680> and<00:35:43.800> epi-plexity<00:35:44.680> can\ntime-bounded entropy and epi-plexity can\ntime-bounded entropy and epi-plexity can be<00:35:45.720> created<00:35:46.160> through<00:35:46.359> computation.\nbe created through computation.\nbe created through computation. So<00:35:47.920> the<00:35:48.000> first<00:35:48.240> example<00:35:49.000> is<00:35:49.120> the<00:35:49.200> one<00:35:49.359> Andrew\nSo the first example is the one Andrew\nSo the first example is the one Andrew mentioned<00:35:50.000> before,<00:35:50.640> which<00:35:50.880> is<00:35:51.240> pseudo-random\nmentioned before, which is pseudo-random\nmentioned before, which is pseudo-random generators.\ngenerators.\ngenerators. So<00:35:54.000> um<00:35:54.359> I<00:35:54.400> think<00:35:54.760> uh<00:35:54.880> Andrew<00:35:55.480> uh<00:35:55.840> right,\nSo um I think uh Andrew uh right,\nSo um I think uh Andrew uh right, alluded<00:35:57.080> and<00:35:57.400> you<00:35:57.440> know,<00:35:57.560> a<00:35:57.600> definition<00:35:58.080> is<00:35:58.400> or\nalluded and you know, a definition is or\nalluded and you know, a definition is or yeah,<00:35:59.280> uh<00:35:59.359> let's<00:35:59.560> see.<00:35:59.800> Um<00:36:00.440> right,<00:36:00.640> so<00:36:00.920> just\nyeah, uh let's see. Um right, so just\nyeah, uh let's see. Um right, so just just<00:36:01.480> reiterating<00:36:02.200> um<00:36:02.880> uh\njust reiterating um uh\njust reiterating um uh that<00:36:03.760> you<00:36:03.880> can<00:36:04.120> define<00:36:04.960> a<00:36:05.600> pseudo-random<00:36:06.520> a\nthat you can define a pseudo-random a\nthat you can define a pseudo-random a generator<00:36:07.520> um<00:36:07.760> in<00:36:07.840> terms<00:36:08.080> of<00:36:08.200> there's<00:36:08.359> no\ngenerator um in terms of there's no\ngenerator um in terms of there's no polynomial<00:36:09.040> size<00:36:09.359> circuit<00:36:10.280> this\npolynomial size circuit this\npolynomial size circuit this discriminator<00:36:11.000> D<00:36:11.240> that<00:36:11.440> can<00:36:11.560> distinguish<00:36:11.960> the\ndiscriminator D that can distinguish the\ndiscriminator D that can distinguish the output<00:36:12.280> sequence<00:36:12.720> from<00:36:12.880> random\noutput sequence from random\noutput sequence from random substantially<00:36:13.800> better<00:36:14.560> than<00:36:15.120> random<00:36:15.440> chance.\nsubstantially better than random chance.\nsubstantially better than random chance. So<00:36:16.400> here<00:36:16.760> is<00:36:17.000> this<00:36:17.480> D,<00:36:18.080> here<00:36:18.320> is<00:36:18.520> this\nSo here is this D, here is this\nSo here is this D, here is this generator<00:36:19.160> G<00:36:19.840> on<00:36:20.120> input<00:36:20.480> seed,<00:36:20.920> and<00:36:21.040> then<00:36:21.160> here\ngenerator G on input seed, and then here\ngenerator G on input seed, and then here is<00:36:21.480> just<00:36:21.920> um<00:36:22.600> uh<00:36:22.800> uniform<00:36:23.280> random.<00:36:24.000> And<00:36:24.120> the\nis just um uh uniform random. And the\nis just um uh uniform random. And the point<00:36:24.520> is<00:36:24.760> that\npoint is that\npoint is that our<00:36:26.160> distinguisher,<00:36:27.280> the<00:36:27.720> uh<00:36:27.880> the<00:36:27.960> difference\nour distinguisher, the uh the difference\nour distinguisher, the uh the difference in<00:36:28.359> those<00:36:28.520> probabilities,<00:36:29.560> is<00:36:30.440> um<00:36:30.800> is\nin those probabilities, is um is\nin those probabilities, is um is actually<00:36:31.240> a<00:36:31.280> negligible<00:36:31.800> function,<00:36:32.359> so<00:36:32.480> it\nactually a negligible function, so it\nactually a negligible function, so it decays<00:36:32.880> faster<00:36:33.320> than<00:36:33.960> uh<00:36:34.080> one<00:36:34.320> over<00:36:34.560> any\ndecays faster than uh one over any\ndecays faster than uh one over any polynomial.\npolynomial.\npolynomial. This<00:36:36.359> is<00:36:36.440> epsilon.\nThis is epsilon.\nThis is epsilon. Uh<00:36:38.400> and<00:36:39.040> what<00:36:39.200> we<00:36:39.320> can<00:36:39.480> show<00:36:40.120> is<00:36:40.440> that<00:36:40.640> these\nUh and what we can show is that these\nUh and what we can show is that these PRGs\nPRGs\nPRGs have\nhave\nhave large<00:36:45.160> time-bounded<00:36:46.160> entropy\nlarge time-bounded entropy\nlarge time-bounded entropy um<00:36:48.200> and<00:36:48.359> low<00:36:48.520> epi-plexity,<00:36:49.320> but<00:36:49.480> large\num and low epi-plexity, but large\num and low epi-plexity, but large time-bounded<00:36:50.359> entropy<00:36:50.840> in<00:36:50.960> contrast<00:36:51.840> with\ntime-bounded entropy in contrast with\ntime-bounded entropy in contrast with Kolmogorov<00:36:53.680> complexity,<00:36:54.480> in<00:36:54.600> contrast<00:36:55.120> with\nKolmogorov complexity, in contrast with\nKolmogorov complexity, in contrast with uh<00:36:56.160> Shannon<00:36:56.440> information,<00:36:56.960> or<00:36:57.080> even\nuh Shannon information, or even\nuh Shannon information, or even time-bounded<00:36:58.400> Kolmogorov<00:36:58.760> complexity.<00:36:59.760> Um\ntime-bounded Kolmogorov complexity. Um\ntime-bounded Kolmogorov complexity. Um where<00:37:00.120> actually<00:37:00.640> that<00:37:01.120> this<00:37:01.720> time-bounded\nwhere actually that this time-bounded\nwhere actually that this time-bounded entropy<00:37:02.480> is<00:37:02.640> nearly<00:37:03.000> maximum.\nentropy is nearly maximum.\nentropy is nearly maximum. Um<00:37:05.160> again,<00:37:05.440> with<00:37:05.560> this<00:37:05.720> epsilon<00:37:06.080> related<00:37:06.359> to\nUm again, with this epsilon related to\nUm again, with this epsilon related to this<00:37:06.640> advantage.\nthis advantage.\nthis advantage. So<00:37:08.480> then<00:37:08.880> also<00:37:09.440> here<00:37:10.080> uh\nSo then also here uh\nSo then also here uh we'll<00:37:10.960> go<00:37:11.320> So<00:37:11.480> this<00:37:11.640> is<00:37:11.760> an<00:37:11.840> example<00:37:12.240> where\nwe'll go So this is an example where\nwe'll go So this is an example where through<00:37:14.200> computation,<00:37:15.080> we<00:37:15.359> are<00:37:15.560> able<00:37:15.800> to\nthrough computation, we are able to\nthrough computation, we are able to produce<00:37:16.200> time-bounded<00:37:16.720> entropy,<00:37:17.440> right?\nproduce time-bounded entropy, right?\nproduce time-bounded entropy, right? Taking<00:37:18.000> the<00:37:18.080> initial<00:37:18.520> what<00:37:18.640> we<00:37:18.760> had,<00:37:19.200> this<00:37:19.400> K\nTaking the initial what we had, this K\nTaking the initial what we had, this K from<00:37:20.200> just<00:37:20.400> the<00:37:20.480> size<00:37:20.760> of<00:37:20.800> the<00:37:20.880> seed,<00:37:21.720> and\nfrom just the size of the seed, and\nfrom just the size of the seed, and turning<00:37:22.120> it<00:37:22.240> into<00:37:22.800> something<00:37:23.120> very<00:37:23.320> close<00:37:23.520> to\nturning it into something very close to\nturning it into something very close to N.\nN.\nN. But\nBut\nBut what<00:37:26.359> we<00:37:26.480> would<00:37:26.600> really<00:37:26.840> like<00:37:27.800> is<00:37:28.560> something\nwhat we would really like is something\nwhat we would really like is something that<00:37:29.280> can<00:37:29.400> create<00:37:30.120> structured<00:37:31.320> information,\nthat can create structured information,\nthat can create structured information, something<00:37:32.160> that<00:37:32.280> can<00:37:32.400> create<00:37:32.680> epi-plexity.\nsomething that can create epi-plexity.\nsomething that can create epi-plexity. That's<00:37:34.000> a<00:37:34.280> a<00:37:34.320> harder<00:37:34.560> beast,<00:37:34.880> but<00:37:35.440> we<00:37:35.600> can<00:37:35.840> at\nThat's a a harder beast, but we can at\nThat's a a harder beast, but we can at least<00:37:36.880> um\nleast um\nleast um turn<00:37:38.080> to<00:37:39.040> uh<00:37:39.240> some<00:37:40.160> uh<00:37:40.320> already<00:37:40.600> studied\nturn to uh some uh already studied\nturn to uh some uh already studied examples<00:37:41.520> like<00:37:42.120> cellular<00:37:42.440> automaton.\nexamples like cellular automaton.\nexamples like cellular automaton. So<00:37:44.080> here<00:37:44.480> are<00:37:44.600> these<00:37:45.280> rule<00:37:45.840> 15,<00:37:46.359> rule<00:37:46.520> 30,<00:37:46.880> and\nSo here are these rule 15, rule 30, and\nSo here are these rule 15, rule 30, and rule<00:37:47.200> 54\nrule 54\nrule 54 um<00:37:48.640> cellular<00:37:48.920> automaton<00:37:49.920> from<00:37:50.280> random\num cellular automaton from random\num cellular automaton from random initial<00:37:50.840> conditions<00:37:51.280> with<00:37:51.400> a<00:37:51.440> fixed<00:37:51.760> width\ninitial conditions with a fixed width\ninitial conditions with a fixed width with<00:37:53.560> time<00:37:53.800> going<00:37:54.040> down.<00:37:54.800> Uh<00:37:54.880> of<00:37:55.000> course,<00:37:55.240> the\nwith time going down. Uh of course, the\nwith time going down. Uh of course, the rule<00:37:55.520> 15,<00:37:56.080> as<00:37:56.200> Andrew<00:37:56.359> mentioned,<00:37:56.680> right,<00:37:56.840> is\nrule 15, as Andrew mentioned, right, is\nrule 15, as Andrew mentioned, right, is this<00:37:57.160> is<00:37:57.400> very<00:37:57.920> um<00:37:58.520> very<00:37:58.720> very<00:37:58.960> boring<00:37:59.400> and<00:37:59.680> and\nthis is very um very very boring and and\nthis is very um very very boring and and just<00:38:00.280> uh<00:38:00.320> predictable.<00:38:01.000> Um<00:38:01.440> rule<00:38:01.640> 30<00:38:02.040> is\njust uh predictable. Um rule 30 is\njust uh predictable. Um rule 30 is essentially<00:38:03.440> uh<00:38:03.560> is<00:38:03.760> very<00:38:04.040> hard<00:38:04.280> to<00:38:04.359> predict\nessentially uh is very hard to predict\nessentially uh is very hard to predict um<00:38:05.280> the<00:38:05.480> the<00:38:05.640> output<00:38:05.920> state,<00:38:06.280> right?<00:38:06.440> It's\num the the output state, right? It's\num the the output state, right? It's seemingly<00:38:06.960> random.<00:38:07.520> And<00:38:07.680> rule<00:38:07.800> 54<00:38:08.440> is<00:38:08.560> instead\nseemingly random. And rule 54 is instead\nseemingly random. And rule 54 is instead some<00:38:09.800> interesting<00:38:10.560> situation<00:38:11.000> in<00:38:11.080> between\nsome interesting situation in between\nsome interesting situation in between where<00:38:11.720> there's<00:38:11.920> all<00:38:12.040> this<00:38:12.760> both<00:38:12.960> structure\nwhere there's all this both structure\nwhere there's all this both structure and<00:38:13.520> randomness.\nand randomness.\nand randomness. So<00:38:15.400> applying<00:38:15.800> this<00:38:16.000> setup<00:38:16.920> to<00:38:18.040> um<00:38:18.560> what<00:38:18.720> we\nSo applying this setup to um what we\nSo applying this setup to um what we have<00:38:19.680> uh<00:38:20.240> with<00:38:20.359> these<00:38:20.520> cellular<00:38:20.720> automaton\nhave uh with these cellular automaton\nhave uh with these cellular automaton where<00:38:21.760> we<00:38:21.920> are<00:38:22.040> trying<00:38:22.359> to<00:38:22.480> predict<00:38:23.120> the<00:38:23.240> final\nwhere we are trying to predict the final\nwhere we are trying to predict the final row<00:38:24.120> from<00:38:24.320> the<00:38:24.400> initial<00:38:24.760> row,\nrow from the initial row,\nrow from the initial row, what<00:38:25.800> we<00:38:25.960> find<00:38:27.160> is<00:38:28.000> So<00:38:28.160> first<00:38:28.440> of<00:38:28.520> all,<00:38:28.640> here<00:38:28.840> is\nwhat we find is So first of all, here is\nwhat we find is So first of all, here is this<00:38:29.120> curve<00:38:29.920> on<00:38:30.040> the<00:38:30.120> left<00:38:30.840> with<00:38:31.000> this<00:38:31.160> total\nthis curve on the left with this total\nthis curve on the left with this total description<00:38:31.800> length<00:38:32.240> as<00:38:32.359> a<00:38:32.440> function<00:38:32.760> of\ndescription length as a function of\ndescription length as a function of compute.\ncompute.\ncompute. For<00:38:34.160> rule<00:38:34.359> 30,<00:38:34.800> we<00:38:34.960> make<00:38:35.160> no<00:38:35.280> progress.\nFor rule 30, we make no progress.\nFor rule 30, we make no progress. We<00:38:37.320> are<00:38:37.440> not<00:38:37.720> able<00:38:37.960> to<00:38:38.080> do<00:38:38.280> predictions<00:38:39.160> better\nWe are not able to do predictions better\nWe are not able to do predictions better than<00:38:39.760> random<00:38:40.000> chance.\nthan random chance.\nthan random chance. So<00:38:41.359> as<00:38:41.520> the<00:38:41.600> total<00:38:41.800> description<00:38:42.160> length<00:38:42.440> is\nSo as the total description length is\nSo as the total description length is just<00:38:43.040> um<00:38:43.440> right,<00:38:44.080> uh<00:38:44.480> the<00:38:45.160> the<00:38:45.280> the<00:38:45.480> total\njust um right, uh the the the total\njust um right, uh the the the total number<00:38:46.000> of<00:38:46.359> um\nnumber of um\nnumber of um uh<00:38:47.320> bits<00:38:47.520> that<00:38:47.600> we<00:38:47.680> need<00:38:47.800> to<00:38:48.000> output.\nuh bits that we need to output.\nuh bits that we need to output. Uh<00:38:49.280> and\nUh and\nUh and for<00:38:51.400> rule<00:38:51.760> 15,<00:38:52.240> we<00:38:52.359> very<00:38:52.560> quickly<00:38:52.840> make\nfor rule 15, we very quickly make\nfor rule 15, we very quickly make progress,\nprogress,\nprogress, but<00:38:54.800> now<00:38:55.280> we<00:38:55.400> have<00:38:55.520> perfect<00:38:55.840> predictions.\nbut now we have perfect predictions.\nbut now we have perfect predictions. There's<00:38:56.840> no<00:38:56.960> more<00:38:57.080> learning<00:38:57.320> to<00:38:57.440> do.<00:38:58.160> Whereas\nThere's no more learning to do. Whereas\nThere's no more learning to do. Whereas for<00:38:58.480> rule<00:38:58.640> 54,<00:38:59.080> we<00:38:59.200> continue<00:38:59.840> to<00:38:59.960> make\nfor rule 54, we continue to make\nfor rule 54, we continue to make progress<00:39:00.920> proving<00:39:01.240> predictions<00:39:01.840> as<00:39:01.960> we<00:39:02.080> spend\nprogress proving predictions as we spend\nprogress proving predictions as we spend additional<00:39:02.840> compute.\nadditional compute.\nadditional compute. And<00:39:04.680> so<00:39:05.080> in<00:39:05.200> terms<00:39:05.440> of<00:39:05.560> epi-plexity<00:39:06.240> and\nAnd so in terms of epi-plexity and\nAnd so in terms of epi-plexity and time-bounded<00:39:06.880> entropy,<00:39:07.280> we<00:39:07.440> see<00:39:07.560> that<00:39:07.760> in\ntime-bounded entropy, we see that in\ntime-bounded entropy, we see that in these<00:39:07.960> two<00:39:08.080> curves.\nthese two curves.\nthese two curves. The<00:39:09.280> time<00:39:09.640> the<00:39:09.840> epi-plexity<00:39:11.000> continues<00:39:11.400> to\nThe time the epi-plexity continues to\nThe time the epi-plexity continues to increase<00:39:12.440> as<00:39:12.600> we<00:39:12.720> spend<00:39:13.320> additional<00:39:13.720> compute\nincrease as we spend additional compute\nincrease as we spend additional compute on<00:39:14.480> this<00:39:14.600> learning<00:39:14.840> task,\non this learning task,\non this learning task, um<00:39:16.520> the<00:39:16.680> conditional<00:39:17.240> one,<00:39:17.520> you<00:39:17.600> know,<00:39:17.680> Y\num the conditional one, you know, Y\num the conditional one, you know, Y given<00:39:18.120> X,<00:39:18.640> the<00:39:18.680> final<00:39:18.920> row<00:39:19.080> given<00:39:19.280> the<00:39:19.320> initial\ngiven X, the final row given the initial\ngiven X, the final row given the initial row,\nrow,\nrow, and<00:39:20.640> then<00:39:20.760> the<00:39:20.840> time-bounded<00:39:21.320> entropy\nand then the time-bounded entropy\nand then the time-bounded entropy decreases.\ndecreases.\ndecreases. But<00:39:23.640> again,\nBut again,\nBut again, for<00:39:25.040> rule<00:39:25.240> 30<00:39:25.600> and<00:39:25.720> rule<00:39:25.840> 15,<00:39:26.680> we<00:39:26.760> do<00:39:26.880> not<00:39:27.120> see\nfor rule 30 and rule 15, we do not see\nfor rule 30 and rule 15, we do not see this<00:39:27.440> increase<00:39:28.120> in<00:39:28.680> epi-plexity.<00:39:29.920> And<00:39:30.080> so\nthis increase in epi-plexity. And so\nthis increase in epi-plexity. And so this<00:39:30.680> is,<00:39:31.440> you<00:39:31.480> know,<00:39:32.000> nicely<00:39:32.720> separating<00:39:33.960> uh\nthis is, you know, nicely separating uh\nthis is, you know, nicely separating uh these<00:39:35.280> uh<00:39:35.560> these<00:39:35.800> these<00:39:36.480> different\nthese uh these these different\nthese uh these these different classifications<00:39:37.600> of<00:39:37.840> these<00:39:38.480> cellular\nclassifications of these cellular\nclassifications of these cellular automaton<00:39:39.440> with<00:39:39.640> rule<00:39:39.760> 54<00:39:40.280> being<00:39:40.480> in<00:39:40.560> its<00:39:40.840> its\nautomaton with rule 54 being in its its\nautomaton with rule 54 being in its its own<00:39:41.160> category,<00:39:41.600> rule<00:39:41.760> 30<00:39:42.000> being<00:39:42.160> in<00:39:42.200> a\nown category, rule 30 being in a\nown category, rule 30 being in a different<00:39:42.520> category.<00:39:42.880> We're<00:39:43.080> able<00:39:43.240> to<00:39:43.320> nicely\ndifferent category. We're able to nicely\ndifferent category. We're able to nicely separate<00:39:43.960> these<00:39:44.560> with<00:39:45.200> looking<00:39:45.640> at\nseparate these with looking at\nseparate these with looking at perplexity\nperplexity\nperplexity and<00:39:47.320> seeing<00:39:47.560> how\nand seeing how\nand seeing how as<00:39:48.600> we<00:39:48.680> spend<00:39:48.880> additional<00:39:49.200> compute,<00:39:50.040> um\nas we spend additional compute, um\nas we spend additional compute, um the<00:39:50.800> perplexity<00:39:51.440> increases.\nthe perplexity increases.\nthe perplexity increases. Right.<00:39:53.000> And<00:39:53.120> it's<00:39:53.240> interesting<00:39:53.720> here<00:39:53.880> where\nRight. And it's interesting here where\nRight. And it's interesting here where it's<00:39:54.720> it's<00:39:54.840> essentially<00:39:55.240> the<00:39:55.400> same\nit's it's essentially the same\nit's it's essentially the same computation<00:39:56.640> but<00:39:56.760> just<00:39:56.960> these<00:39:57.080> tiny<00:39:57.440> tweaks\ncomputation but just these tiny tweaks\ncomputation but just these tiny tweaks to\nto\nto what<00:39:59.360> exactly<00:39:59.680> the<00:39:59.760> rule<00:40:00.080> is<00:40:00.200> being\nwhat exactly the rule is being\nwhat exactly the rule is being implemented,<00:40:01.040> and<00:40:01.120> we're<00:40:01.200> going<00:40:01.320> to<00:40:01.360> have\nimplemented, and we're going to have\nimplemented, and we're going to have three<00:40:01.680> very<00:40:01.920> different<00:40:02.240> outcomes,<00:40:02.720> right?<00:40:02.880> We\nthree very different outcomes, right? We\nthree very different outcomes, right? We can<00:40:03.120> essentially<00:40:03.520> if<00:40:03.640> we're<00:40:03.800> thinking<00:40:04.000> about\ncan essentially if we're thinking about\ncan essentially if we're thinking about this<00:40:04.360> in<00:40:04.480> terms<00:40:04.720> of<00:40:04.800> making<00:40:04.960> useful<00:40:05.200> data,<00:40:06.120> one\nthis in terms of making useful data, one\nthis in terms of making useful data, one outcome<00:40:06.640> is<00:40:06.800> that<00:40:06.880> we<00:40:07.000> make\noutcome is that we make\noutcome is that we make this<00:40:08.280> boring\nthis boring\nthis boring super<00:40:09.840> predictable<00:40:10.240> data.<00:40:10.640> Another<00:40:11.000> is<00:40:11.120> that\nsuper predictable data. Another is that\nsuper predictable data. Another is that we<00:40:11.320> make<00:40:12.040> kind<00:40:12.200> of<00:40:12.280> chaotic\nwe make kind of chaotic\nwe make kind of chaotic completely<00:40:14.000> unpredictable<00:40:14.520> data<00:40:14.800> that's\ncompletely unpredictable data that's\ncompletely unpredictable data that's also<00:40:15.560> not<00:40:15.720> useful<00:40:15.960> to<00:40:16.080> us.\nalso not useful to us.\nalso not useful to us. But<00:40:17.160> with<00:40:17.280> the<00:40:17.360> same<00:40:17.520> computation,<00:40:18.080> we<00:40:18.160> can\nBut with the same computation, we can\nBut with the same computation, we can also<00:40:18.520> make<00:40:18.800> data<00:40:19.040> that<00:40:19.240> is<00:40:19.640> is<00:40:20.080> interesting<00:40:20.520> to\nalso make data that is is interesting to\nalso make data that is is interesting to predict.<00:40:20.960> That<00:40:21.080> is<00:40:21.200> we<00:40:21.320> spend<00:40:21.640> more\npredict. That is we spend more\npredict. That is we spend more computation,<00:40:22.480> we<00:40:22.520> make<00:40:22.680> better<00:40:22.880> predictions.\ncomputation, we make better predictions.\ncomputation, we make better predictions. So<00:40:25.120> then<00:40:25.320> going<00:40:25.600> to<00:40:25.720> paradox<00:40:26.160> two,\nSo then going to paradox two,\nSo then going to paradox two, information<00:40:28.840> is<00:40:29.000> independent<00:40:29.600> factorization\ninformation is independent factorization\ninformation is independent factorization order.\norder.\norder. Well,<00:40:32.280> we're<00:40:32.800> we'll<00:40:32.960> show<00:40:33.200> that<00:40:33.360> actually\nWell, we're we'll show that actually\nWell, we're we'll show that actually time-bounded<00:40:34.240> entropy<00:40:34.680> and<00:40:34.800> perplexity\ntime-bounded entropy and perplexity\ntime-bounded entropy and perplexity depend<00:40:36.200> on<00:40:36.320> the<00:40:36.400> data<00:40:36.640> ordering.\nSo,\nSo,\nSo, um<00:40:41.280> right.<00:40:41.720> We<00:40:41.840> have<00:40:42.000> one-way<00:40:42.200> functions,\num right. We have one-way functions,\num right. We have one-way functions, which<00:40:43.000> Andrew<00:40:43.720> uh<00:40:43.920> briefly<00:40:44.160> mentioned,<00:40:45.160> um\nwhich Andrew uh briefly mentioned, um\nwhich Andrew uh briefly mentioned, um where<00:40:46.640> the<00:40:47.360> we<00:40:47.520> have\nwhere the we have\nwhere the we have a<00:40:48.840> function<00:40:49.600> that<00:40:50.640> uh\na function that uh\na function that uh is<00:40:51.760> very<00:40:51.960> difficult<00:40:52.600> to<00:40:52.720> find<00:40:53.080> elements<00:40:53.920> in<00:40:54.520> in\nis very difficult to find elements in in\nis very difficult to find elements in in its<00:40:54.760> inverse,<00:40:55.520> right?<00:40:55.680> The<00:40:55.760> inverse<00:40:56.120> asset.\nits inverse, right? The inverse asset.\nits inverse, right? The inverse asset. Um<00:40:57.480> where<00:40:57.680> the<00:40:57.800> probability<00:40:58.680> of<00:40:59.520> outputting\nUm where the probability of outputting\nUm where the probability of outputting an<00:41:00.320> element<00:41:00.640> in<00:41:00.680> the<00:41:00.800> inverse<00:41:01.520> can<00:41:01.720> be<00:41:01.920> again\nan element in the inverse can be again\nan element in the inverse can be again bounded<00:41:02.760> by<00:41:02.920> a<00:41:03.000> negligible<00:41:03.920> function,<00:41:04.600> in\nbounded by a negligible function, in\nbounded by a negligible function, in this<00:41:04.840> case<00:41:05.280> of<00:41:05.360> the<00:41:05.480> size<00:41:06.040> of<00:41:06.720> this<00:41:07.240> um\nthis case of the size of this um\nthis case of the size of this um state.\nstate.\nstate. So,<00:41:10.640> and<00:41:10.800> of<00:41:10.880> course<00:41:11.120> this<00:41:11.280> is<00:41:11.440> used\nSo, and of course this is used\nSo, and of course this is used that<00:41:12.800> is<00:41:13.080> the<00:41:13.200> foundation<00:41:13.800> for<00:41:13.960> cryptography.\nthat is the foundation for cryptography.\nthat is the foundation for cryptography. And<00:41:16.520> we<00:41:16.640> can<00:41:16.760> show<00:41:17.400> that\nAnd we can show that\nAnd we can show that um\num\num taking<00:41:20.280> the<00:41:20.360> input<00:41:20.640> and<00:41:20.720> output<00:41:20.960> pairs<00:41:21.440> of<00:41:21.560> a\ntaking the input and output pairs of a\ntaking the input and output pairs of a of<00:41:21.880> a<00:41:21.920> one-way<00:41:22.200> function,\nof a one-way function,\nof a one-way function, that<00:41:23.960> they<00:41:24.080> have<00:41:24.240> this<00:41:24.560> asymmetry<00:41:25.160> with\nthat they have this asymmetry with\nthat they have this asymmetry with respect<00:41:25.840> to<00:41:26.040> the<00:41:26.160> time-bounded<00:41:26.600> entropy.<00:41:27.440> So,\nrespect to the time-bounded entropy. So,\nrespect to the time-bounded entropy. So, in<00:41:28.200> one<00:41:28.400> direction<00:41:28.920> it'll<00:41:29.120> appear<00:41:29.360> random<00:41:29.880> and\nin one direction it'll appear random and\nin one direction it'll appear random and the<00:41:30.080> other<00:41:30.560> not.\nthe other not.\nthe other not. So,<00:41:31.880> we<00:41:32.000> have<00:41:32.160> a<00:41:32.200> theorem<00:41:32.560> here.<00:41:32.960> Um<00:41:33.200> so,<00:41:33.400> for<00:41:33.640> a\nSo, we have a theorem here. Um so, for a\nSo, we have a theorem here. Um so, for a one-way<00:41:34.320> permutation,<00:41:35.160> so<00:41:36.000> we<00:41:36.040> also<00:41:36.200> want<00:41:36.320> it\none-way permutation, so we also want it\none-way permutation, so we also want it to<00:41:36.440> be<00:41:36.520> a<00:41:36.560> bijection,<00:41:37.720> um<00:41:38.360> we<00:41:38.480> can<00:41:38.640> show<00:41:38.880> that\nto be a bijection, um we can show that\nto be a bijection, um we can show that this<00:41:40.320> uh\nthis uh\nthis uh time-bounded<00:41:41.800> entropy<00:41:42.320> with<00:41:42.800> polynomial\ntime-bounded entropy with polynomial\ntime-bounded entropy with polynomial time<00:41:43.800> bound\ntime bound\ntime bound um<00:41:45.680> for<00:41:45.920> X<00:41:46.080> given<00:41:46.280> Y<00:41:46.480> plus<00:41:46.960> uh<00:41:47.240> time-bounded\num for X given Y plus uh time-bounded\num for X given Y plus uh time-bounded entropy<00:41:47.840> of<00:41:47.920> Y<00:41:48.200> is<00:41:48.400> greater<00:41:48.720> than<00:41:48.960> Y<00:41:49.120> given<00:41:49.360> X\nentropy of Y is greater than Y given X\nentropy of Y is greater than Y given X uh<00:41:50.400> plus<00:41:50.640> H<00:41:50.840> of<00:41:50.920> X<00:41:51.560> plus<00:41:52.600> um\nuh plus H of X plus um\nuh plus H of X plus um omega<00:41:54.160> of<00:41:54.280> log<00:41:54.480> n.<00:41:54.760> So,<00:41:54.920> there's<00:41:55.120> a<00:41:55.200> separation\nomega of log n. So, there's a separation\nomega of log n. So, there's a separation that<00:41:56.240> scales\nthat scales\nthat scales uh<00:41:58.440> faster<00:41:59.120> than<00:41:59.360> log<00:41:59.600> n.\nuh faster than log n.\nuh faster than log n. And<00:42:02.320> we<00:42:02.440> also<00:42:02.640> have<00:42:03.000> an<00:42:03.120> empirical<00:42:03.480> experiment\nAnd we also have an empirical experiment\nAnd we also have an empirical experiment um<00:42:04.640> demonstrating<00:42:05.760> uh<00:42:06.080> something<00:42:06.520> to<00:42:06.920> this\num demonstrating uh something to this\num demonstrating uh something to this effect.<00:42:07.840> So,<00:42:08.080> here<00:42:08.480> the<00:42:08.600> difficulty<00:42:09.120> is<00:42:09.320> that\neffect. So, here the difficulty is that\neffect. So, here the difficulty is that you<00:42:10.120> need<00:42:10.320> to<00:42:10.400> find<00:42:10.680> a<00:42:10.720> function<00:42:11.440> where<00:42:12.080> your\nyou need to find a function where your\nyou need to find a function where your uh<00:42:13.080> model<00:42:13.320> class<00:42:13.640> that<00:42:13.800> you're<00:42:13.920> searching<00:42:14.240> in\nuh model class that you're searching in\nuh model class that you're searching in can<00:42:14.800> actually<00:42:15.040> fit<00:42:15.240> the<00:42:15.320> forward<00:42:15.520> direction.\ncan actually fit the forward direction.\ncan actually fit the forward direction. That<00:42:16.720> is<00:42:16.880> also<00:42:17.640> a<00:42:17.720> conjectured<00:42:18.200> one-way\nThat is also a conjectured one-way\nThat is also a conjectured one-way function.\nfunction.\nfunction. So,<00:42:19.560> here<00:42:20.080> we<00:42:20.240> use<00:42:21.040> um\nSo, here we use um\nSo, here we use um we<00:42:21.920> actually<00:42:22.240> use<00:42:22.480> again<00:42:23.280> uh<00:42:23.400> well,<00:42:23.600> okay.\nwe actually use again uh well, okay.\nwe actually use again uh well, okay. Yes,<00:42:24.040> so<00:42:24.200> so<00:42:24.320> we<00:42:24.480> we<00:42:24.680> again<00:42:24.960> use<00:42:25.400> um\nYes, so so we we again use um\nYes, so so we we again use um uh\nuh\nuh uh\nuh\nuh uh<00:42:28.120> cellular<00:42:28.440> automata<00:42:28.760> here,<00:42:29.000> but<00:42:29.480> uh<00:42:29.760> using\nuh cellular automata here, but uh using\nuh cellular automata here, but uh using the<00:42:30.160> conjectured<00:42:30.600> one-way<00:42:31.200> uh<00:42:31.400> properties<00:42:31.920> of\nthe conjectured one-way uh properties of\nthe conjectured one-way uh properties of uh<00:42:32.880> of<00:42:32.960> rule<00:42:33.080> 30<00:42:33.480> and<00:42:33.600> then<00:42:33.720> look<00:42:33.920> at<00:42:34.040> the\nuh of rule 30 and then look at the\nuh of rule 30 and then look at the forward<00:42:34.400> prediction<00:42:34.720> versus<00:42:34.960> the<00:42:35.040> reverse\nforward prediction versus the reverse\nforward prediction versus the reverse prediction.<00:42:36.200> In<00:42:36.320> the<00:42:36.440> forward<00:42:36.720> direction,\nprediction. In the forward direction,\nprediction. In the forward direction, um<00:42:38.000> you<00:42:38.160> line<00:42:38.400> up<00:42:38.520> right<00:42:38.640> with<00:42:38.760> the<00:42:38.840> entropy<00:42:39.800> so\num you line up right with the entropy so\num you line up right with the entropy so you<00:42:40.000> have<00:42:40.080> random<00:42:40.360> initial<00:42:40.560> conditions<00:42:41.160> in\nyou have random initial conditions in\nyou have random initial conditions in forward.<00:42:41.800> And<00:42:41.960> then<00:42:42.120> the<00:42:42.200> reverse<00:42:42.480> direction,\nforward. And then the reverse direction,\nforward. And then the reverse direction, you<00:42:43.200> have<00:42:43.400> this<00:42:43.560> gap.<00:42:44.440> Um<00:42:45.040> and<00:42:45.680> yeah,<00:42:45.840> I<00:42:45.880> guess\nyou have this gap. Um and yeah, I guess\nyou have this gap. Um and yeah, I guess it<00:42:46.120> would<00:42:46.200> be<00:42:46.320> good<00:42:46.480> to<00:42:46.760> to<00:42:46.880> see<00:42:47.080> like<00:42:47.280> yeah,\nit would be good to to see like yeah,\nit would be good to to see like yeah, does<00:42:47.600> this<00:42:47.800> this<00:42:47.960> gap<00:42:48.200> actually<00:42:49.040> grow<00:42:49.320> with\ndoes this this gap actually grow with\ndoes this this gap actually grow with log<00:42:49.720> n?<00:42:49.920> We<00:42:50.040> don't<00:42:50.400> quite<00:42:50.600> have<00:42:50.720> the\nlog n? We don't quite have the\nlog n? We don't quite have the resolution<00:42:51.200> here<00:42:51.600> to<00:42:51.720> see<00:42:51.840> that.<00:42:52.520> Um<00:42:52.800> but\nresolution here to see that. Um but\nresolution here to see that. Um but right,<00:42:53.760> we're<00:42:53.880> able<00:42:54.000> to<00:42:54.080> see<00:42:54.160> it\nright, we're able to see it\nright, we're able to see it theoretically<00:42:54.800> and<00:42:54.880> empirically.\ntheoretically and empirically.\ntheoretically and empirically. Another<00:42:56.760> example,<00:42:57.640> or<00:42:57.760> practical<00:42:58.040> example,\nAnother example, or practical example,\nAnother example, or practical example, um<00:42:59.200> right<00:42:59.520> uh<00:42:59.560> so<00:42:59.720> so<00:42:59.920> we<00:43:00.360> uh<00:43:00.440> looked<00:43:00.640> at<00:43:00.800> say<00:43:01.040> at\num right uh so so we uh looked at say at\num right uh so so we uh looked at say at some<00:43:02.240> real<00:43:02.440> data<00:43:02.760> like<00:43:03.240> well,<00:43:03.360> okay.<00:43:03.600> So<00:43:03.760> so\nsome real data like well, okay. So so\nsome real data like well, okay. So so synthetic<00:43:04.800> data,<00:43:05.080> but<00:43:05.520> uh<00:43:06.000> data<00:43:06.400> of<00:43:06.880> mapping\nsynthetic data, but uh data of mapping\nsynthetic data, but uh data of mapping chess<00:43:08.040> moves<00:43:08.480> to<00:43:08.960> a<00:43:09.040> chessboard<00:43:10.080> versus<00:43:11.000> um<00:43:11.600> so\nchess moves to a chessboard versus um so\nchess moves to a chessboard versus um so a<00:43:11.800> sequence<00:43:12.160> of<00:43:12.240> chess<00:43:12.440> moves<00:43:12.920> to<00:43:13.280> the<00:43:13.400> final\na sequence of chess moves to the final\na sequence of chess moves to the final chessboard<00:43:14.720> versus<00:43:15.120> taking<00:43:15.320> the<00:43:15.400> final\nchessboard versus taking the final\nchessboard versus taking the final chessboard<00:43:16.400> and<00:43:16.520> then<00:43:16.640> mapping<00:43:16.920> that<00:43:17.200> to<00:43:17.440> the\nchessboard and then mapping that to the\nchessboard and then mapping that to the sequence<00:43:17.880> of<00:43:17.960> chess<00:43:18.160> moves<00:43:18.360> that<00:43:18.480> got<00:43:18.680> there.\nsequence of chess moves that got there.\nsequence of chess moves that got there. In<00:43:19.320> one<00:43:19.440> direction,<00:43:19.920> all<00:43:20.080> you<00:43:20.160> need<00:43:20.320> to<00:43:20.400> do<00:43:20.680> is\nIn one direction, all you need to do is\nIn one direction, all you need to do is um<00:43:21.520> keep<00:43:21.760> track<00:43:22.040> of<00:43:22.120> the<00:43:22.240> state.<00:43:23.000> You<00:43:23.120> need<00:43:23.320> to\num keep track of the state. You need to\num keep track of the state. You need to basically<00:43:24.080> run<00:43:24.440> this,<00:43:25.080> you<00:43:25.160> know,<00:43:25.480> um<00:43:25.960> where\nbasically run this, you know, um where\nbasically run this, you know, um where does<00:43:26.360> this<00:43:26.520> move<00:43:26.720> bring<00:43:26.920> you?<00:43:27.080> Where<00:43:27.200> does\ndoes this move bring you? Where does\ndoes this move bring you? Where does this<00:43:27.440> move<00:43:27.600> bring<00:43:27.800> you<00:43:28.280> on<00:43:28.360> the<00:43:28.440> board?<00:43:29.080> In<00:43:29.200> the\nthis move bring you on the board? In the\nthis move bring you on the board? In the other<00:43:29.440> direction,<00:43:29.880> you<00:43:29.960> have<00:43:30.080> to<00:43:30.160> do<00:43:30.280> some\nother direction, you have to do some\nother direction, you have to do some kind<00:43:30.560> of<00:43:30.640> inference.<00:43:31.120> You<00:43:31.200> have<00:43:31.320> to<00:43:31.440> do<00:43:31.520> some\nkind of inference. You have to do some\nkind of inference. You have to do some kind<00:43:31.800> of<00:43:31.880> induction<00:43:32.400> of<00:43:32.600> like,<00:43:32.800> \"Hmm,<00:43:33.240> how<00:43:33.360> did\nkind of induction of like, \"Hmm, how did\nkind of induction of like, \"Hmm, how did we<00:43:33.600> get<00:43:33.720> here?<00:43:33.960> Maybe<00:43:34.160> there<00:43:34.280> are<00:43:34.320> multiple\nwe get here? Maybe there are multiple\nwe get here? Maybe there are multiple ways<00:43:34.800> to<00:43:34.880> get<00:43:35.040> there.\"<00:43:35.360> Have<00:43:35.520> to<00:43:35.600> do<00:43:35.720> some\nways to get there.\" Have to do some\nways to get there.\" Have to do some And<00:43:36.720> what<00:43:36.840> we<00:43:36.920> find<00:43:37.240> is<00:43:37.360> that<00:43:37.880> of<00:43:38.000> course<00:43:38.320> in\nAnd what we find is that of course in\nAnd what we find is that of course in the<00:43:38.800> more<00:43:39.080> straightforward<00:43:39.560> direction,<00:43:40.040> the\nthe more straightforward direction, the\nthe more straightforward direction, the the<00:43:40.200> time-bounded<00:43:40.640> entropy<00:43:40.800> is<00:43:40.880> lower,<00:43:41.680> um\nthe time-bounded entropy is lower, um\nthe time-bounded entropy is lower, um but<00:43:43.000> that<00:43:43.280> actually<00:43:44.120> uh\nbut that actually uh\nbut that actually uh the\nthe\nthe perplexity<00:43:46.600> is<00:43:47.200> also<00:43:47.760> lower.<00:43:48.440> So,<00:43:48.680> yeah,<00:43:48.840> it's\nperplexity is also lower. So, yeah, it's\nperplexity is also lower. So, yeah, it's also<00:43:49.160> lower.\nalso lower.\nalso lower. Um<00:43:51.040> right.<00:43:51.280> And<00:43:51.400> so,<00:43:51.520> we<00:43:51.640> can<00:43:51.760> actually<00:43:52.160> find\nUm right. And so, we can actually find\nUm right. And so, we can actually find ways<00:43:52.720> of<00:43:52.840> tweaking<00:43:53.200> the<00:43:53.320> data<00:43:53.640> to<00:43:53.760> make<00:43:53.920> it\nways of tweaking the data to make it\nways of tweaking the data to make it harder,<00:43:54.520> but<00:43:54.760> harder<00:43:55.080> in<00:43:55.240> an<00:43:55.320> interesting\nharder, but harder in an interesting\nharder, but harder in an interesting way.<00:43:56.200> And<00:43:56.320> then<00:43:56.440> also<00:43:56.640> you<00:43:56.760> have<00:43:56.880> data,<00:43:57.200> you\nway. And then also you have data, you\nway. And then also you have data, you know,<00:43:57.480> evidence<00:43:57.800> from<00:43:57.960> arrow<00:43:58.160> of<00:43:58.240> time<00:43:58.520> and\nknow, evidence from arrow of time and\nknow, evidence from arrow of time and LLMs,<00:43:59.240> like<00:43:59.359> I<00:43:59.400> had<00:43:59.480> mentioned.<00:44:00.359> Um<00:44:01.160> and<00:44:01.640> so\nLLMs, like I had mentioned. Um and so\nLLMs, like I had mentioned. Um and so I'll<00:44:02.600> now<00:44:02.720> move<00:44:02.960> on<00:44:03.120> to<00:44:03.359> paradox<00:44:03.760> three,<00:44:04.440> um\nI'll now move on to paradox three, um\nI'll now move on to paradox three, um likelihood<00:44:05.400> modeling<00:44:05.800> is<00:44:05.960> merely\nlikelihood modeling is merely\nlikelihood modeling is merely distribution<00:44:06.680> matching.\ndistribution matching.\ndistribution matching. So,\nSo,\nSo, uh<00:44:10.160> it<00:44:10.280> is<00:44:10.440> our<00:44:10.640> contention<00:44:11.120> that<00:44:11.640> uh\nuh it is our contention that uh\nuh it is our contention that uh All<00:44:12.480> right.<00:44:12.680> So<00:44:12.800> so<00:44:12.960> yeah,<00:44:13.160> so<00:44:13.400> but<00:44:14.160> actually\nAll right. So so yeah, so but actually\nAll right. So so yeah, so but actually uh<00:44:15.240> where<00:44:15.440> do<00:44:15.560> you<00:44:15.640> know<00:44:16.080> um<00:44:16.640> that<00:44:17.240> uh<00:44:17.560> again\nuh where do you know um that uh again\nuh where do you know um that uh again that<00:44:18.840> that<00:44:19.040> actually<00:44:19.280> time-bounded\nthat that actually time-bounded\nthat that actually time-bounded perplexity<00:44:20.280> can<00:44:20.400> be<00:44:20.480> greater<00:44:20.800> than<00:44:20.960> the<00:44:21.000> size\nperplexity can be greater than the size\nperplexity can be greater than the size of<00:44:21.320> the<00:44:21.400> generating<00:44:21.720> program<00:44:22.200> with<00:44:22.359> a<00:44:22.400> couple\nof the generating program with a couple\nof the generating program with a couple of<00:44:22.720> examples.\nof examples.\nof examples. So,<00:44:25.040> um<00:44:25.680> let<00:44:25.800> me<00:44:25.840> just<00:44:26.040> quickly<00:44:26.280> go<00:44:26.359> through\nSo, um let me just quickly go through\nSo, um let me just quickly go through this.<00:44:27.120> Uh<00:44:27.280> right.<00:44:27.480> So<00:44:27.600> so\nthis. Uh right. So so\nthis. Uh right. So so where<00:44:28.680> this<00:44:28.880> intuition<00:44:29.240> is<00:44:29.320> coming<00:44:29.560> from,\nwhere this intuition is coming from,\nwhere this intuition is coming from, right?<00:44:30.280> This<00:44:30.480> is<00:44:30.640> this<00:44:31.400> uh<00:44:31.920> thing<00:44:32.080> that<00:44:32.200> people\nright? This is this uh thing that people\nright? This is this uh thing that people have<00:44:32.640> expressed<00:44:33.440> of<00:44:34.200> uh\nhave expressed of uh\nhave expressed of uh that<00:44:36.280> somehow<00:44:36.600> if<00:44:36.720> we<00:44:36.800> train<00:44:37.000> on<00:44:37.080> human<00:44:37.280> data,\nthat somehow if we train on human data,\nthat somehow if we train on human data, we<00:44:37.840> can<00:44:37.960> never<00:44:38.280> exceed<00:44:38.720> human<00:44:38.960> capabilities,\nwe can never exceed human capabilities,\nwe can never exceed human capabilities, right?<00:44:40.440> We<00:44:41.400> uh<00:44:41.760> or<00:44:42.200> that<00:44:42.760> um<00:44:43.040> okay,<00:44:43.680> uh<00:44:44.040> the\nright? We uh or that um okay, uh the\nright? We uh or that um okay, uh the model<00:44:44.400> that<00:44:44.520> minimizes<00:44:45.000> the<00:44:45.040> cross-entropy\nmodel that minimizes the cross-entropy\nmodel that minimizes the cross-entropy loss<00:44:46.200> is<00:44:46.440> just<00:44:47.080> the<00:44:47.880> uh\nloss is just the uh\nloss is just the uh the<00:44:48.920> distribution<00:44:49.400> that<00:44:49.520> generated<00:44:49.840> the\nthe distribution that generated the\nthe distribution that generated the data.<00:44:50.480> So<00:44:50.600> then<00:44:50.960> as<00:44:51.240> we<00:44:51.359> minimize<00:44:51.760> our\ndata. So then as we minimize our\ndata. So then as we minimize our cross-entropy<00:44:52.359> loss,<00:44:52.600> we<00:44:52.720> should<00:44:52.880> expect\ncross-entropy loss, we should expect\ncross-entropy loss, we should expect just<00:44:53.400> to<00:44:53.480> approach<00:44:53.760> that<00:44:54.000> and<00:44:54.080> not<00:44:54.240> be<00:44:54.320> able<00:44:54.440> to\njust to approach that and not be able to\njust to approach that and not be able to do<00:44:54.560> anything<00:44:54.760> better.\ndo anything better.\ndo anything better. But<00:44:56.000> uh<00:44:56.520> there's<00:44:56.600> a<00:44:56.640> great<00:44:56.840> quote<00:44:57.080> from<00:44:57.359> Ilya\nBut uh there's a great quote from Ilya\nBut uh there's a great quote from Ilya Sutskever.<00:44:58.520> Um<00:44:59.280> so,<00:44:59.440> you're<00:44:59.560> reading<00:44:59.800> a\nSutskever. Um so, you're reading a\nSutskever. Um so, you're reading a murder<00:45:00.080> mystery<00:45:00.520> and<00:45:00.600> at<00:45:00.680> some<00:45:00.840> point<00:45:01.040> the\nmurder mystery and at some point the\nmurder mystery and at some point the text<00:45:01.359> reveals<00:45:01.680> the<00:45:01.720> identity<00:45:02.200> of<00:45:02.320> the\ntext reveals the identity of the\ntext reveals the identity of the criminal.<00:45:03.120> The<00:45:03.240> model<00:45:03.480> can<00:45:03.640> predict<00:45:04.240> the<00:45:04.320> name\ncriminal. The model can predict the name\ncriminal. The model can predict the name of<00:45:04.920> that<00:45:05.080> criminal,<00:45:05.440> then<00:45:05.600> it<00:45:05.680> must<00:45:05.840> have\nof that criminal, then it must have\nof that criminal, then it must have figured<00:45:06.280> out<00:45:06.440> who<00:45:06.600> perpetrated<00:45:07.080> the<00:45:07.160> murder\nfigured out who perpetrated the murder\nfigured out who perpetrated the murder from<00:45:07.560> the<00:45:07.640> evidence<00:45:07.920> provided.<00:45:08.680> And<00:45:08.800> the<00:45:08.880> key\nfrom the evidence provided. And the key\nfrom the evidence provided. And the key point<00:45:09.480> here<00:45:10.080> is<00:45:10.320> that<00:45:10.640> the<00:45:10.880> author<00:45:11.359> of<00:45:11.480> the\npoint here is that the author of the\npoint here is that the author of the book<00:45:12.400> may<00:45:12.560> not<00:45:13.080> have<00:45:13.440> needed<00:45:13.840> to<00:45:13.960> make<00:45:14.120> that\nbook may not have needed to make that\nbook may not have needed to make that same<00:45:14.560> induction.<00:45:15.520> Instead,<00:45:15.880> they<00:45:15.960> may<00:45:16.080> have\nsame induction. Instead, they may have\nsame induction. Instead, they may have decided<00:45:16.640> ahead<00:45:16.840> of<00:45:16.920> time<00:45:17.720> how<00:45:17.840> they're<00:45:17.960> going\ndecided ahead of time how they're going\ndecided ahead of time how they're going to<00:45:18.120> craft<00:45:18.320> the<00:45:18.400> story<00:45:18.920> in<00:45:19.000> terms<00:45:19.280> of<00:45:19.359> the\nto craft the story in terms of the\nto craft the story in terms of the murderer.\nmurderer.\nmurderer. Um<00:45:21.120> but<00:45:21.280> then<00:45:21.359> the<00:45:21.480> person<00:45:21.840> reading<00:45:22.160> the<00:45:22.240> book\nUm but then the person reading the book\nUm but then the person reading the book and<00:45:22.760> making<00:45:23.040> predictions<00:45:23.560> token<00:45:23.840> by<00:45:23.960> token\nand making predictions token by token\nand making predictions token by token does<00:45:24.720> have<00:45:24.880> to<00:45:24.960> do<00:45:25.080> this<00:45:25.200> induction.<00:45:25.640> So,\ndoes have to do this induction. So,\ndoes have to do this induction. So, there's<00:45:25.960> an<00:45:26.120> asymmetry<00:45:26.680> here<00:45:26.880> between<00:45:27.160> the\nthere's an asymmetry here between the\nthere's an asymmetry here between the two<00:45:27.440> tasks<00:45:27.960> required<00:45:28.400> by<00:45:28.480> the<00:45:28.600> person<00:45:28.840> who\ntwo tasks required by the person who\ntwo tasks required by the person who generated<00:45:29.359> the<00:45:29.440> data<00:45:30.040> and<00:45:30.120> the<00:45:30.200> person<00:45:30.520> who<00:45:30.680> is\ngenerated the data and the person who is\ngenerated the data and the person who is making<00:45:31.080> the<00:45:31.160> predictions<00:45:31.600> on<00:45:31.680> the<00:45:31.720> data.<00:45:32.480> And\nmaking the predictions on the data. And\nmaking the predictions on the data. And we<00:45:32.720> have<00:45:32.920> a<00:45:33.000> toy<00:45:33.240> attack<00:45:33.600> where<00:45:33.760> we<00:45:33.880> have<00:45:34.080> a\nwe have a toy attack where we have a\nwe have a toy attack where we have a experimental<00:45:34.760> analog<00:45:35.160> of<00:45:35.240> this<00:45:35.480> where<00:45:35.680> we<00:45:36.240> we\nexperimental analog of this where we we\nexperimental analog of this where we we have<00:45:36.520> some<00:45:36.680> state<00:45:37.000> n,<00:45:37.680> we<00:45:37.800> apply<00:45:38.120> it<00:45:38.240> through\nhave some state n, we apply it through\nhave some state n, we apply it through some<00:45:38.560> function<00:45:38.920> f,<00:45:39.560> and<00:45:39.720> then<00:45:39.880> also<00:45:40.240> we\nsome function f, and then also we\nsome function f, and then also we consider<00:45:40.840> a<00:45:40.920> version<00:45:41.320> where<00:45:41.520> we<00:45:41.680> remove<00:45:42.160> some\nconsider a version where we remove some\nconsider a version where we remove some of<00:45:42.400> the<00:45:42.480> information<00:45:43.040> from<00:45:43.320> the<00:45:43.440> original\nof the information from the original\nof the information from the original state.<00:45:44.320> And<00:45:44.440> then<00:45:44.560> we<00:45:44.680> make<00:45:44.840> predictions<00:45:45.600> with\nstate. And then we make predictions with\nstate. And then we make predictions with this\nthis\nthis uh<00:45:46.680> ablated<00:45:47.280> input<00:45:47.760> and<00:45:47.960> then<00:45:48.320> with<00:45:48.480> this\nuh ablated input and then with this\nuh ablated input and then with this output<00:45:48.880> of<00:45:48.960> this<00:45:49.120> function.\noutput of this function.\noutput of this function. Um<00:45:51.480> the<00:45:51.600> key<00:45:51.760> point<00:45:51.960> here<00:45:52.120> is<00:45:52.200> that<00:45:52.320> this\nUm the key point here is that this\nUm the key point here is that this function<00:45:52.800> f<00:45:53.000> is<00:45:53.120> not<00:45:53.320> so<00:45:53.440> hard<00:45:53.640> to<00:45:53.720> compute.<00:45:54.560> Um\nfunction f is not so hard to compute. Um\nfunction f is not so hard to compute. Um however,<00:45:55.960> uh<00:45:56.359> we<00:45:56.520> can<00:45:56.680> consider<00:45:57.080> what<00:45:57.240> happens\nhowever, uh we can consider what happens\nhowever, uh we can consider what happens as<00:45:58.040> the<00:45:58.480> f<00:45:58.760> inverse<00:45:59.640> is<00:46:00.080> hard<00:46:00.400> or<00:46:00.520> easy<00:46:00.680> to\nas the f inverse is hard or easy to\nas the f inverse is hard or easy to compute.<00:46:01.120> So,<00:46:01.280> here<00:46:01.480> we<00:46:01.600> have<00:46:01.680> an<00:46:01.760> example\ncompute. So, here we have an example\ncompute. So, here we have an example where<00:46:02.240> it's<00:46:02.400> hard<00:46:02.640> to<00:46:02.720> compute.\nwhere it's hard to compute.\nwhere it's hard to compute. And<00:46:04.560> what<00:46:04.680> we<00:46:04.800> see<00:46:05.040> is<00:46:05.200> that<00:46:05.400> actually<00:46:05.640> by\nAnd what we see is that actually by\nAnd what we see is that actually by removing<00:46:06.680> elements<00:46:07.240> of<00:46:07.320> the<00:46:07.440> input,\nremoving elements of the input,\nremoving elements of the input, now<00:46:09.720> the<00:46:09.840> model<00:46:10.240> has<00:46:10.480> to<00:46:10.600> do<00:46:10.800> this<00:46:10.960> induction\nnow the model has to do this induction\nnow the model has to do this induction over<00:46:11.800> what<00:46:12.040> was<00:46:12.320> the<00:46:12.440> input<00:46:12.760> that<00:46:12.880> is\nover what was the input that is\nover what was the input that is consistent<00:46:13.560> with<00:46:13.640> the<00:46:13.760> output<00:46:14.040> that<00:46:14.120> it's\nconsistent with the output that it's\nconsistent with the output that it's seen<00:46:14.600> so<00:46:14.760> far.\nseen so far.\nseen so far. And<00:46:15.880> this<00:46:16.560> um<00:46:16.800> leads<00:46:17.520> to<00:46:18.400> a<00:46:18.480> greater\nAnd this um leads to a greater\nAnd this um leads to a greater perplexity<00:46:20.080> in<00:46:20.200> the<00:46:20.280> model.<00:46:20.560> We<00:46:20.680> also<00:46:20.880> see\nperplexity in the model. We also see\nperplexity in the model. We also see some<00:46:21.200> other<00:46:21.400> interesting<00:46:21.720> behavior<00:46:22.120> of<00:46:22.480> uh\nsome other interesting behavior of uh\nsome other interesting behavior of uh basically<00:46:22.960> where<00:46:23.359> the<00:46:23.840> uh<00:46:24.240> the<00:46:24.359> learning<00:46:24.880> is\nbasically where the uh the learning is\nbasically where the uh the learning is pushed<00:46:25.520> out<00:46:25.960> exponentially<00:46:26.680> in<00:46:26.800> the<00:46:26.880> number\npushed out exponentially in the number\npushed out exponentially in the number of<00:46:27.200> bits<00:46:27.560> because<00:46:28.320> what<00:46:28.440> the<00:46:28.560> model<00:46:28.840> has<00:46:29.000> to<00:46:29.080> do\nof bits because what the model has to do\nof bits because what the model has to do is<00:46:29.560> is<00:46:29.760> really<00:46:30.040> just<00:46:30.320> a<00:46:30.560> a<00:46:30.640> brute<00:46:30.920> force<00:46:31.240> search\nis is really just a a brute force search\nis is really just a a brute force search over<00:46:32.280> what<00:46:32.480> are<00:46:32.680> the<00:46:32.760> missing<00:46:33.080> bits<00:46:33.400> in<00:46:33.520> the\nover what are the missing bits in the\nover what are the missing bits in the input.\ninput.\ninput. Um<00:46:34.960> but<00:46:35.080> again,<00:46:35.320> you<00:46:35.920> you<00:46:36.040> have<00:46:36.160> this\nUm but again, you you have this\nUm but again, you you have this asymmetry<00:46:36.760> where<00:46:37.120> this<00:46:37.280> masking<00:46:37.680> function<00:46:38.000> is\nasymmetry where this masking function is\nasymmetry where this masking function is a<00:46:38.160> very<00:46:38.320> simple<00:46:38.560> function.<00:46:38.920> This<00:46:39.120> f<00:46:39.280> is<00:46:39.400> a<00:46:39.440> very\na very simple function. This f is a very\na very simple function. This f is a very simple<00:46:39.840> function.<00:46:40.480> But<00:46:40.640> somehow<00:46:41.400> what<00:46:41.520> the\nsimple function. But somehow what the\nsimple function. But somehow what the model<00:46:42.000> with<00:46:42.280> where<00:46:43.160> it's<00:46:43.400> training<00:46:43.640> on<00:46:43.720> this\nmodel with where it's training on this\nmodel with where it's training on this data,<00:46:44.120> it<00:46:44.280> has<00:46:44.400> to<00:46:44.480> learn<00:46:44.640> something<00:46:44.920> more\ndata, it has to learn something more\ndata, it has to learn something more complex.\ncomplex.\ncomplex. And<00:46:46.720> same<00:46:46.920> with<00:46:47.040> this<00:46:47.160> example<00:46:47.480> here,\nAnd same with this example here,\nAnd same with this example here, um<00:46:48.640> although<00:46:48.840> this<00:46:49.040> example<00:46:49.400> is<00:46:49.520> one<00:46:49.680> where\num although this example is one where\num although this example is one where we've<00:46:50.000> made<00:46:50.440> the<00:46:50.520> induction<00:46:50.880> problem<00:46:51.160> much\nwe've made the induction problem much\nwe've made the induction problem much easier,<00:46:52.080> there's<00:46:52.280> still<00:46:52.560> an<00:46:52.680> asymmetry<00:46:53.120> which\neasier, there's still an asymmetry which\neasier, there's still an asymmetry which I<00:46:53.320> mean<00:46:53.440> there's<00:46:53.600> still,<00:46:53.960> you<00:46:54.040> know,<00:46:54.520> a\nI mean there's still, you know, a\nI mean there's still, you know, a interesting<00:46:55.400> inverse<00:46:55.720> to<00:46:55.840> learn,<00:46:56.359> but<00:46:56.520> it's\ninteresting inverse to learn, but it's\ninteresting inverse to learn, but it's no<00:46:56.880> longer<00:46:57.320> pushing<00:46:57.680> out<00:46:58.000> the<00:46:58.560> where<00:46:58.720> that\nno longer pushing out the where that\nno longer pushing out the where that learning<00:46:59.120> happens<00:46:59.520> exponentially.\nlearning happens exponentially.\nlearning happens exponentially. Um<00:47:01.080> and<00:47:01.240> instead<00:47:01.560> again,<00:47:01.800> we<00:47:01.920> find<00:47:02.160> this\nUm and instead again, we find this\nUm and instead again, we find this increase<00:47:03.000> in<00:47:03.080> perplexity<00:47:03.720> as<00:47:03.960> we\nincrease in perplexity as we\nincrease in perplexity as we as<00:47:05.200> we<00:47:05.280> actually<00:47:05.560> remove<00:47:06.080> information<00:47:06.520> from\nas we actually remove information from\nas we actually remove information from the<00:47:06.720> input.\nthe input.\nthe input. And<00:47:08.560> then<00:47:08.760> another<00:47:09.120> really<00:47:09.400> interesting\nAnd then another really interesting\nAnd then another really interesting example,<00:47:10.440> um\nexample, um\nexample, um uh<00:47:11.960> going<00:47:12.240> back<00:47:12.520> to<00:47:12.640> the<00:47:12.720> cellular<00:47:12.920> automaton\nuh going back to the cellular automaton\nuh going back to the cellular automaton is<00:47:14.520> um\nis um\nis um uh<00:47:15.600> right,<00:47:15.840> is<00:47:16.240> is<00:47:16.560> is<00:47:16.680> thinking<00:47:16.920> about\nuh right, is is is thinking about\nuh right, is is is thinking about emergent<00:47:17.440> phenomena.\nemergent phenomena.\nemergent phenomena. So,<00:47:20.200> um<00:47:20.600> you<00:47:20.680> know,<00:47:20.760> there's<00:47:20.880> a<00:47:20.920> lot<00:47:21.080> to<00:47:21.160> say\nSo, um you know, there's a lot to say\nSo, um you know, there's a lot to say here<00:47:21.800> and<00:47:22.520> I<00:47:22.560> probably<00:47:22.720> won't<00:47:22.880> have<00:47:23.000> time<00:47:23.160> to\nhere and I probably won't have time to\nhere and I probably won't have time to say<00:47:23.359> all<00:47:23.560> of<00:47:23.640> it,<00:47:23.920> um<00:47:24.320> but<00:47:25.240> I<00:47:25.320> think<00:47:25.840> it<00:47:26.000> is\nsay all of it, um but I think it is\nsay all of it, um but I think it is interesting<00:47:26.840> reflecting<00:47:27.359> on<00:47:27.440> the<00:47:27.520> fact<00:47:27.840> that\ninteresting reflecting on the fact that\ninteresting reflecting on the fact that uh\nuh\nuh we\nwe\nwe uh<00:47:31.359> right,<00:47:31.520> with<00:47:31.640> a<00:47:31.680> game<00:47:31.880> like<00:47:32.400> uh<00:47:32.480> game<00:47:32.640> of\nuh right, with a game like uh game of\nuh right, with a game like uh game of life,<00:47:33.320> right?<00:47:33.520> We<00:47:33.640> have\nlife, right? We have\nlife, right? We have uh<00:47:34.920> we<00:47:35.040> can<00:47:35.160> observe<00:47:35.440> all<00:47:35.560> these<00:47:35.720> different\nuh we can observe all these different\nuh we can observe all these different patterns<00:47:36.960> and<00:47:37.240> and<00:47:37.400> persistent<00:47:37.800> structures\npatterns and and persistent structures\npatterns and and persistent structures like,<00:47:38.560> you<00:47:38.640> know,<00:47:38.720> these<00:47:38.800> still<00:47:39.000> lives<00:47:39.280> and\nlike, you know, these still lives and\nlike, you know, these still lives and oscillators<00:47:40.000> and<00:47:40.080> spaceships.\noscillators and spaceships.\noscillators and spaceships. And\nAnd\nAnd with<00:47:43.680> large<00:47:44.040> compute,<00:47:44.880> we<00:47:45.120> can<00:47:45.600> if<00:47:45.720> we're\nwith large compute, we can if we're\nwith large compute, we can if we're imagining<00:47:46.640> predicting<00:47:47.320> the<00:47:47.480> final<00:47:47.840> state\nimagining predicting the final state\nimagining predicting the final state from<00:47:48.400> the<00:47:48.440> initial<00:47:48.760> state<00:47:49.320> um<00:47:49.640> after<00:47:50.160> the\nfrom the initial state um after the\nfrom the initial state um after the final<00:47:50.480> state<00:47:50.640> after<00:47:50.800> many<00:47:51.080> steps<00:47:51.520> after<00:47:51.720> the\nfinal state after many steps after the\nfinal state after many steps after the initial<00:47:52.000> state.<00:47:52.520> With<00:47:52.720> large<00:47:53.040> compute,<00:47:53.400> we\ninitial state. With large compute, we\ninitial state. With large compute, we can<00:47:53.720> run<00:47:54.359> the<00:47:55.000> the<00:47:55.160> rule<00:47:55.480> directly,<00:47:56.160> right?<00:47:56.400> We\ncan run the the rule directly, right? We\ncan run the the rule directly, right? We can<00:47:56.760> expect<00:47:57.160> our<00:47:57.560> our<00:47:58.080> language<00:47:58.440> model<00:47:58.680> to\ncan expect our our language model to\ncan expect our our language model to implement<00:47:59.200> it<00:47:59.440> and<00:47:59.680> run<00:47:59.840> it.\nimplement it and run it.\nimplement it and run it. And<00:48:01.240> then<00:48:01.520> we<00:48:01.600> don't<00:48:01.920> need<00:48:02.320> to<00:48:02.440> have<00:48:02.600> a<00:48:02.680> complex\nAnd then we don't need to have a complex\nAnd then we don't need to have a complex model<00:48:03.560> to<00:48:03.840> perfectly<00:48:04.400> fit<00:48:04.720> the<00:48:04.840> predictions.\nmodel to perfectly fit the predictions.\nmodel to perfectly fit the predictions. But<00:48:06.160> with<00:48:06.280> limited<00:48:06.640> compute,<00:48:07.760> you<00:48:08.240> with\nBut with limited compute, you with\nBut with limited compute, you with compute<00:48:08.760> that<00:48:08.880> is<00:48:08.960> not<00:48:09.240> enough<00:48:09.440> to<00:48:09.600> run<00:48:09.800> it,\ncompute that is not enough to run it,\ncompute that is not enough to run it, then<00:48:10.240> you<00:48:10.320> have<00:48:10.440> to<00:48:10.520> do<00:48:10.640> something\nthen you have to do something\nthen you have to do something interesting,<00:48:11.720> right?<00:48:12.200> And<00:48:12.640> you<00:48:12.720> can<00:48:12.840> have\ninteresting, right? And you can have\ninteresting, right? And you can have very<00:48:13.160> much<00:48:13.400> you<00:48:13.480> can<00:48:13.600> imagine<00:48:14.160> how<00:48:14.760> a<00:48:14.800> model\nvery much you can imagine how a model\nvery much you can imagine how a model here<00:48:15.480> is<00:48:16.080> um\nhere is um\nhere is um basically<00:48:17.680> looking<00:48:18.040> at<00:48:18.240> what<00:48:19.000> structures<00:48:19.560> are\nbasically looking at what structures are\nbasically looking at what structures are in<00:48:20.000> the<00:48:20.080> input,\nin the input,\nin the input, trying<00:48:22.080> to\ntrying to\ntrying to uh\nuh\nuh relate<00:48:24.160> that<00:48:24.400> to<00:48:24.520> a<00:48:24.560> bank<00:48:25.120> of<00:48:25.320> these<00:48:25.480> different\nrelate that to a bank of these different\nrelate that to a bank of these different persistent<00:48:26.160> structures<00:48:26.680> that<00:48:26.800> each<00:48:26.960> have\npersistent structures that each have\npersistent structures that each have their<00:48:27.200> own<00:48:27.280> properties.<00:48:27.720> Some<00:48:27.880> of<00:48:27.960> them\ntheir own properties. Some of them\ntheir own properties. Some of them generate<00:48:29.040> other<00:48:29.320> structures,<00:48:30.160> some<00:48:30.320> of<00:48:30.400> them\ngenerate other structures, some of them\ngenerate other structures, some of them move<00:48:30.760> in<00:48:30.840> a<00:48:30.880> certain<00:48:31.080> direction,<00:48:31.640> right?<00:48:32.080> And\nmove in a certain direction, right? And\nmove in a certain direction, right? And then<00:48:32.400> trying<00:48:32.640> to<00:48:32.960> think<00:48:33.200> about,<00:48:33.440> \"Okay,<00:48:33.680> well,\nthen trying to think about, \"Okay, well,\nthen trying to think about, \"Okay, well, we<00:48:34.520> have<00:48:34.640> this<00:48:34.800> one<00:48:35.000> which<00:48:35.160> goes<00:48:35.320> in<00:48:35.359> this<00:48:35.720> this\nwe have this one which goes in this this\nwe have this one which goes in this this direction.<00:48:36.400> We<00:48:36.440> have<00:48:36.520> this<00:48:36.680> one<00:48:36.840> which<00:48:36.960> stays\ndirection. We have this one which stays\ndirection. We have this one which stays still,<00:48:37.640> right?\"<00:48:38.440> Hmm,<00:48:38.720> there's<00:48:38.880> going<00:48:39.000> to<00:48:39.080> be\nstill, right?\" Hmm, there's going to be\nstill, right?\" Hmm, there's going to be a<00:48:39.200> collision<00:48:39.640> between<00:48:39.920> these<00:48:40.080> two.<00:48:40.520> This<00:48:40.800> kind\na collision between these two. This kind\na collision between these two. This kind of<00:48:41.120> prediction<00:48:41.800> can<00:48:41.960> be<00:48:42.120> done\nof prediction can be done\nof prediction can be done with<00:48:43.720> much<00:48:43.960> less<00:48:44.200> compute<00:48:44.880> than<00:48:45.040> running<00:48:45.400> the\nwith much less compute than running the\nwith much less compute than running the full<00:48:45.720> grid.\nfull grid.\nfull grid. Um\nUm\nUm and<00:48:50.920> it's<00:48:51.280> not<00:48:51.600> going<00:48:51.720> to<00:48:51.800> be<00:48:52.200> you're<00:48:52.280> not\nand it's not going to be you're not\nand it's not going to be you're not going<00:48:52.520> to<00:48:52.560> be<00:48:52.640> able<00:48:52.760> to<00:48:52.800> make<00:48:52.880> perfect\ngoing to be able to make perfect\ngoing to be able to make perfect predictions<00:48:53.640> this<00:48:53.840> way,<00:48:54.640> but<00:48:55.680> what<00:48:55.840> you<00:48:56.000> are\npredictions this way, but what you are\npredictions this way, but what you are going<00:48:56.480> to<00:48:56.560> have<00:48:57.120> is\ngoing to have is\ngoing to have is a<00:48:58.359> lots<00:48:58.840> of<00:48:58.960> interesting<00:48:59.440> structures<00:48:59.960> within\na lots of interesting structures within\na lots of interesting structures within this<00:49:00.320> model.<00:49:01.040> So,<00:49:01.160> what<00:49:01.280> we<00:49:01.359> should<00:49:01.480> expect<00:49:01.880> is\nthis model. So, what we should expect is\nthis model. So, what we should expect is actually<00:49:02.480> with<00:49:02.640> limited<00:49:03.000> compute,<00:49:03.520> we<00:49:03.600> should\nactually with limited compute, we should\nactually with limited compute, we should have<00:49:03.880> a<00:49:04.000> higher<00:49:04.680> perplexity<00:49:05.560> for<00:49:05.640> this<00:49:05.760> data\nhave a higher perplexity for this data\nhave a higher perplexity for this data than<00:49:06.560> with<00:49:06.720> very<00:49:06.880> large<00:49:07.120> compute.\nthan with very large compute.\nthan with very large compute. So,<00:49:09.040> we<00:49:09.160> set<00:49:09.320> out<00:49:09.480> to<00:49:10.040> um<00:49:10.120> to<00:49:10.240> try<00:49:10.560> to\nSo, we set out to um to try to\nSo, we set out to um to try to experimentally<00:49:11.320> measure<00:49:11.560> this.<00:49:12.359> Um<00:49:12.840> we<00:49:13.000> have\nexperimentally measure this. Um we have\nexperimentally measure this. Um we have a<00:49:13.160> very<00:49:13.359> toy<00:49:13.520> set<00:49:13.680> up<00:49:13.800> here,<00:49:14.080> which<00:49:14.280> is<00:49:14.359> just\na very toy set up here, which is just\na very toy set up here, which is just using<00:49:15.240> again<00:49:15.600> a<00:49:15.680> one-dimensional<00:49:16.440> cellular\nusing again a one-dimensional cellular\nusing again a one-dimensional cellular automaton.<00:49:17.040> We'd<00:49:17.160> like<00:49:17.280> to<00:49:17.359> repeat<00:49:17.600> this<00:49:17.880> for\nautomaton. We'd like to repeat this for\nautomaton. We'd like to repeat this for a<00:49:18.200> more<00:49:18.400> complex<00:49:18.800> one.<00:49:19.520> Um<00:49:19.880> but<00:49:20.040> again,<00:49:20.280> with\na more complex one. Um but again, with\na more complex one. Um but again, with the<00:49:20.840> this<00:49:21.080> this<00:49:21.280> rule<00:49:21.400> 54.<00:49:22.440> And<00:49:22.560> then<00:49:22.680> we<00:49:22.800> use<00:49:23.240> a\nthe this this rule 54. And then we use a\nthe this this rule 54. And then we use a version<00:49:23.760> of<00:49:23.920> a<00:49:24.000> loop<00:49:24.240> transformer<00:49:25.280> so<00:49:25.600> that<00:49:26.640> um\nversion of a loop transformer so that um\nversion of a loop transformer so that um if<00:49:27.720> we<00:49:27.960> find<00:49:29.120> a<00:49:29.359> neural<00:49:29.600> network<00:49:29.960> that<00:49:30.120> does\nif we find a neural network that does\nif we find a neural network that does fit<00:49:31.160> this<00:49:31.359> rule<00:49:31.520> directly,<00:49:32.080> that<00:49:32.280> it<00:49:32.400> can\nfit this rule directly, that it can\nfit this rule directly, that it can actually<00:49:32.840> be<00:49:32.920> simple.\nactually be simple.\nactually be simple. We<00:49:34.200> include<00:49:34.520> this<00:49:34.640> in<00:49:34.720> the<00:49:34.800> hypothesis<00:49:35.240> space.\nWe include this in the hypothesis space.\nWe include this in the hypothesis space. And<00:49:36.280> what<00:49:36.400> we<00:49:36.480> find<00:49:36.800> is<00:49:36.960> that<00:49:37.120> at<00:49:37.240> some\nAnd what we find is that at some\nAnd what we find is that at some threshold<00:49:38.200> for<00:49:38.360> compute,<00:49:39.520> the<00:49:39.760> optimal\nthreshold for compute, the optimal\nthreshold for compute, the optimal two-part<00:49:41.040> code<00:49:41.280> length<00:49:41.600> goes<00:49:42.000> from<00:49:42.160> being\ntwo-part code length goes from being\ntwo-part code length goes from being the<00:49:43.360> ordinary<00:49:44.000> transformer<00:49:45.000> to<00:49:45.120> the<00:49:45.200> loop\nthe ordinary transformer to the loop\nthe ordinary transformer to the loop transformer,<00:49:45.960> although<00:49:46.200> we<00:49:46.320> consider<00:49:46.640> both\ntransformer, although we consider both\ntransformer, although we consider both across<00:49:47.720> the<00:49:47.840> compute<00:49:48.160> range.\nacross the compute range.\nacross the compute range. And<00:49:49.680> when<00:49:49.840> that<00:49:50.000> happens,<00:49:51.040> right,<00:49:51.400> the\nAnd when that happens, right, the\nAnd when that happens, right, the the<00:49:52.880> model<00:49:53.240> finally<00:49:53.560> has<00:49:53.720> enough<00:49:53.880> compute<00:49:54.280> to\nthe model finally has enough compute to\nthe model finally has enough compute to actually<00:49:54.760> implement<00:49:55.120> this<00:49:55.280> rule.<00:49:55.880> And<00:49:56.040> so\nactually implement this rule. And so\nactually implement this rule. And so then<00:49:56.560> the<00:49:56.880> two-part<00:49:57.200> code<00:49:57.400> length<00:49:57.560> goes<00:49:57.760> way\nthen the two-part code length goes way\nthen the two-part code length goes way down.\ndown.\ndown. And<00:49:59.120> so<00:49:59.400> also<00:49:59.760> does<00:50:00.120> the<00:50:00.320> epiplexity.\nAnd so also does the epiplexity.\nAnd so also does the epiplexity. So<00:50:01.920> the<00:50:01.960> epiplexity<00:50:02.440> actually<00:50:02.680> goes<00:50:02.920> up<00:50:03.840> with\nSo the epiplexity actually goes up with\nSo the epiplexity actually goes up with compute<00:50:04.440> and<00:50:04.560> then<00:50:04.920> eventually<00:50:05.320> comes<00:50:05.520> down.\ncompute and then eventually comes down.\ncompute and then eventually comes down. And<00:50:07.320> we<00:50:07.440> attempt<00:50:07.760> to<00:50:07.960> mathematize,<00:50:08.680> so<00:50:08.800> that's\nAnd we attempt to mathematize, so that's\nAnd we attempt to mathematize, so that's this<00:50:09.920> phenomenon<00:50:10.280> that<00:50:10.480> we<00:50:10.600> were<00:50:11.360> um\nthis phenomenon that we were um\nthis phenomenon that we were um uh<00:50:12.400> just<00:50:12.560> speaking<00:50:12.720> about<00:50:12.840> before.<00:50:13.040> And<00:50:13.120> we\nuh just speaking about before. And we\nuh just speaking about before. And we attempt<00:50:13.360> to<00:50:13.440> mathematize<00:50:13.960> this<00:50:14.200> with<00:50:14.800> with\nattempt to mathematize this with with\nattempt to mathematize this with with this<00:50:15.520> um<00:50:16.000> description<00:50:16.360> here<00:50:16.720> where<00:50:17.280> we\nthis um description here where we\nthis um description here where we consider<00:50:18.160> two<00:50:18.400> time<00:50:18.680> bounds.<00:50:19.320> One<00:50:19.600> of<00:50:19.680> them\nconsider two time bounds. One of them\nconsider two time bounds. One of them where<00:50:20.920> uh<00:50:21.360> T1,<00:50:22.040> where<00:50:22.280> you<00:50:22.360> do<00:50:22.520> have<00:50:22.640> enough\nwhere uh T1, where you do have enough\nwhere uh T1, where you do have enough time<00:50:23.240> to<00:50:23.680> essentially<00:50:24.000> just<00:50:24.200> run<00:50:24.400> this<00:50:24.560> rule.\ntime to essentially just run this rule.\ntime to essentially just run this rule. And<00:50:25.360> T2,<00:50:25.760> where<00:50:25.920> you<00:50:26.040> don't<00:50:26.320> have<00:50:26.440> enough<00:50:26.640> time\nAnd T2, where you don't have enough time\nAnd T2, where you don't have enough time to<00:50:27.040> run<00:50:27.640> the<00:50:27.760> full<00:50:27.920> step<00:50:28.200> rule,<00:50:28.560> although<00:50:28.800> you\nto run the full step rule, although you\nto run the full step rule, although you do<00:50:29.280> have<00:50:29.440> enough<00:50:29.600> time<00:50:29.880> to<00:50:30.000> run<00:50:30.280> the<00:50:30.440> one<00:50:30.600> step\ndo have enough time to run the one step\ndo have enough time to run the one step rule.<00:50:31.240> So<00:50:31.320> it's<00:50:31.440> not<00:50:31.600> that<00:50:31.760> you<00:50:32.080> you<00:50:32.560> you<00:50:32.640> know\nrule. So it's not that you you you know\nrule. So it's not that you you you know you<00:50:32.920> can't<00:50:33.160> you<00:50:33.280> can't<00:50:33.760> uh<00:50:33.840> run<00:50:33.960> that.<00:50:34.680> Um\nyou can't you can't uh run that. Um\nyou can't you can't uh run that. Um and<00:50:36.320> uh\nand uh\nand uh what<00:50:37.480> we<00:50:37.560> say<00:50:37.720> here<00:50:38.160> is\nwhat we say here is\nwhat we say here is um\num\num the<00:50:40.680> thought<00:50:41.000> is<00:50:41.600> hm\nthe thought is hm\nthe thought is hm perhaps\nperhaps\nperhaps uh<00:50:43.840> the\nuh the\nuh the uh<00:50:45.000> what's<00:50:45.120> going<00:50:45.280> on<00:50:45.360> here<00:50:45.760> is<00:50:46.000> that<00:50:46.760> the\nuh what's going on here is that the\nuh what's going on here is that the uh<00:50:48.240> the<00:50:48.320> difference<00:50:48.760> between<00:50:49.040> these<00:50:49.200> two\nuh the difference between these two\nuh the difference between these two epiplexities<00:50:50.360> for<00:50:50.680> the<00:50:50.800> one<00:50:51.000> step<00:50:51.240> rule\nepiplexities for the one step rule\nepiplexities for the one step rule is\nis\nis constant.<00:50:54.000> But<00:50:54.320> that<00:50:55.080> um\nconstant. But that um\nconstant. But that um your<00:50:57.120> the<00:50:57.200> difference<00:50:57.520> in<00:50:57.600> epiplexities<00:50:58.240> for\nyour the difference in epiplexities for\nyour the difference in epiplexities for the<00:50:58.440> case<00:50:58.760> step<00:50:59.280> rule<00:50:59.520> for<00:50:59.640> these<00:50:59.800> two<00:50:59.920> time\nthe case step rule for these two time\nthe case step rule for these two time bounds<00:51:00.880> is<00:51:01.040> actually\nbounds is actually\nbounds is actually asymptotically<00:51:02.880> greater<00:51:03.120> than<00:51:03.240> constant,\nasymptotically greater than constant,\nasymptotically greater than constant, right?<00:51:03.880> Essentially<00:51:04.200> growing<00:51:04.880> with<00:51:05.160> the\nright? Essentially growing with the\nright? Essentially growing with the state<00:51:05.560> size\nstate size\nstate size and<00:51:07.080> the<00:51:07.160> number<00:51:07.360> of<00:51:07.440> steps<00:51:08.160> or<00:51:08.320> the<00:51:08.400> number<00:51:08.600> of\nand the number of steps or the number of\nand the number of steps or the number of steps.\nsteps.\nsteps. Um<00:51:09.960> right.<00:51:10.200> So<00:51:10.360> the<00:51:10.480> thing<00:51:10.720> that<00:51:10.880> like<00:51:11.080> as<00:51:11.200> you\nUm right. So the thing that like as you\nUm right. So the thing that like as you make<00:51:11.400> the<00:51:11.480> state<00:51:11.720> larger,<00:51:12.160> there<00:51:12.280> are<00:51:12.360> more\nmake the state larger, there are more\nmake the state larger, there are more and<00:51:12.600> more<00:51:12.720> structures<00:51:13.120> they<00:51:13.240> actually<00:51:13.520> need\nand more structures they actually need\nand more structures they actually need to<00:51:14.280> to<00:51:15.000> the<00:51:15.240> that<00:51:15.440> are<00:51:15.520> possible<00:51:15.880> to<00:51:15.960> configure\nto to the that are possible to configure\nto to the that are possible to configure inside<00:51:16.560> there<00:51:16.680> that<00:51:16.800> you<00:51:16.880> need<00:51:17.000> to<00:51:17.080> know\ninside there that you need to know\ninside there that you need to know about.<00:51:17.920> Okay.<00:51:18.720> Um<00:51:19.440> I<00:51:19.520> guess<00:51:19.720> in<00:51:19.800> the<00:51:19.840> interest\nabout. Okay. Um I guess in the interest\nabout. Okay. Um I guess in the interest of<00:51:20.160> time<00:51:20.320> we'll<00:51:20.440> just<00:51:20.880> uh<00:51:21.000> continue,<00:51:21.520> but<00:51:21.800> um\nof time we'll just uh continue, but um\nof time we'll just uh continue, but um we'd<00:51:22.200> love<00:51:22.400> to<00:51:22.640> talk<00:51:22.880> about<00:51:23.080> this<00:51:23.440> uh<00:51:23.920> later\nwe'd love to talk about this uh later\nwe'd love to talk about this uh later on.<00:51:24.640> So<00:51:24.760> then<00:51:24.960> yeah,<00:51:25.080> we<00:51:25.200> also<00:51:25.440> look<00:51:25.640> at<00:51:25.920> um<00:51:26.440> uh\non. So then yeah, we also look at um uh\non. So then yeah, we also look at um uh you<00:51:27.120> know,<00:51:27.200> we<00:51:27.280> have<00:51:27.440> this\nyou know, we have this\nyou know, we have this the<00:51:28.560> thing<00:51:28.760> about<00:51:29.000> this<00:51:29.200> the<00:51:29.320> structure<00:51:29.680> in\nthe thing about this the structure in\nthe thing about this the structure in the<00:51:29.800> model.<00:51:30.520> Well,<00:51:30.760> is<00:51:30.880> the<00:51:31.000> structure<00:51:31.800> how\nthe model. Well, is the structure how\nthe model. Well, is the structure how does<00:51:32.000> the<00:51:32.080> structure<00:51:32.440> relate<00:51:32.760> to<00:51:32.880> what<00:51:33.040> we're\ndoes the structure relate to what we're\ndoes the structure relate to what we're interested<00:51:33.560> in<00:51:34.040> in<00:51:34.160> machine<00:51:34.400> learning<00:51:35.080> for\ninterested in in machine learning for\ninterested in in machine learning for making<00:51:35.560> more<00:51:36.400> uh<00:51:36.600> performant<00:51:36.920> models,\nmaking more uh performant models,\nmaking more uh performant models, thinking<00:51:37.840> about<00:51:38.160> OD<00:51:38.600> transfer<00:51:39.080> OD\nthinking about OD transfer OD\nthinking about OD transfer OD generalization<00:51:40.200> OD<00:51:40.400> performance.\ngeneralization OD performance.\ngeneralization OD performance. And<00:51:41.960> I<00:51:42.000> think<00:51:42.160> there's<00:51:42.280> a<00:51:42.320> nice<00:51:42.480> story<00:51:42.760> here\nAnd I think there's a nice story here\nAnd I think there's a nice story here that<00:51:43.560> um\nthat um\nthat um with<00:51:45.520> a<00:51:45.600> lot<00:51:45.880> of<00:51:46.000> structures<00:51:46.600> in<00:51:46.680> the<00:51:46.760> model,\nwith a lot of structures in the model,\nwith a lot of structures in the model, circuits,<00:51:48.680> induction<00:51:49.040> heads,<00:51:49.560> so<00:51:49.720> forth,\ncircuits, induction heads, so forth,\ncircuits, induction heads, so forth, there's<00:51:50.720> a<00:51:50.760> lot<00:51:50.960> more<00:51:51.520> to<00:51:51.640> draw<00:51:51.880> upon<00:51:52.320> for\nthere's a lot more to draw upon for\nthere's a lot more to draw upon for transfer,<00:51:53.120> right?<00:51:53.400> So<00:51:54.000> at<00:51:54.200> least<00:51:54.520> in\ntransfer, right? So at least in\ntransfer, right? So at least in principle,<00:51:55.160> if<00:51:55.280> we<00:51:55.360> have<00:51:55.520> some<00:51:55.720> other<00:51:55.920> task,\nprinciple, if we have some other task,\nprinciple, if we have some other task, there's<00:51:56.960> more<00:51:57.360> that<00:51:58.120> might<00:51:58.560> be<00:51:59.080> uh<00:51:59.200> that<00:51:59.280> we\nthere's more that might be uh that we\nthere's more that might be uh that we can<00:51:59.600> leverage<00:52:00.000> those<00:52:00.160> existing<00:52:00.520> circuits.\ncan leverage those existing circuits.\ncan leverage those existing circuits. Versus<00:52:01.560> if<00:52:01.720> you<00:52:01.800> have<00:52:02.040> a<00:52:02.080> very<00:52:02.280> small\nVersus if you have a very small\nVersus if you have a very small epiplexity<00:52:03.280> and<00:52:03.400> the<00:52:03.480> model<00:52:03.920> ends<00:52:04.080> up<00:52:04.160> very\nepiplexity and the model ends up very\nepiplexity and the model ends up very small,<00:52:05.000> then<00:52:05.120> there's<00:52:05.280> very<00:52:05.480> little<00:52:05.840> reuse\nsmall, then there's very little reuse\nsmall, then there's very little reuse that<00:52:06.320> can<00:52:06.440> happen.\nthat can happen.\nthat can happen. So<00:52:08.040> we<00:52:08.160> do<00:52:08.320> some<00:52:08.640> interesting<00:52:09.000> analysis<00:52:09.560> of<00:52:10.280> um\nSo we do some interesting analysis of um\nSo we do some interesting analysis of um now<00:52:11.000> this<00:52:11.200> is<00:52:11.600> uh\nnow this is uh\nnow this is uh uh\nuh\nuh we<00:52:13.040> do<00:52:13.160> some<00:52:13.280> analysis<00:52:13.680> based<00:52:13.880> on<00:52:14.000> scaling\nwe do some analysis based on scaling\nwe do some analysis based on scaling laws<00:52:14.720> of<00:52:15.160> um<00:52:15.400> of<00:52:15.480> different<00:52:16.040> uh<00:52:16.360> natural\nlaws of um of different uh natural\nlaws of um of different uh natural domains<00:52:17.200> uh<00:52:17.640> language,<00:52:18.560> images<00:52:19.120> with<00:52:19.240> vector\ndomains uh language, images with vector\ndomains uh language, images with vector quantization.\nquantization.\nquantization. Now<00:52:21.480> I<00:52:21.520> will<00:52:21.640> say<00:52:21.840> that<00:52:22.200> this<00:52:22.440> estimation<00:52:22.840> of\nNow I will say that this estimation of\nNow I will say that this estimation of epiplexity<00:52:23.400> is<00:52:23.520> much<00:52:24.120> uh<00:52:24.320> not<00:52:24.520> nearly<00:52:25.320> done<00:52:25.560> as\nepiplexity is much uh not nearly done as\nepiplexity is much uh not nearly done as as<00:52:26.000> precisely<00:52:26.520> and<00:52:26.640> I<00:52:26.680> think<00:52:26.840> that<00:52:26.920> there<00:52:27.040> are\nas precisely and I think that there are\nas precisely and I think that there are some<00:52:27.520> some<00:52:27.680> challenges<00:52:28.040> there.<00:52:28.520> Uh<00:52:28.640> we're\nsome some challenges there. Uh we're\nsome some challenges there. Uh we're just<00:52:28.920> taking<00:52:29.160> it<00:52:29.280> from<00:52:29.400> scaling<00:52:29.640> laws,<00:52:29.840> but<00:52:29.920> we\njust taking it from scaling laws, but we\njust taking it from scaling laws, but we try<00:52:30.120> to<00:52:30.200> do<00:52:30.280> our<00:52:30.400> best.<00:52:31.040> Um<00:52:31.400> and<00:52:31.560> we<00:52:31.680> find<00:52:31.960> that\ntry to do our best. Um and we find that\ntry to do our best. Um and we find that um<00:52:33.040> that<00:52:33.800> uh<00:52:33.880> for<00:52:34.040> the<00:52:34.160> same<00:52:34.400> compute,<00:52:35.360> um<00:52:35.600> the\num that uh for the same compute, um the\num that uh for the same compute, um the language<00:52:36.080> has<00:52:36.200> a<00:52:36.280> higher<00:52:36.640> epiplexity<00:52:37.320> than<00:52:37.840> um\nlanguage has a higher epiplexity than um\nlanguage has a higher epiplexity than um than<00:52:38.240> images,<00:52:38.760> which<00:52:38.960> is<00:52:39.120> is<00:52:39.280> kind<00:52:39.440> of\nthan images, which is is kind of\nthan images, which is is kind of interesting<00:52:39.960> that<00:52:40.040> is<00:52:40.240> what<00:52:40.480> we're<00:52:40.560> following\ninteresting that is what we're following\ninteresting that is what we're following up<00:52:40.960> on.\nup on.\nup on. Um<00:52:42.000> okay.<00:52:42.440> So<00:52:43.000> uh<00:52:43.080> we<00:52:43.200> also<00:52:43.560> look<00:52:43.800> at<00:52:44.160> uh<00:52:44.280> some\nUm okay. So uh we also look at uh some\nUm okay. So uh we also look at uh some uh<00:52:45.240> downstream<00:52:45.560> performance.<00:52:46.120> Maybe<00:52:46.440> I<00:52:46.560> will\nuh downstream performance. Maybe I will\nuh downstream performance. Maybe I will uh<00:52:46.920> skip<00:52:47.120> past<00:52:47.400> this,<00:52:47.560> but<00:52:47.680> we<00:52:47.760> do<00:52:47.880> some\nuh skip past this, but we do some\nuh skip past this, but we do some preliminary<00:52:48.680> investigation<00:52:49.240> showing<00:52:49.520> that\npreliminary investigation showing that\npreliminary investigation showing that um<00:52:50.840> at<00:52:50.960> least<00:52:51.120> in<00:52:51.200> some<00:52:51.400> cases,<00:52:51.880> training<00:52:52.120> LLMs\num at least in some cases, training LLMs\num at least in some cases, training LLMs on<00:52:52.680> data<00:52:52.840> with<00:52:52.960> higher<00:52:53.160> epiplexity<00:52:53.840> leads<00:52:54.080> to\non data with higher epiplexity leads to\non data with higher epiplexity leads to higher<00:52:54.640> downstream<00:52:55.000> performance<00:52:55.560> for\nhigher downstream performance for\nhigher downstream performance for downstream<00:52:56.520> tasks.<00:52:57.200> But<00:52:57.320> of<00:52:57.400> course<00:52:57.560> this\ndownstream tasks. But of course this\ndownstream tasks. But of course this won't<00:52:57.840> always<00:52:58.080> be<00:52:58.160> the<00:52:58.240> case.<00:52:59.000> You<00:52:59.320> need<00:52:59.920> some\nwon't always be the case. You need some\nwon't always be the case. You need some shared<00:53:00.680> structure<00:53:01.080> between<00:53:01.440> the<00:53:01.520> tasks.\nshared structure between the tasks.\nshared structure between the tasks. Um\nUm\nUm and<00:53:04.840> then<00:53:05.560> uh\nand then uh\nand then uh yeah,<00:53:06.520> so<00:53:06.760> there<00:53:06.880> are<00:53:06.920> a<00:53:06.960> lot<00:53:07.080> of<00:53:07.160> things<00:53:07.320> that\nyeah, so there are a lot of things that\nyeah, so there are a lot of things that we're<00:53:07.520> we're<00:53:07.720> really<00:53:07.920> excited<00:53:08.160> about<00:53:08.560> um<00:53:09.360> uh\nwe're we're really excited about um uh\nwe're we're really excited about um uh doing<00:53:09.840> with<00:53:09.960> this<00:53:10.080> work.<00:53:10.320> I<00:53:10.360> think<00:53:10.520> there's<00:53:10.640> a\ndoing with this work. I think there's a\ndoing with this work. I think there's a lot<00:53:10.840> of<00:53:10.880> different<00:53:11.120> things<00:53:11.280> to<00:53:11.360> do.<00:53:11.480> Here<00:53:11.640> are\nlot of different things to do. Here are\nlot of different things to do. Here are a<00:53:11.760> few<00:53:11.960> things<00:53:12.200> that<00:53:12.280> we're<00:53:12.400> interested<00:53:12.760> in.\na few things that we're interested in.\na few things that we're interested in. Um<00:53:13.840> you<00:53:13.920> know,<00:53:14.000> there's<00:53:14.200> this<00:53:14.360> recent<00:53:14.600> paper\nUm you know, there's this recent paper\nUm you know, there's this recent paper on<00:53:15.240> neural<00:53:15.440> cellular<00:53:15.680> automaton.<00:53:16.200> I<00:53:16.240> know\non neural cellular automaton. I know\non neural cellular automaton. I know neural<00:53:16.640> cellular<00:53:16.840> automaton,<00:53:17.200> you<00:53:17.360> know,<00:53:17.480> is\nneural cellular automaton, you know, is\nneural cellular automaton, you know, is is<00:53:17.840> something<00:53:18.040> that<00:53:18.120> came<00:53:18.280> out<00:53:18.360> of<00:53:18.840> uh<00:53:19.040> your\nis something that came out of uh your\nis something that came out of uh your group,<00:53:19.400> but<00:53:19.480> you<00:53:19.560> have<00:53:19.640> basically\ngroup, but you have basically\ngroup, but you have basically pre-training<00:53:20.560> pre-pre-training<00:53:21.200> on<00:53:21.280> neural\npre-training pre-pre-training on neural\npre-training pre-pre-training on neural cellular<00:53:21.680> automaton<00:53:22.000> data<00:53:22.560> and<00:53:22.640> how<00:53:22.760> that\ncellular automaton data and how that\ncellular automaton data and how that could<00:53:23.000> actually<00:53:23.240> be<00:53:23.320> useful<00:53:23.720> for<00:53:24.200> um<00:53:24.760> you\ncould actually be useful for um you\ncould actually be useful for um you know,<00:53:25.000> uh<00:53:25.280> language<00:53:26.120> uh<00:53:26.200> for<00:53:26.360> code,<00:53:26.840> for<00:53:27.120> math.\nknow, uh language uh for code, for math.\nknow, uh language uh for code, for math. Um<00:53:28.480> and<00:53:28.680> I<00:53:28.720> think<00:53:29.320> very<00:53:29.560> interesting<00:53:30.360> also\nUm and I think very interesting also\nUm and I think very interesting also other<00:53:31.080> things<00:53:31.280> about<00:53:31.440> synthetic<00:53:31.760> data.<00:53:31.880> I\nother things about synthetic data. I\nother things about synthetic data. I think<00:53:32.080> that's<00:53:32.240> something<00:53:32.480> that<00:53:32.600> has<00:53:32.680> been\nthink that's something that has been\nthink that's something that has been under<00:53:33.600> uh\nunder uh\nunder uh uh<00:53:34.320> appreciated.<00:53:34.920> Um\nuh appreciated. Um\nuh appreciated. Um Okay,<00:53:35.760> yeah.<00:53:36.120> Interconnecting<00:53:36.640> this\nOkay, yeah. Interconnecting this\nOkay, yeah. Interconnecting this different<00:53:37.120> demands,<00:53:37.920> thinking<00:53:38.080> more<00:53:38.240> about\ndifferent demands, thinking more about\ndifferent demands, thinking more about emergent<00:53:38.800> phenomena,<00:53:39.280> thinking<00:53:39.520> about\nemergent phenomena, thinking about\nemergent phenomena, thinking about chaos.<00:53:40.560> Um<00:53:40.960> yeah,<00:53:41.160> and<00:53:41.240> I<00:53:41.320> guess<00:53:41.520> maybe<00:53:41.760> I'll\nchaos. Um yeah, and I guess maybe I'll\nchaos. Um yeah, and I guess maybe I'll just<00:53:42.440> open<00:53:42.680> up<00:53:42.760> for<00:53:42.880> your<00:53:42.960> questions.<00:53:43.640> Uh<00:53:43.800> all\njust open up for your questions. Uh all\njust open up for your questions. Uh all right,<00:53:44.000> so<00:53:44.120> so<00:53:44.280> here<00:53:44.360> here<00:53:44.600> is<00:53:44.760> just<00:53:45.040> um<00:53:45.680> just<00:53:45.880> a\nright, so so here here is just um just a\nright, so so here here is just um just a nice<00:53:46.240> highlight<00:53:46.520> of<00:53:46.880> okay,<00:53:47.720> some<00:53:47.920> of<00:53:48.000> the<00:53:48.320> the\nnice highlight of okay, some of the the\nnice highlight of okay, some of the the different<00:53:48.920> objects<00:53:49.240> that<00:53:49.320> we<00:53:49.400> talked<00:53:49.640> about,\ndifferent objects that we talked about,\ndifferent objects that we talked about, right?<00:53:50.160> Um<00:53:50.920> ones<00:53:51.160> which<00:53:51.359> have<00:53:51.800> high<00:53:52.040> time<00:53:52.280> data\nright? Um ones which have high time data\nright? Um ones which have high time data entropy<00:53:53.040> and<00:53:53.840> also<00:53:54.160> high<00:53:54.320> complexity,<00:53:54.840> things\nentropy and also high complexity, things\nentropy and also high complexity, things that<00:53:55.120> are<00:53:55.160> actually<00:53:55.440> random,<00:53:56.040> right?<00:53:56.320> Things\nthat are actually random, right? Things\nthat are actually random, right? Things that<00:53:56.600> have<00:53:56.720> high<00:53:56.880> time<00:53:57.120> data<00:53:57.320> complexity,<00:53:57.920> but\nthat have high time data complexity, but\nthat have high time data complexity, but actually<00:53:58.440> low<00:53:59.040> Kolmogorov<00:53:59.400> complexity,<00:53:59.960> low\nactually low Kolmogorov complexity, low\nactually low Kolmogorov complexity, low entropy<00:54:00.920> because<00:54:01.600> they're<00:54:01.720> somehow\nentropy because they're somehow\nentropy because they're somehow computationally<00:54:02.760> random,<00:54:03.440> but<00:54:03.600> not<00:54:04.320> uh<00:54:04.520> but\ncomputationally random, but not uh but\ncomputationally random, but not uh but not<00:54:05.000> if<00:54:05.040> you<00:54:05.120> have<00:54:05.240> infinite<00:54:05.520> computation,\nnot if you have infinite computation,\nnot if you have infinite computation, right?<00:54:06.680> And<00:54:06.800> then<00:54:07.000> things<00:54:07.200> that<00:54:07.280> have<00:54:07.400> high<00:54:08.200> uh\nright? And then things that have high uh\nright? And then things that have high uh epiplexity<00:54:10.320> um<00:54:10.640> like<00:54:10.800> these<00:54:10.960> things<00:54:11.160> here.\nepiplexity um like these things here.\nepiplexity um like these things here. And<00:54:11.560> most<00:54:11.880> of<00:54:11.960> these,<00:54:12.359> you<00:54:12.440> know,<00:54:12.560> of<00:54:12.680> course\nAnd most of these, you know, of course\nAnd most of these, you know, of course you<00:54:12.920> have<00:54:13.000> natural<00:54:13.280> phenomena,<00:54:13.640> maybe<00:54:13.880> those\nyou have natural phenomena, maybe those\nyou have natural phenomena, maybe those are<00:54:14.200> actually<00:54:14.440> high<00:54:14.560> complexity.<00:54:15.359> But<00:54:15.480> most\nare actually high complexity. But most\nare actually high complexity. But most of<00:54:15.800> these<00:54:16.240> but<00:54:16.359> all<00:54:16.520> of<00:54:16.600> these<00:54:16.920> are<00:54:17.080> actually\nof these but all of these are actually\nof these but all of these are actually ones<00:54:17.680> where<00:54:18.120> we<00:54:18.240> can<00:54:18.359> say<00:54:18.520> that<00:54:18.680> the<00:54:19.000> the\nones where we can say that the the\nones where we can say that the the Kolmogorov<00:54:19.560> complexity,<00:54:20.120> the<00:54:20.240> entropy<00:54:20.720> are\nKolmogorov complexity, the entropy are\nKolmogorov complexity, the entropy are very<00:54:21.000> low,<00:54:21.600> but<00:54:21.760> somehow<00:54:22.400> they<00:54:22.520> have<00:54:22.720> high\nvery low, but somehow they have high\nvery low, but somehow they have high epiplexity.\nepiplexity.\nepiplexity. Um<00:54:24.680> maybe<00:54:24.840> I'll<00:54:24.920> just<00:54:25.080> open<00:54:25.280> up<00:54:25.359> for\nUm maybe I'll just open up for\nUm maybe I'll just open up for questions.<00:54:26.120> Yeah,<00:54:26.600> uh\nquestions. Yeah, uh\nquestions. Yeah, uh Yeah.\nYeah.\nYeah. Thank<00:54:29.440> you<00:54:29.520> very<00:54:29.680> much.<00:54:30.160> I<00:54:30.280> have<00:54:30.480> some\nThank you very much. I have some\nThank you very much. I have some question<00:54:31.520> uh<00:54:31.680> so<00:54:31.840> so<00:54:32.600> uh\nquestion uh so so uh\nquestion uh so so uh the<00:54:33.480> first<00:54:33.800> question<00:54:34.120> is<00:54:34.480> a<00:54:34.560> little<00:54:34.800> bit<00:54:35.320> uh\nthe first question is a little bit uh\nthe first question is a little bit uh technical.<00:54:36.359> So<00:54:36.760> when<00:54:37.000> you<00:54:37.760> use<00:54:38.000> a<00:54:38.080> method<00:54:38.520> to\ntechnical. So when you use a method to\ntechnical. So when you use a method to train<00:54:39.120> on<00:54:39.400> cellular<00:54:39.680> automaton,\ntrain on cellular automaton,\ntrain on cellular automaton, do<00:54:41.000> you<00:54:41.080> predict<00:54:41.680> a<00:54:42.120> T<00:54:42.280> plus<00:54:42.560> one<00:54:42.840> from<00:54:43.120> T<00:54:43.440> or<00:54:43.720> T\ndo you predict a T plus one from T or T\ndo you predict a T plus one from T or T plus<00:54:44.400> like<00:54:44.640> delta<00:54:45.000> T<00:54:45.280> from<00:54:45.520> T?<00:54:46.040> Yeah,<00:54:46.240> so<00:54:46.400> we\nplus like delta T from T? Yeah, so we\nplus like delta T from T? Yeah, so we predict<00:54:46.920> T<00:54:47.120> T<00:54:47.320> plus<00:54:47.800> uh<00:54:47.920> delta<00:54:48.160> T.<00:54:48.320> So<00:54:48.520> it's\npredict T T plus uh delta T. So it's\npredict T T plus uh delta T. So it's something<00:54:49.120> like<00:54:49.480> um<00:54:49.760> in<00:54:49.840> some<00:54:50.000> of<00:54:50.040> the\nsomething like um in some of the\nsomething like um in some of the experiments<00:54:50.440> we<00:54:50.520> do,<00:54:50.760> 16<00:54:51.120> steps<00:54:51.359> ahead,<00:54:51.720> some\nexperiments we do, 16 steps ahead, some\nexperiments we do, 16 steps ahead, some of<00:54:51.960> them<00:54:52.120> 64<00:54:52.560> steps.<00:54:53.440> Um<00:54:54.040> somewhere<00:54:54.320> around\nof them 64 steps. Um somewhere around\nof them 64 steps. Um somewhere around this,<00:54:54.640> but<00:54:54.800> a<00:54:54.840> lot<00:54:55.120> of<00:54:55.200> steps<00:54:55.440> ahead.<00:54:55.880> Yeah.\nthis, but a lot of steps ahead. Yeah.\nthis, but a lot of steps ahead. Yeah. And<00:54:57.200> um<00:54:57.680> that<00:54:57.920> that<00:54:58.120> being<00:54:58.280> a<00:54:58.320> key<00:54:58.520> part.<00:54:58.760> So<00:54:58.880> if\nAnd um that that being a key part. So if\nAnd um that that being a key part. So if you<00:54:59.120> only<00:54:59.359> predicted<00:54:59.800> one<00:54:59.920> step<00:55:00.120> ahead,<00:55:00.400> then\nyou only predicted one step ahead, then\nyou only predicted one step ahead, then uh\nuh\nuh yeah,<00:55:02.040> then<00:55:02.280> then<00:55:02.720> in<00:55:02.800> in\nyeah, then then in in\nyeah, then then in in in<00:55:03.640> most<00:55:03.920> of<00:55:03.960> the<00:55:04.040> cases<00:55:04.400> that<00:55:04.680> I<00:55:04.760> mean<00:55:05.080> I<00:55:05.160> think\nin most of the cases that I mean I think\nin most of the cases that I mean I think in<00:55:05.800> essentially<00:55:06.160> all<00:55:06.280> of<00:55:06.359> the<00:55:06.400> cases<00:55:06.640> the\nin essentially all of the cases the\nin essentially all of the cases the model<00:55:06.880> would<00:55:06.960> just<00:55:07.120> be<00:55:07.200> able<00:55:07.359> to<00:55:07.960> um<00:55:08.480> to<00:55:08.640> do\nmodel would just be able to um to do\nmodel would just be able to um to do this<00:55:09.098> [clears throat]<00:55:09.480> to<00:55:09.600> implement<00:55:10.000> that\nthis [clears throat] to implement that\nthis [clears throat] to implement that one<00:55:10.280> step<00:55:10.520> rule.\none step rule.\none step rule. Yeah,<00:55:11.680> how<00:55:11.960> do<00:55:12.040> you<00:55:12.120> choose<00:55:12.440> the<00:55:12.560> delta<00:55:12.880> T?\nYeah, how do you choose the delta T?\nYeah, how do you choose the delta T? Yeah,<00:55:13.960> so<00:55:14.320> um<00:55:14.960> and<00:55:15.080> that<00:55:15.240> depends<00:55:15.640> on<00:55:15.800> kind<00:55:15.920> of\nYeah, so um and that depends on kind of\nYeah, so um and that depends on kind of which<00:55:16.680> uh<00:55:16.920> which<00:55:17.080> phenomena<00:55:17.440> we're<00:55:17.560> trying<00:55:18.040> to\nwhich uh which phenomena we're trying to\nwhich uh which phenomena we're trying to see.<00:55:18.840> So<00:55:19.440> um\nsee. So um\nsee. So um for<00:55:21.040> uh\nfor uh\nfor uh uh<00:55:22.640> yeah,<00:55:23.080> so<00:55:23.320> for<00:55:23.640> these<00:55:23.920> experiments,<00:55:24.400> we\nuh yeah, so for these experiments, we\nuh yeah, so for these experiments, we choose<00:55:24.840> the<00:55:25.080> delta<00:55:25.400> T<00:55:25.600> pretty<00:55:26.200> um\nchoose the delta T pretty um\nchoose the delta T pretty um uh<00:55:27.040> pretty<00:55:27.240> large,<00:55:27.600> right?<00:55:27.760> So<00:55:27.880> we<00:55:28.000> want<00:55:28.240> the\nuh pretty large, right? So we want the\nuh pretty large, right? So we want the delta<00:55:28.560> T<00:55:28.800> to<00:55:28.880> be<00:55:29.000> large<00:55:29.280> enough<00:55:29.480> that<00:55:29.600> the\ndelta T to be large enough that the\ndelta T to be large enough that the model<00:55:29.920> actually<00:55:30.280> cannot<00:55:30.880> learn<00:55:31.160> that\nmodel actually cannot learn that\nmodel actually cannot learn that multi-step<00:55:31.880> rule,<00:55:32.200> right?<00:55:32.880> Uh<00:55:32.960> so<00:55:33.080> I<00:55:33.120> think\nmulti-step rule, right? Uh so I think\nmulti-step rule, right? Uh so I think this<00:55:33.520> was<00:55:33.640> 64.\nthis was 64.\nthis was 64. Um<00:55:35.800> for<00:55:36.080> some<00:55:36.359> experiments,<00:55:36.920> we<00:55:37.080> might<00:55:37.359> want\nUm for some experiments, we might want\nUm for some experiments, we might want to<00:55:37.720> be<00:55:37.800> in<00:55:37.880> this<00:55:38.040> regime<00:55:38.560> where<00:55:39.160> um<00:55:39.600> where<00:55:39.800> we\nto be in this regime where um where we\nto be in this regime where um where we actually<00:55:40.240> can<00:55:41.160> uh<00:55:41.320> learn<00:55:41.840> this<00:55:42.040> forward\nactually can uh learn this forward\nactually can uh learn this forward function,<00:55:42.800> right?<00:55:43.040> So<00:55:43.760> um<00:55:43.960> say<00:55:44.160> like<00:55:44.440> in<00:55:44.560> in\nfunction, right? So um say like in in\nfunction, right? So um say like in in this<00:55:45.000> setup<00:55:45.560> or<00:55:46.400> um\nthis setup or um\nthis setup or um uh<00:55:47.480> or<00:55:47.760> or<00:55:47.880> in<00:55:47.960> this<00:55:48.280> actually<00:55:48.520> this<00:55:48.840> is<00:55:48.960> one,\nuh or or in this actually this is one,\nuh or or in this actually this is one, right?<00:55:49.600> Um<00:55:49.880> so<00:55:50.160> actually<00:55:50.400> that's<00:55:50.600> where<00:55:50.720> this\nright? Um so actually that's where this\nright? Um so actually that's where this this<00:55:51.080> hard<00:55:51.240> function<00:55:51.560> came<00:55:51.720> from.<00:55:52.160> We<00:55:52.359> we<00:55:52.520> we\nthis hard function came from. We we we\nthis hard function came from. We we we use<00:55:52.800> it<00:55:52.880> quite<00:55:53.040> a<00:55:53.080> bit.<00:55:53.680> Um<00:55:54.080> so<00:55:54.200> this<00:55:54.400> is<00:55:54.520> where\nuse it quite a bit. Um so this is where\nuse it quite a bit. Um so this is where we<00:55:54.840> we<00:55:55.000> set<00:55:55.200> that<00:55:55.320> delta<00:55:55.560> T<00:55:55.680> to<00:55:55.760> be<00:55:56.200> much\nwe we set that delta T to be much\nwe we set that delta T to be much smaller,<00:55:56.760> something<00:55:57.040> like<00:55:57.200> 10<00:55:57.400> steps,<00:55:58.080> where\nsmaller, something like 10 steps, where\nsmaller, something like 10 steps, where um<00:55:58.640> with<00:55:58.800> 10<00:55:59.000> steps,<00:56:00.000> if<00:56:00.040> you<00:56:00.120> train<00:56:00.320> a<00:56:00.359> large\num with 10 steps, if you train a large\num with 10 steps, if you train a large enough<00:56:00.760> model,<00:56:01.200> it<00:56:01.280> can<00:56:01.520> eventually<00:56:01.840> learn\nenough model, it can eventually learn\nenough model, it can eventually learn it,<00:56:02.200> but<00:56:02.320> it's<00:56:02.480> difficult.\nit, but it's difficult.\nit, but it's difficult. Okay.<00:56:04.359> Yeah,<00:56:04.800> the<00:56:04.960> reason<00:56:05.280> I<00:56:05.400> ask<00:56:05.760> you<00:56:05.880> this\nOkay. Yeah, the reason I ask you this\nOkay. Yeah, the reason I ask you this question<00:56:06.400> because<00:56:06.640> this<00:56:07.120> really<00:56:07.440> reminds<00:56:08.000> me\nquestion because this really reminds me\nquestion because this really reminds me of<00:56:08.680> uh<00:56:09.200> Stephen<00:56:09.560> Wolfram's<00:56:10.240> uh<00:56:10.359> computational\nof uh Stephen Wolfram's uh computational\nof uh Stephen Wolfram's uh computational irreducibility.\nirreducibility.\nirreducibility. It's<00:56:12.840> it's<00:56:13.000> saying<00:56:13.480> when<00:56:13.680> you<00:56:13.880> have<00:56:14.120> some<00:56:14.520> some\nIt's it's saying when you have some some\nIt's it's saying when you have some some model<00:56:15.400> like<00:56:16.240> rule<00:56:16.440> 30,<00:56:17.320> when<00:56:17.480> you<00:56:17.600> want<00:56:17.880> to\nmodel like rule 30, when you want to\nmodel like rule 30, when you want to predict<00:56:18.359> the<00:56:18.440> future,<00:56:18.840> you<00:56:18.920> can't\npredict the future, you can't\npredict the future, you can't jump<00:56:20.560> to<00:56:20.680> the<00:56:20.800> future.<00:56:21.160> You<00:56:21.320> must<00:56:21.680> do<00:56:22.080> step<00:56:22.359> by\njump to the future. You must do step by\njump to the future. You must do step by step.<00:56:22.880> So<00:56:23.120> I<00:56:23.320> I<00:56:23.440> wondering<00:56:24.440> how<00:56:24.680> how<00:56:24.800> do<00:56:24.880> you\nstep. So I I wondering how how do you\nstep. So I I wondering how how do you see<00:56:25.280> the<00:56:25.560> relationship<00:56:26.320> between<00:56:26.640> your<00:56:27.000> work\nsee the relationship between your work\nsee the relationship between your work and<00:56:28.040> uh<00:56:28.120> this<00:56:28.440> computational\nand uh this computational\nand uh this computational irreducibility?\nirreducibility?\nirreducibility? Yeah,<00:56:31.040> so<00:56:31.240> I<00:56:31.280> mean<00:56:31.440> we're<00:56:31.560> definitely<00:56:31.840> heavily\nYeah, so I mean we're definitely heavily\nYeah, so I mean we're definitely heavily inspired<00:56:32.440> by<00:56:32.760> you<00:56:32.800> know,<00:56:32.920> some<00:56:33.120> of<00:56:33.240> Wolfram's\ninspired by you know, some of Wolfram's\ninspired by you know, some of Wolfram's work.<00:56:34.400> Um<00:56:34.800> and<00:56:35.000> I<00:56:35.080> think<00:56:35.359> that<00:56:35.800> the<00:56:36.560> uh<00:56:36.760> right,\nwork. Um and I think that the uh right,\nwork. Um and I think that the uh right, the<00:56:37.200> the<00:56:37.480> computational<00:56:38.000> irreducibility\nthe the computational irreducibility\nthe the computational irreducibility speaks<00:56:39.200> to<00:56:39.760> um\nspeaks to um\nspeaks to um uh<00:56:41.680> right,<00:56:41.880> there<00:56:42.000> are<00:56:42.040> there<00:56:42.160> are<00:56:42.200> certain\nuh right, there are there are certain\nuh right, there are there are certain elements<00:56:42.680> where<00:56:43.080> yeah,<00:56:43.240> you<00:56:43.320> you're<00:56:43.680> right,\nelements where yeah, you you're right,\nelements where yeah, you you're right, you<00:56:43.920> can't<00:56:44.280> you<00:56:44.359> can't<00:56:44.600> jump<00:56:44.800> ahead<00:56:45.320> um\nyou can't you can't jump ahead um\nyou can't you can't jump ahead um completely,<00:56:45.840> but<00:56:45.960> I<00:56:46.040> think<00:56:46.320> that<00:56:47.080> even<00:56:47.720> in\ncompletely, but I think that even in\ncompletely, but I think that even in many<00:56:48.040> of<00:56:48.120> these<00:56:48.280> cases,<00:56:49.440> um<00:56:50.280> say<00:56:51.200> uh<00:56:51.440> with<00:56:52.359> rule\nmany of these cases, um say uh with rule\nmany of these cases, um say uh with rule 54<00:56:53.520> or<00:56:54.160> ones<00:56:54.600> that<00:56:54.960> you<00:56:55.160> do<00:56:55.280> not<00:56:55.520> have<00:56:55.680> this\n54 or ones that you do not have this\n54 or ones that you do not have this completely<00:56:56.200> unpredictable<00:56:56.680> output,<00:56:57.400> there\ncompletely unpredictable output, there\ncompletely unpredictable output, there are<00:56:58.080> there<00:56:58.359> is<00:56:58.560> a<00:56:58.640> lot<00:56:59.240> that<00:56:59.400> you<00:56:59.520> can<00:56:59.720> jump\nare there is a lot that you can jump\nare there is a lot that you can jump ahead<00:57:00.160> for.<00:57:00.600> And<00:57:00.760> that<00:57:00.960> part<00:57:01.240> is<00:57:01.640> where\nahead for. And that part is where\nahead for. And that part is where actually<00:57:02.920> with<00:57:03.120> small<00:57:03.480> compute,<00:57:04.040> you<00:57:04.120> can\nactually with small compute, you can\nactually with small compute, you can still<00:57:04.480> make<00:57:04.680> progress.<00:57:05.720> Um<00:57:06.240> right,<00:57:06.720> with<00:57:07.040> with\nstill make progress. Um right, with with\nstill make progress. Um right, with with not<00:57:07.640> enough<00:57:07.880> compute<00:57:08.200> to<00:57:08.320> run<00:57:08.480> the<00:57:08.560> full\nnot enough compute to run the full\nnot enough compute to run the full cellular<00:57:09.120> automaton.<00:57:09.520> So<00:57:09.640> that's<00:57:09.880> that's<00:57:10.080> the\ncellular automaton. So that's that's the\ncellular automaton. So that's that's the regime<00:57:10.480> that<00:57:10.640> these<00:57:11.040> are<00:57:11.320> in.<00:57:11.960> Um<00:57:12.440> and<00:57:12.760> so<00:57:13.480> in\nregime that these are in. Um and so in\nregime that these are in. Um and so in this<00:57:13.800> setting,<00:57:14.480> uh<00:57:14.680> you<00:57:14.760> know,<00:57:14.840> what<00:57:14.960> I'd<00:57:15.120> say\nthis setting, uh you know, what I'd say\nthis setting, uh you know, what I'd say is<00:57:15.520> that<00:57:16.240> the<00:57:16.400> the<00:57:16.520> fact<00:57:16.800> that<00:57:16.920> we<00:57:17.000> can<00:57:17.120> make\nis that the the fact that we can make\nis that the the fact that we can make continued<00:57:17.760> gains<00:57:18.359> with<00:57:18.720> compute<00:57:19.240> that<00:57:19.400> is<00:57:19.520> not\ncontinued gains with compute that is not\ncontinued gains with compute that is not enough<00:57:20.080> to<00:57:20.359> fit<00:57:20.640> the<00:57:20.920> the<00:57:21.000> final<00:57:21.240> function\nenough to fit the the final function\nenough to fit the the final function says<00:57:22.280> that<00:57:22.400> there's<00:57:22.560> actually<00:57:22.840> a<00:57:22.880> lot<00:57:23.280> of<00:57:23.440> kind\nsays that there's actually a lot of kind\nsays that there's actually a lot of kind of<00:57:23.800> reducible<00:57:24.440> components<00:57:24.960> along<00:57:25.280> the<00:57:25.400> way,\nof reducible components along the way,\nof reducible components along the way, ways<00:57:26.520> that<00:57:26.640> you<00:57:26.760> can<00:57:27.000> make<00:57:27.160> predictions\nways that you can make predictions\nways that you can make predictions effectively<00:57:28.760> without<00:57:29.280> running<00:57:29.520> the<00:57:29.640> full\neffectively without running the full\neffectively without running the full rule.<00:57:30.680> And<00:57:31.160> um<00:57:31.600> of<00:57:31.720> course<00:57:32.000> with<00:57:32.160> rule<00:57:32.320> 30,\nrule. And um of course with rule 30,\nrule. And um of course with rule 30, the<00:57:33.840> one<00:57:34.040> that<00:57:34.160> is<00:57:34.400> is<00:57:34.600> conjectured<00:57:35.040> to<00:57:35.120> be,\nthe one that is is conjectured to be,\nthe one that is is conjectured to be, you<00:57:35.320> know,<00:57:35.520> a<00:57:35.600> computationally<00:57:36.160> irreducible,\nyou know, a computationally irreducible,\nyou know, a computationally irreducible, um<00:57:37.280> you<00:57:37.440> you<00:57:37.520> don't<00:57:37.720> see<00:57:37.840> that<00:57:38.000> happening.\num you you don't see that happening.\num you you don't see that happening. So<00:57:39.359> I<00:57:39.440> think<00:57:39.720> that<00:57:40.480> um<00:57:41.240> that<00:57:42.320> uh<00:57:42.680> thinking\nSo I think that um that uh thinking\nSo I think that um that uh thinking about<00:57:43.400> useful<00:57:43.760> data<00:57:44.359> for<00:57:44.480> us<00:57:44.600> to<00:57:44.680> train<00:57:44.920> on,<00:57:45.240> it\nabout useful data for us to train on, it\nabout useful data for us to train on, it is<00:57:45.600> data<00:57:45.880> that<00:57:46.240> has<00:57:46.560> some<00:57:46.720> level<00:57:46.960> of<00:57:47.040> computa-\nis data that has some level of computa-\nis data that has some level of computa- that<00:57:47.680> is<00:57:47.880> some<00:57:48.080> level<00:57:48.280> of<00:57:48.359> computationally\nthat is some level of computationally\nthat is some level of computationally reducible\nreducible\nreducible um<00:57:50.520> is<00:57:50.720> is<00:57:50.880> what<00:57:51.040> I<00:57:51.359> how<00:57:51.800> I<00:57:51.880> think<00:57:52.080> about<00:57:52.240> that,\num is is what I how I think about that,\num is is what I how I think about that, which<00:57:52.600> where<00:57:53.040> people<00:57:53.400> with<00:57:53.640> limited\nwhich where people with limited\nwhich where people with limited computation<00:57:54.520> looking<00:57:54.720> at<00:57:54.800> the<00:57:54.880> data<00:57:55.400> that\ncomputation looking at the data that\ncomputation looking at the data that don't<00:57:55.760> have<00:57:55.920> enough<00:57:56.400> that<00:57:56.520> can't<00:57:56.720> just<00:57:56.880> run\ndon't have enough that can't just run\ndon't have enough that can't just run the<00:57:57.320> the<00:57:57.600> computation<00:57:58.000> directly<00:57:58.400> can<00:57:58.560> still\nthe the computation directly can still\nthe the computation directly can still um\num\num uh<00:57:59.840> make<00:58:00.080> interesting<00:58:00.480> predictions,<00:58:00.920> can\nuh make interesting predictions, can\nuh make interesting predictions, can still<00:58:01.200> learn<00:58:01.400> interesting<00:58:01.880> things,<00:58:02.560> you\nstill learn interesting things, you\nstill learn interesting things, you know,<00:58:02.800> like<00:58:03.600> say<00:58:03.800> how<00:58:04.280> uh\nknow, like say how uh\nknow, like say how uh how<00:58:05.240> you<00:58:05.320> don't<00:58:05.480> need<00:58:05.640> to<00:58:05.760> know<00:58:06.040> all<00:58:06.280> of<00:58:06.440> the<00:58:06.960> uh\nhow you don't need to know all of the uh\nhow you don't need to know all of the uh the<00:58:07.400> positions<00:58:07.920> of<00:58:08.040> the<00:58:08.240> atoms<00:58:08.640> in<00:58:08.720> a<00:58:08.760> gas<00:58:09.480> to\nthe positions of the atoms in a gas to\nthe positions of the atoms in a gas to be<00:58:09.680> able<00:58:09.880> to<00:58:09.960> say<00:58:10.120> something<00:58:10.480> about<00:58:10.960> its\nbe able to say something about its\nbe able to say something about its pressure<00:58:11.640> or<00:58:11.760> temperature<00:58:12.359> or<00:58:12.600> volume,<00:58:13.080> these\npressure or temperature or volume, these\npressure or temperature or volume, these kinds<00:58:13.440> of<00:58:13.520> things.\nThank<00:58:17.920> you.\nUh\nUh\nUh do<00:58:22.920> do<00:58:23.080> you<00:58:23.120> mind<00:58:23.880> uh<00:58:23.960> going<00:58:24.320> back<00:58:24.680> to<00:58:24.800> that\ndo do you mind uh going back to that\ndo do you mind uh going back to that example<00:58:26.120> uh<00:58:26.200> with<00:58:26.440> low<00:58:26.920> Kolmogorov\nexample uh with low Kolmogorov\nexample uh with low Kolmogorov complexity<00:58:28.240> and<00:58:28.400> high<00:58:28.960> epiplexity?<00:58:29.920> I<00:58:30.040> I<00:58:30.080> I<00:58:30.120> I\ncomplexity and high epiplexity? I I I I\ncomplexity and high epiplexity? I I I I I'd<00:58:31.080> like<00:58:31.280> to<00:58:31.359> understand<00:58:31.800> that<00:58:31.920> a<00:58:31.960> little\nI'd like to understand that a little\nI'd like to understand that a little bit.\nbit.\nbit. Uh<00:58:33.920> low<00:58:34.120> Kolmogorov<00:58:34.480> complexity?<00:58:35.080> Yeah,<00:58:35.760> uh\nUh low Kolmogorov complexity? Yeah, uh\nUh low Kolmogorov complexity? Yeah, uh right.<00:58:36.440> So<00:58:37.200> um\nright. So um\nright. So um uh\nuh\nuh Do<00:58:40.040> you<00:58:40.120> remember<00:58:40.359> which<00:58:40.600> one<00:58:40.800> that<00:58:40.920> was?<00:58:41.720> You\nDo you remember which one that was? You\nDo you remember which one that was? You mean<00:58:41.880> the<00:58:41.960> one<00:58:42.080> that\nmean the one that\nmean the one that >> I<00:58:42.359> I<00:58:42.400> think<00:58:42.560> it<00:58:42.640> was<00:58:42.760> towards<00:58:43.000> the<00:58:43.120> end.<00:58:43.840> Yeah,\n>> I I think it was towards the end. Yeah,\n>> I I think it was towards the end. Yeah, this<00:58:44.080> this<00:58:44.240> one<00:58:44.359> here?\nthis this one here?\nthis this one here? Right.\nRight.\nRight. Uh<00:58:47.359> is<00:58:47.520> it<00:58:47.600> this<00:58:47.800> slide?\nUh is it this slide?\nUh is it this slide? Uh<00:58:50.400> So<00:58:50.560> here<00:58:50.920> is<00:58:51.000> maybe<00:58:51.200> a<00:58:51.240> summary<00:58:51.560> of<00:58:51.640> what\nUh So here is maybe a summary of what\nUh So here is maybe a summary of what you<00:58:51.920> Yeah,<00:58:52.120> I<00:58:52.359> I<00:58:52.440> think<00:58:52.640> this<00:58:52.760> is<00:58:52.800> the<00:58:52.840> one.\nyou Yeah, I I think this is the one.\nyou Yeah, I I think this is the one. Yeah,<00:58:53.160> yeah,<00:58:53.240> yeah.<00:58:53.640> Right.\nYeah, yeah, yeah. Right.\nYeah, yeah, yeah. Right. So<00:58:54.920> um<00:58:55.320> so<00:58:55.520> these<00:58:55.920> guys<00:58:56.160> here,<00:58:56.560> right?<00:58:56.920> Uh\nSo um so these guys here, right? Uh\nSo um so these guys here, right? Uh low<00:58:58.040> Kolmogorov<00:58:58.400> complexity<00:58:59.080> and<00:58:59.280> oh<00:58:59.359> sorry,\nlow Kolmogorov complexity and oh sorry,\nlow Kolmogorov complexity and oh sorry, low<00:58:59.760> Kolmogorov<00:59:00.080> complexity<00:59:00.400> and<00:59:00.480> high\nlow Kolmogorov complexity and high\nlow Kolmogorov complexity and high epiplexity.<00:59:01.560> That<00:59:01.760> that's<00:59:02.040> the<00:59:02.160> these<00:59:02.400> ones.\nepiplexity. That that's the these ones.\nepiplexity. That that's the these ones. >> Yeah.\n>> Yeah.\n>> Yeah. Right.<00:59:04.520> So<00:59:04.680> that<00:59:05.120> um<00:59:05.520> you<00:59:05.600> know,<00:59:05.720> key<00:59:05.840> example\nRight. So that um you know, key example\nRight. So that um you know, key example is<00:59:06.280> being<00:59:06.520> right<00:59:06.680> like<00:59:07.280> uh<00:59:07.600> rule<00:59:07.760> 54,<00:59:08.960> um<00:59:09.200> this\nis being right like uh rule 54, um this\nis being right like uh rule 54, um this AlphaZero,<00:59:10.359> say<00:59:10.840> like<00:59:11.200> a<00:59:11.240> data<00:59:11.600> produced<00:59:11.840> from\nAlphaZero, say like a data produced from\nAlphaZero, say like a data produced from a<00:59:12.000> fractal.<00:59:12.760> In<00:59:12.880> each<00:59:13.040> of<00:59:13.120> these<00:59:13.240> cases,<00:59:13.680> we\na fractal. In each of these cases, we\na fractal. In each of these cases, we have<00:59:14.320> a<00:59:14.520> short<00:59:14.760> program<00:59:15.200> that<00:59:15.480> can<00:59:15.720> produce\nhave a short program that can produce\nhave a short program that can produce the<00:59:16.640> outputs,<00:59:17.120> right?<00:59:17.359> In<00:59:17.440> the<00:59:17.520> case<00:59:17.680> of<00:59:17.760> the\nthe outputs, right? In the case of the\nthe outputs, right? In the case of the fractal,<00:59:18.240> we<00:59:18.320> just<00:59:18.480> have<00:59:18.640> this<00:59:19.240> iterating<00:59:19.600> the\nfractal, we just have this iterating the\nfractal, we just have this iterating the complex<00:59:20.040> plane,<00:59:20.560> right?<00:59:21.280> Um<00:59:21.720> it<00:59:21.800> just<00:59:21.920> takes<00:59:22.080> a\ncomplex plane, right? Um it just takes a\ncomplex plane, right? Um it just takes a lot<00:59:22.240> of<00:59:22.320> computation<00:59:22.840> to<00:59:22.920> make<00:59:23.120> all<00:59:23.240> these\nlot of computation to make all these\nlot of computation to make all these different<00:59:23.840> uh\ndifferent uh\ndifferent uh uh<00:59:24.800> you<00:59:24.880> know,<00:59:25.040> pixels.<00:59:26.000> Um<00:59:26.920> uh\nuh you know, pixels. Um uh\nuh you know, pixels. Um uh and<00:59:28.080> for<00:59:28.680> uh<00:59:29.000> right,<00:59:29.520> uh\nand for uh right, uh\nand for uh right, uh but<00:59:30.520> if<00:59:30.680> we<00:59:31.160> are<00:59:31.480> training<00:59:31.880> on<00:59:32.000> it<00:59:32.240> with<00:59:32.880> a\nbut if we are training on it with a\nbut if we are training on it with a model<00:59:33.600> that<00:59:34.520> has<00:59:34.960> limited<00:59:35.240> computation,<00:59:36.360> then\nmodel that has limited computation, then\nmodel that has limited computation, then actually<00:59:37.240> we<00:59:37.360> see<00:59:37.520> this<00:59:37.920> as<00:59:38.040> complex<00:59:38.600> and\nactually we see this as complex and\nactually we see this as complex and interesting.\ninteresting.\ninteresting. And<00:59:40.600> perhaps,<00:59:41.120> you<00:59:41.240> know,<00:59:41.480> mapping<00:59:42.000> a<00:59:42.040> little\nAnd perhaps, you know, mapping a little\nAnd perhaps, you know, mapping a little bit<00:59:42.440> on<00:59:42.600> to<00:59:43.320> I<00:59:43.360> mean<00:59:43.720> a<00:59:43.760> human<00:59:44.040> looks<00:59:44.280> at<00:59:44.400> this\nbit on to I mean a human looks at this\nbit on to I mean a human looks at this and<00:59:44.920> they<00:59:45.080> think<00:59:45.320> you<00:59:45.400> know<00:59:45.480> they<00:59:45.560> think<00:59:45.720> this\nand they think you know they think this\nand they think you know they think this is<00:59:46.120> really<00:59:46.760> this<00:59:47.000> this<00:59:47.200> is<00:59:47.280> really\nis really this this is really\nis really this this is really interesting<00:59:47.880> and<00:59:47.960> there's<00:59:48.080> things<00:59:48.280> to<00:59:48.400> learn\ninteresting and there's things to learn\ninteresting and there's things to learn here,<00:59:48.960> right?<00:59:49.840> Um<00:59:50.080> and<00:59:50.240> that<00:59:50.480> is<00:59:50.560> somehow<00:59:50.800> true\nhere, right? Um and that is somehow true\nhere, right? Um and that is somehow true at<00:59:51.200> the<00:59:51.280> same<00:59:51.480> time<00:59:51.960> as<00:59:52.240> there<00:59:52.400> being<00:59:52.560> a<00:59:52.600> very\nat the same time as there being a very\nat the same time as there being a very simple<00:59:53.000> rule<00:59:53.120> that<00:59:53.240> generated<00:59:53.680> it.<00:59:54.160> Um\nsimple rule that generated it. Um\nsimple rule that generated it. Um another<00:59:54.920> example,<00:59:55.200> right?<00:59:55.440> The<00:59:55.640> rule<00:59:55.760> 54,<00:59:56.720> the\nanother example, right? The rule 54, the\nanother example, right? The rule 54, the rule<00:59:57.240> itself<00:59:57.720> has<00:59:57.960> a<00:59:58.000> very<00:59:58.160> short\nrule itself has a very short\nrule itself has a very short description.\ndescription.\ndescription. Uh<01:00:00.080> if<01:00:00.440> we<01:00:01.280> uh\nUh if we uh\nUh if we uh I<01:00:02.240> guess<01:00:02.880> either<01:00:03.080> you<01:00:03.200> could<01:00:03.360> consider<01:00:03.680> the\nI guess either you could consider the\nI guess either you could consider the version<01:00:04.160> where<01:00:04.600> we<01:00:04.720> have<01:00:05.160> um\nversion where we have um\nversion where we have um random<01:00:06.640> initial<01:00:06.920> states<01:00:07.320> and<01:00:07.480> we're\nrandom initial states and we're\nrandom initial states and we're considering<01:00:07.880> the<01:00:07.960> prediction<01:00:08.320> problem<01:00:08.600> of\nconsidering the prediction problem of\nconsidering the prediction problem of the<01:00:08.800> final<01:00:09.080> state<01:00:09.320> given<01:00:09.520> the<01:00:09.600> initial\nthe final state given the initial\nthe final state given the initial states.<01:00:10.280> That<01:00:10.400> could<01:00:10.480> be<01:00:10.600> one<01:00:10.720> version<01:00:11.160> where\nstates. That could be one version where\nstates. That could be one version where that<01:00:11.560> would<01:00:11.680> be<01:00:12.080> high<01:00:12.240> epiplexity<01:00:12.880> but<01:00:13.080> low\nthat would be high epiplexity but low\nthat would be high epiplexity but low Kolmogorov<01:00:13.960> complexity<01:00:14.960> um<01:00:15.320> because<01:00:15.600> again,\nKolmogorov complexity um because again,\nKolmogorov complexity um because again, you<01:00:16.240> know,<01:00:16.320> you<01:00:16.760> you<01:00:16.880> know<01:00:17.040> the<01:00:17.120> rule,<01:00:17.440> you\nyou know, you you know the rule, you\nyou know, you you know the rule, you could<01:00:17.640> just<01:00:17.840> unroll<01:00:18.160> it.<01:00:18.680> Um<01:00:18.800> or<01:00:19.080> you<01:00:19.200> could<01:00:19.360> do\ncould just unroll it. Um or you could do\ncould just unroll it. Um or you could do say<01:00:20.040> uh\nsay uh\nsay uh where<01:00:20.920> you<01:00:21.040> just<01:00:21.240> have<01:00:21.360> some<01:00:21.480> deterministic\nwhere you just have some deterministic\nwhere you just have some deterministic initial<01:00:22.600> states<01:00:23.280> and<01:00:23.480> then<01:00:24.400> um\ninitial states and then um\ninitial states and then um uh<01:00:25.640> right<01:00:25.840> and<01:00:26.080> all<01:00:26.240> you're<01:00:26.320> doing<01:00:26.520> is<01:00:26.640> trying\nuh right and all you're doing is trying\nuh right and all you're doing is trying to<01:00:26.840> predict<01:00:27.080> the<01:00:27.160> final<01:00:27.400> state.<01:00:27.760> And<01:00:27.840> again,\nto predict the final state. And again,\nto predict the final state. And again, that<01:00:28.320> would<01:00:29.000> have<01:00:29.200> the<01:00:29.280> same<01:00:29.520> thing<01:00:29.720> of<01:00:29.920> low\nthat would have the same thing of low\nthat would have the same thing of low Kolmogorov<01:00:30.520> complexity<01:00:31.520> um<01:00:31.720> high<01:00:32.480> uh\nKolmogorov complexity um high uh\nKolmogorov complexity um high uh epiplexity.<01:00:34.080> Uh<01:00:34.240> also<01:00:34.520> the<01:00:34.600> AlphaZero,\nepiplexity. Uh also the AlphaZero,\nepiplexity. Uh also the AlphaZero, right?<01:00:35.680> Again,<01:00:36.040> the<01:00:36.200> this<01:00:36.720> the<01:00:36.840> seed,<01:00:37.280> the\nright? Again, the this the seed, the\nright? Again, the this the seed, the algorithm,<01:00:37.800> the<01:00:37.840> rules<01:00:38.040> of<01:00:38.120> the<01:00:38.200> game,<01:00:38.800> they\nalgorithm, the rules of the game, they\nalgorithm, the rules of the game, they all<01:00:39.000> have<01:00:39.080> a<01:00:39.120> short<01:00:39.320> description.<01:00:40.160> You<01:00:40.240> can\nall have a short description. You can\nall have a short description. You can write<01:00:40.520> that<01:00:40.640> down<01:00:40.840> as<01:00:41.000> a<01:00:41.080> computer<01:00:41.440> program<01:00:41.960> in\nwrite that down as a computer program in\nwrite that down as a computer program in in<01:00:42.480> just<01:00:42.680> a<01:00:42.760> few<01:00:42.920> thousand<01:00:43.200> lines<01:00:43.400> of<01:00:43.480> code.\nin just a few thousand lines of code.\nin just a few thousand lines of code. But<01:00:44.800> you<01:00:44.880> run<01:00:45.080> that<01:00:45.680> and<01:00:45.800> you<01:00:46.400> produce,<01:00:47.000> you\nBut you run that and you produce, you\nBut you run that and you produce, you know,<01:00:47.200> millions<01:00:47.760> or<01:00:47.880> billion<01:00:48.200> parameter\nknow, millions or billion parameter\nknow, millions or billion parameter models<01:00:49.440> um<01:00:49.600> that<01:00:49.840> seems<01:00:50.040> to<01:00:50.120> have<01:00:50.240> a<01:00:50.280> very<01:00:50.480> deep\nmodels um that seems to have a very deep\nmodels um that seems to have a very deep understanding<01:00:51.240> of<01:00:51.320> all<01:00:51.440> these<01:00:51.560> different<01:00:51.840> end\nunderstanding of all these different end\nunderstanding of all these different end game<01:00:52.120> variations.<01:00:53.120> Um\ngame variations. Um\ngame variations. Um and<01:00:54.160> to<01:00:54.280> human<01:00:54.560> they<01:00:54.680> would<01:00:54.800> say<01:00:54.920> that<01:00:55.080> the\nand to human they would say that the\nand to human they would say that the model<01:00:55.480> has<01:00:55.800> learned<01:00:56.080> all<01:00:56.200> this<01:00:56.360> information\nmodel has learned all this information\nmodel has learned all this information about<01:00:57.040> all<01:00:57.120> these<01:00:57.240> different<01:00:57.480> end<01:00:57.560> game\nabout all these different end game\nabout all these different end game variations<01:00:58.360> and<01:00:58.480> this<01:00:58.640> thing<01:00:58.840> and<01:00:58.920> that<01:00:59.200> and\nvariations and this thing and that and\nvariations and this thing and that and um\num\num right.<01:01:00.720> Uh<01:01:00.880> and<01:01:01.120> so<01:01:01.800> at<01:01:01.920> some<01:01:02.040> level<01:01:02.240> we<01:01:02.360> know\nright. Uh and so at some level we know\nright. Uh and so at some level we know that<01:01:03.000> the<01:01:03.120> Kolmogorov<01:01:03.440> complexity<01:01:03.960> is<01:01:04.080> low,\nthat the Kolmogorov complexity is low,\nthat the Kolmogorov complexity is low, Shannon<01:01:04.880> information<01:01:05.360> is<01:01:05.520> low<01:01:06.280> um<01:01:06.640> because<01:01:06.960> of\nShannon information is low um because of\nShannon information is low um because of just<01:01:07.400> what<01:01:07.640> went<01:01:07.840> into<01:01:08.080> this,<01:01:08.760> you<01:01:08.840> know,<01:01:09.280> the\njust what went into this, you know, the\njust what went into this, you know, the this<01:01:09.600> program<01:01:09.840> they<01:01:09.960> use<01:01:10.160> it.<01:01:10.520> But<01:01:10.680> then\nthis program they use it. But then\nthis program they use it. But then uh\nuh\nuh somehow<01:01:13.280> that's<01:01:13.480> not<01:01:13.640> mapping<01:01:13.920> on<01:01:14.000> to<01:01:14.080> the\nsomehow that's not mapping on to the\nsomehow that's not mapping on to the complexity<01:01:14.760> that<01:01:15.080> that<01:01:15.280> we<01:01:15.400> mean<01:01:15.720> when<01:01:15.880> we<01:01:15.960> say\ncomplexity that that we mean when we say\ncomplexity that that we mean when we say it<01:01:16.400> has<01:01:16.520> learned<01:01:16.720> all<01:01:16.800> these<01:01:16.960> end<01:01:17.080> game\nit has learned all these end game\nit has learned all these end game variations.<01:01:18.000> Um<01:01:18.200> so<01:01:18.920> uh<01:01:19.040> this<01:01:19.240> is<01:01:19.440> one<01:01:19.640> where\nvariations. Um so uh this is one where\nvariations. Um so uh this is one where we<01:01:19.880> would<01:01:20.000> expect<01:01:20.480> to<01:01:20.720> have<01:01:20.960> high<01:01:21.440> epiplexity\nwe would expect to have high epiplexity\nwe would expect to have high epiplexity um\num\num just<01:01:23.440> again<01:01:23.720> thinking<01:01:24.000> about<01:01:24.520> uh\njust again thinking about uh\njust again thinking about uh uh\nuh\nuh yeah,<01:01:26.760> basically<01:01:27.240> compressing<01:01:27.680> this<01:01:27.760> data\nyeah, basically compressing this data\nyeah, basically compressing this data that<01:01:28.120> was<01:01:28.240> produced<01:01:28.600> through<01:01:28.720> this<01:01:28.840> process.\nthat was produced through this process.\nthat was produced through this process. So<01:01:30.880> so\nSo so\nSo so So<01:01:32.120> what<01:01:32.240> you're<01:01:32.320> suggesting<01:01:32.920> is<01:01:33.040> if<01:01:33.160> you<01:01:33.280> push\nSo what you're suggesting is if you push\nSo what you're suggesting is if you push this<01:01:33.920> available<01:01:34.400> compute<01:01:34.800> time<01:01:35.080> to<01:01:35.200> infinity,\nthis available compute time to infinity,\nthis available compute time to infinity, then<01:01:36.040> the<01:01:36.280> plexity<01:01:37.080> would<01:01:37.240> reduce.<01:01:37.920> That's\nthen the plexity would reduce. That's\nthen the plexity would reduce. That's right.<01:01:38.440> Yeah,<01:01:38.520> okay.<01:01:38.800> Yeah,<01:01:39.000> I<01:01:39.040> should<01:01:39.440> have\nright. Yeah, okay. Yeah, I should have\nright. Yeah, okay. Yeah, I should have said<01:01:39.680> that.<01:01:39.840> Yeah,<01:01:40.000> so<01:01:40.360> uh\nsaid that. Yeah, so uh\nsaid that. Yeah, so uh um<01:01:41.520> here<01:01:41.800> I<01:01:41.840> meant<01:01:42.040> like<01:01:42.360> with<01:01:42.480> time<01:01:42.720> bounds\num here I meant like with time bounds\num here I meant like with time bounds that<01:01:43.320> are<01:01:43.880> um<01:01:44.400> are<01:01:44.520> modest.<01:01:44.880> So<01:01:45.040> in<01:01:45.160> this<01:01:45.320> case\nthat are um are modest. So in this case\nthat are um are modest. So in this case like<01:01:45.760> time<01:01:45.960> bounds<01:01:46.200> that<01:01:46.320> are<01:01:46.440> less<01:01:46.720> than<01:01:46.960> the\nlike time bounds that are less than the\nlike time bounds that are less than the amount<01:01:47.280> of<01:01:47.360> time<01:01:47.600> to<01:01:48.240> to<01:01:48.360> run<01:01:48.520> the<01:01:48.600> rule.<01:01:49.280> Um<01:01:49.560> in\namount of time to to run the rule. Um in\namount of time to to run the rule. Um in this<01:01:49.840> case<01:01:50.120> time<01:01:50.280> bounds<01:01:50.520> that<01:01:50.640> are<01:01:50.720> less<01:01:50.920> than\nthis case time bounds that are less than\nthis case time bounds that are less than the<01:01:51.120> amount<01:01:51.280> of<01:01:51.360> time<01:01:51.600> to<01:01:51.840> to<01:01:52.200> to<01:01:52.360> generate<01:01:52.880> the\nthe amount of time to to to generate the\nthe amount of time to to to generate the uh<01:01:53.640> you<01:01:53.720> know,<01:01:53.840> to<01:01:54.040> go<01:01:54.200> through<01:01:54.360> this\nuh you know, to go through this\nuh you know, to go through this recurrence<01:01:55.000> for<01:01:55.160> all<01:01:55.280> these<01:01:55.400> different\nrecurrence for all these different\nrecurrence for all these different points<01:01:55.880> that<01:01:56.000> you<01:01:56.120> care<01:01:56.280> about,<01:01:56.680> right?<01:01:57.400> Um\npoints that you care about, right? Um\npoints that you care about, right? Um you<01:01:58.000> know,<01:01:58.080> for<01:01:58.200> this<01:01:58.440> one<01:01:59.120> uh<01:01:59.240> time<01:01:59.640> in<01:01:59.760> this\nyou know, for this one uh time in this\nyou know, for this one uh time in this case<01:02:00.120> I'd<01:02:00.240> say<01:02:00.360> time<01:02:00.600> bound<01:02:00.880> less<01:02:01.240> than<01:02:01.760> enough\ncase I'd say time bound less than enough\ncase I'd say time bound less than enough to<01:02:02.160> run<01:02:02.400> the<01:02:02.480> AlphaZero<01:02:02.880> process,<01:02:03.440> right?<01:02:03.640> So\nto run the AlphaZero process, right? So\nto run the AlphaZero process, right? So this<01:02:03.920> would<01:02:04.040> actually<01:02:04.320> be<01:02:04.800> basically<01:02:05.320> if<01:02:05.520> you\nthis would actually be basically if you\nthis would actually be basically if you had<01:02:06.320> Look,<01:02:06.680> if<01:02:06.800> you're<01:02:06.920> looking<01:02:07.200> at<01:02:07.280> the\nhad Look, if you're looking at the\nhad Look, if you're looking at the weights,<01:02:07.840> right?<01:02:08.240> Um<01:02:08.680> or<01:02:09.080> the<01:02:09.200> predictions\nweights, right? Um or the predictions\nweights, right? Um or the predictions the<01:02:09.720> model<01:02:09.960> makes<01:02:10.520> and<01:02:10.640> you<01:02:10.680> don't<01:02:10.880> have\nthe model makes and you don't have\nthe model makes and you don't have enough<01:02:11.160> time<01:02:11.400> to<01:02:11.560> rerun<01:02:11.920> the<01:02:12.000> entire\nenough time to rerun the entire\nenough time to rerun the entire AlphaZero<01:02:12.800> process,<01:02:13.520> but<01:02:13.680> you're<01:02:13.800> trying<01:02:14.000> to\nAlphaZero process, but you're trying to\nAlphaZero process, but you're trying to say<01:02:14.280> like<01:02:14.560> hm<01:02:15.240> uh\nsay like hm uh\nsay like hm uh let<01:02:16.240> what<01:02:16.400> is<01:02:16.480> the<01:02:16.560> best<01:02:16.720> compression<01:02:17.200> I<01:02:17.240> can\nlet what is the best compression I can\nlet what is the best compression I can do<01:02:17.520> of<01:02:17.600> that<01:02:17.960> given<01:02:18.240> a<01:02:18.280> much<01:02:18.400> shorter<01:02:18.680> time,\ndo of that given a much shorter time,\ndo of that given a much shorter time, then<01:02:19.600> you<01:02:19.720> would<01:02:19.880> say,<01:02:20.120> \"Oh<01:02:20.240> wow,<01:02:20.480> there's\nthen you would say, \"Oh wow, there's\nthen you would say, \"Oh wow, there's just<01:02:20.840> like<01:02:21.000> there's<01:02:21.160> a<01:02:21.200> lot<01:02:21.480> to<01:02:21.560> compress\njust like there's a lot to compress\njust like there's a lot to compress here,<01:02:22.080> you<01:02:22.160> know,<01:02:22.240> there's<01:02:22.400> a<01:02:22.480> lot<01:02:22.640> of\nhere, you know, there's a lot of\nhere, you know, there's a lot of structure,<01:02:23.040> there's<01:02:23.240> a<01:02:23.280> lot<01:02:23.400> of<01:02:23.640> you<01:02:23.720> know,\nstructure, there's a lot of you know,\nstructure, there's a lot of you know, yeah.\"\nyeah.\"\nyeah.\" So<01:02:25.560> for<01:02:25.720> sure,<01:02:26.000> the<01:02:26.120> time<01:02:26.320> bound<01:02:26.480> is<01:02:26.920> is\nSo for sure, the time bound is is\nSo for sure, the time bound is is critical<01:02:27.480> here<01:02:27.840> and<01:02:28.600> if<01:02:28.840> you<01:02:29.040> set<01:02:29.520> this<01:02:29.800> time\ncritical here and if you set this time\ncritical here and if you set this time bound<01:02:30.680> to<01:02:31.160> as<01:02:31.320> it<01:02:31.440> gets<01:02:31.600> larger<01:02:31.840> and<01:02:31.920> larger<01:02:32.640> um\nbound to as it gets larger and larger um\nbound to as it gets larger and larger um in<01:02:33.520> in<01:02:33.600> many<01:02:33.760> of<01:02:33.840> these<01:02:33.960> cases,<01:02:34.400> then<01:02:35.280> the<01:02:36.080> uh\nin in many of these cases, then the uh\nin in many of these cases, then the uh time<01:02:37.400> bound<01:02:37.520> entropy<01:02:37.880> just<01:02:38.160> collapses<01:02:38.560> down\ntime bound entropy just collapses down\ntime bound entropy just collapses down to<01:02:39.440> um\nto um\nto um the<01:02:40.080> entropy,<01:02:40.640> right?<01:02:41.360> Uh\nthe entropy, right? Uh\nthe entropy, right? Uh Uh<01:02:43.640> yeah.\nUh yeah.\nUh yeah. Uh\nUh\nUh sorry.<01:02:45.760> No,<01:02:46.040> actually\nsorry. No, actually\nsorry. No, actually um<01:02:47.320> well,<01:02:47.520> right.<01:02:47.680> It<01:02:48.200> it<01:02:48.280> gets<01:02:48.520> it<01:02:48.640> gets<01:02:49.160> you\num well, right. It it gets it gets you\num well, right. It it gets it gets you basically<01:02:49.680> go<01:02:49.960> towards<01:02:50.360> the<01:02:50.480> time<01:02:50.680> bound\nbasically go towards the time bound\nbasically go towards the time bound sorry,<01:02:51.360> towards<01:02:51.720> um<01:02:51.960> Kolmogorov<01:02:52.360> complexity\nsorry, towards um Kolmogorov complexity\nsorry, towards um Kolmogorov complexity and<01:02:53.480> an<01:02:53.560> entropy<01:02:53.800> much<01:02:54.040> much<01:02:54.200> more<01:02:54.320> similar<01:02:54.600> to\nand an entropy much much more similar to\nand an entropy much much more similar to that<01:02:55.040> um<01:02:55.360> as<01:02:55.520> you<01:02:55.600> have<01:02:55.720> more<01:02:55.840> and<01:02:55.920> more\nthat um as you have more and more\nthat um as you have more and more compute.\ncompute.\ncompute. So<01:02:58.280> uh<01:02:58.680> thinking<01:02:58.920> about<01:02:59.200> like,<01:02:59.480> okay,<01:02:59.680> the\nSo uh thinking about like, okay, the\nSo uh thinking about like, okay, the AlphaZero<01:03:00.200> game<01:03:00.400> playing<01:03:00.640> agent,<01:03:01.120> right?<01:03:01.400> Can\nAlphaZero game playing agent, right? Can\nAlphaZero game playing agent, right? Can be<01:03:01.680> expressed<01:03:02.120> in<01:03:02.200> just<01:03:02.520> for<01:03:02.640> chess<01:03:02.920> can<01:03:03.040> just\nbe expressed in just for chess can just\nbe expressed in just for chess can just be<01:03:03.280> expressed<01:03:03.760> as<01:03:03.960> the<01:03:04.480> the<01:03:04.560> minimax<01:03:05.000> search.\nbe expressed as the the minimax search.\nbe expressed as the the minimax search. Um<01:03:06.040> that<01:03:06.320> can<01:03:06.440> be<01:03:06.520> done<01:03:06.680> a<01:03:06.720> very<01:03:06.880> short\nUm that can be done a very short\nUm that can be done a very short program.<01:03:07.920> Um<01:03:08.760> Right.<01:03:09.160> But<01:03:09.320> then<01:03:09.800> if<01:03:10.040> you<01:03:10.280> don't\nprogram. Um Right. But then if you don't\nprogram. Um Right. But then if you don't have<01:03:10.600> enough<01:03:10.880> time<01:03:11.240> to<01:03:11.360> run<01:03:11.560> that<01:03:11.680> search,\nhave enough time to run that search,\nhave enough time to run that search, then<01:03:12.480> the<01:03:12.600> moves<01:03:12.920> of<01:03:13.040> that<01:03:13.160> game<01:03:13.360> playing\nthen the moves of that game playing\nthen the moves of that game playing agent<01:03:13.880> could<01:03:14.040> look<01:03:14.240> very<01:03:14.480> interesting<01:03:14.920> and\nagent could look very interesting and\nagent could look very interesting and complex,<01:03:15.440> a<01:03:15.480> lot<01:03:15.720> to<01:03:15.840> learn<01:03:16.000> from.\ncomplex, a lot to learn from.\ncomplex, a lot to learn from. Yeah,<01:03:17.520> I<01:03:17.600> just<01:03:17.840> want<01:03:18.000> to<01:03:18.120> add<01:03:18.360> one<01:03:18.520> thing<01:03:18.840> uh\nYeah, I just want to add one thing uh\nYeah, I just want to add one thing uh real<01:03:19.160> quick.<01:03:19.800> It<01:03:19.960> reminds<01:03:20.400> me<01:03:21.320> uh\nreal quick. It reminds me uh\nreal quick. It reminds me uh some<01:03:22.800> of<01:03:22.880> the<01:03:23.080> theories<01:03:24.120> uh\nsome of the theories uh\nsome of the theories uh of<01:03:24.960> decision<01:03:25.480> making<01:03:26.040> under<01:03:26.360> uncertainty<01:03:26.960> in\nof decision making under uncertainty in\nof decision making under uncertainty in cognitive<01:03:27.560> science.<01:03:27.920> And<01:03:28.040> one<01:03:28.200> of<01:03:28.280> the<01:03:28.400> things\ncognitive science. And one of the things\ncognitive science. And one of the things they<01:03:28.760> have<01:03:29.000> this<01:03:29.400> is<01:03:29.560> is<01:03:29.720> called<01:03:30.040> the\nthey have this is is called the\nthey have this is is called the heuristics,<01:03:30.840> right?<01:03:31.080> It's<01:03:31.200> kind<01:03:31.400> of<01:03:31.960> rule<01:03:32.120> of\nheuristics, right? It's kind of rule of\nheuristics, right? It's kind of rule of thumb.<01:03:32.520> So<01:03:32.680> if<01:03:32.840> you<01:03:32.960> if<01:03:33.120> you<01:03:33.200> only<01:03:33.400> have<01:03:33.560> a\nthumb. So if you if you only have a\nthumb. So if you if you only have a limited<01:03:34.200> amount<01:03:34.440> of<01:03:34.560> time,<01:03:34.880> then<01:03:35.040> people\nlimited amount of time, then people\nlimited amount of time, then people resort<01:03:35.800> to<01:03:35.880> using<01:03:36.160> some<01:03:36.320> sort<01:03:36.520> of<01:03:37.040> rule<01:03:37.200> of\nresort to using some sort of rule of\nresort to using some sort of rule of thumb<01:03:37.600> kind<01:03:37.760> of<01:03:37.880> patterns<01:03:38.600> or<01:03:38.880> rules<01:03:39.960> um\nthumb kind of patterns or rules um\nthumb kind of patterns or rules um which<01:03:41.000> maximizes<01:03:41.760> their<01:03:42.240> decision<01:03:42.560> making.\nwhich maximizes their decision making.\nwhich maximizes their decision making. Uh<01:03:44.120> maybe<01:03:44.480> there<01:03:44.680> is<01:03:45.160> some<01:03:45.400> connection<01:03:45.920> there\nUh maybe there is some connection there\nUh maybe there is some connection there that<01:03:46.440> you<01:03:46.520> could<01:03:46.720> explore<01:03:47.000> if<01:03:47.120> you<01:03:47.200> have<01:03:47.359> any\nthat you could explore if you have any\nthat you could explore if you have any idea.<01:03:48.200> Absolutely.\nidea. Absolutely.\nidea. Absolutely. Yeah,<01:03:50.440> a<01:03:50.480> lot<01:03:50.680> of<01:03:50.760> things<01:03:50.920> that<01:03:51.040> I<01:03:51.080> would<01:03:51.200> like\nYeah, a lot of things that I would like\nYeah, a lot of things that I would like to<01:03:51.400> explore<01:03:51.720> and<01:03:51.800> that's<01:03:51.960> that's<01:03:52.280> something\nto explore and that's that's something\nto explore and that's that's something we'll<01:03:52.640> have<01:03:52.760> to<01:03:52.840> follow<01:03:53.000> up<01:03:53.120> on.\nUh<01:03:56.200> can<01:03:56.359> I<01:03:56.520> add<01:03:57.240> a<01:03:57.640> additional<01:03:58.000> question?<01:03:58.440> So<01:03:58.680> I\nUh can I add a additional question? So I\nUh can I add a additional question? So I just<01:03:59.040> shared<01:03:59.400> a<01:03:59.720> a<01:04:00.320> link<01:04:00.640> in<01:04:00.800> the<01:04:00.880> chat.<01:04:01.440> So\njust shared a a link in the chat. So\njust shared a a link in the chat. So there's\nthere's\nthere's I<01:04:02.880> think<01:04:03.200> a\nI think a\nI think a two<01:04:04.760> years<01:04:04.960> ago<01:04:05.200> or<01:04:05.400> one<01:04:05.560> years<01:04:05.720> ago<01:04:06.520> uh<01:04:06.840> some\ntwo years ago or one years ago uh some\ntwo years ago or one years ago uh some people<01:04:07.640> using<01:04:08.640> uh<01:04:09.160> MDL<01:04:09.800> to<01:04:10.440> to<01:04:10.720> to<01:04:10.920> solve<01:04:11.280> the\npeople using uh MDL to to to solve the\npeople using uh MDL to to to solve the ARC<01:04:12.600> AGI.<01:04:13.240> So<01:04:13.680> this<01:04:14.560> really<01:04:14.840> reminds<01:04:15.359> me<01:04:15.880> of<01:04:16.240> uh\nARC AGI. So this really reminds me of uh\nARC AGI. So this really reminds me of uh relates<01:04:16.760> to<01:04:16.960> to<01:04:17.120> your<01:04:17.280> work<01:04:17.600> because<01:04:18.359> first\nrelates to to your work because first\nrelates to to your work because first your<01:04:19.320> work<01:04:19.560> is<01:04:20.040> defined<01:04:20.520> based<01:04:20.840> on<01:04:21.480> MDL<01:04:22.480> and\nyour work is defined based on MDL and\nyour work is defined based on MDL and you<01:04:23.120> also<01:04:23.320> mentioned<01:04:24.359> by<01:04:24.560> choosing<01:04:25.040> a<01:04:25.120> better\nyou also mentioned by choosing a better\nyou also mentioned by choosing a better epiplexity\nepiplexity\nepiplexity uh\nuh\nuh uh<01:04:28.560> you<01:04:28.800> will<01:04:28.960> get<01:04:29.520> better<01:04:30.520> generalization.\nuh you will get better generalization.\nuh you will get better generalization. And<01:04:32.320> interestingly,<01:04:33.200> ARC<01:04:33.520> AGI<01:04:34.040> is<01:04:34.320> something\nAnd interestingly, ARC AGI is something\nAnd interestingly, ARC AGI is something that's<01:04:35.760> testing<01:04:36.320> how<01:04:36.640> how<01:04:36.800> fast<01:04:37.240> you<01:04:37.359> can\nthat's testing how how fast you can\nthat's testing how how fast you can generalize<01:04:38.200> or<01:04:38.400> how<01:04:38.600> good<01:04:39.080> you<01:04:39.200> can\ngeneralize or how good you can\ngeneralize or how good you can generalize.<01:04:40.400> And<01:04:40.920> I<01:04:41.040> just\ngeneralize. And I just\ngeneralize. And I just uh\nuh\nuh intuitively<01:04:43.920> feel<01:04:44.320> the\nintuitively feel the\nintuitively feel the their<01:04:45.480> work<01:04:46.000> might<01:04:46.920> deeply<01:04:47.280> relate<01:04:47.760> to<01:04:47.920> your\ntheir work might deeply relate to your\ntheir work might deeply relate to your to<01:04:48.320> your<01:04:48.960> to<01:04:49.080> your<01:04:49.240> method.<01:04:50.200> What<01:04:50.400> what<01:04:50.520> do<01:04:50.600> you\nto your to your method. What what do you\nto your to your method. What what do you think?\nthink?\nthink? Let's<01:04:53.080> see.<01:04:53.760> Um\nYeah,<01:04:58.600> so<01:04:59.120> I<01:04:59.440> think\nYeah, so I think\nYeah, so I think um\num\num I<01:05:03.920> haven't<01:05:04.160> thought<01:05:04.320> about<01:05:04.520> it<01:05:04.560> very<01:05:04.720> much.\nI haven't thought about it very much.\nI haven't thought about it very much. Um<01:05:06.080> I<01:05:06.200> think\nUm I think\nUm I think at<01:05:08.240> some<01:05:08.400> level<01:05:08.600> it<01:05:08.680> makes<01:05:08.880> sense<01:05:09.240> that<01:05:10.200> uh\nat some level it makes sense that uh\nat some level it makes sense that uh Right.<01:05:11.800> ARC<01:05:12.000> AGI<01:05:12.280> is<01:05:12.400> testing<01:05:12.720> this<01:05:12.840> very\nRight. ARC AGI is testing this very\nRight. ARC AGI is testing this very high-level<01:05:13.920> pattern<01:05:14.240> matching<01:05:15.320> ability.\nhigh-level pattern matching ability.\nhigh-level pattern matching ability. Yeah,<01:05:17.000> similar<01:05:17.320> to<01:05:17.440> like<01:05:17.840> yeah,<01:05:18.200> um<01:05:19.080> and<01:05:20.320> it\nYeah, similar to like yeah, um and it\nYeah, similar to like yeah, um and it makes<01:05:20.600> sense<01:05:20.800> that<01:05:21.240> would<01:05:21.520> leverage<01:05:22.720> a<01:05:22.800> lot<01:05:23.040> of\nmakes sense that would leverage a lot of\nmakes sense that would leverage a lot of the<01:05:23.520> existing<01:05:24.040> circuits<01:05:24.520> and<01:05:24.640> patterns\nthe existing circuits and patterns\nthe existing circuits and patterns within<01:05:25.120> a<01:05:25.160> model.<01:05:25.480> So<01:05:25.720> think<01:05:25.960> about<01:05:26.760> working\nwithin a model. So think about working\nwithin a model. So think about working with<01:05:27.240> existing<01:05:27.560> models.<01:05:28.359> Yeah,<01:05:28.560> and<01:05:28.680> then\nwith existing models. Yeah, and then\nwith existing models. Yeah, and then again,<01:05:29.440> I<01:05:29.520> know<01:05:29.680> that<01:05:29.800> there's<01:05:30.000> some<01:05:30.400> you\nagain, I know that there's some you\nagain, I know that there's some you mentioned<01:05:30.840> there's<01:05:30.960> some<01:05:31.200> works<01:05:31.520> that\nmentioned there's some works that\nmentioned there's some works that that<01:05:33.120> don't<01:05:33.400> even<01:05:33.600> use<01:05:33.840> a<01:05:34.040> big<01:05:34.240> model<01:05:34.480> for\nthat don't even use a big model for\nthat don't even use a big model for that.<01:05:35.040> Um\nthat. Um\nthat. Um Yeah,<01:05:37.240> I<01:05:37.359> I<01:05:37.440> guess<01:05:38.120> in<01:05:38.240> terms<01:05:38.520> of<01:05:38.680> the<01:05:39.040> the<01:05:39.280> big\nYeah, I I guess in terms of the the big\nYeah, I I guess in terms of the the big model<01:05:39.840> or<01:05:39.920> small<01:05:40.160> model<01:05:40.800> being<01:05:41.080> useful.<01:05:41.359> I\nmodel or small model being useful. I\nmodel or small model being useful. I mean<01:05:41.880> there<01:05:42.200> there<01:05:42.359> are<01:05:42.400> also<01:05:42.600> points<01:05:42.840> that<01:05:42.920> go\nmean there there are also points that go\nmean there there are also points that go in<01:05:43.280> in<01:05:43.440> both<01:05:43.640> directions,<01:05:44.040> right?<01:05:44.240> There's<01:05:44.880> um\nin in both directions, right? There's um\nin in both directions, right? There's um I<01:05:45.880> guess\nI guess\nI guess you<01:05:46.720> know,<01:05:47.240> I<01:05:47.320> guess<01:05:47.640> you<01:05:47.720> know,<01:05:47.800> we<01:05:47.880> have<01:05:48.000> this\nyou know, I guess you know, we have this\nyou know, I guess you know, we have this perspective<01:05:48.560> about<01:05:49.440> the<01:05:49.560> reuse<01:05:50.600> a<01:05:50.960> big<01:05:51.160> model\nperspective about the reuse a big model\nperspective about the reuse a big model like<01:05:51.640> having<01:05:51.960> lots<01:05:52.240> inside<01:05:52.640> a<01:05:52.680> model<01:05:52.920> is<01:05:53.000> good\nlike having lots inside a model is good\nlike having lots inside a model is good because<01:05:53.520> then<01:05:53.720> there's<01:05:53.840> lots<01:05:54.080> of<01:05:54.120> reuse<01:05:54.480> for\nbecause then there's lots of reuse for\nbecause then there's lots of reuse for other<01:05:54.720> things.<01:05:55.480> Um<01:05:56.160> there's<01:05:56.320> also<01:05:56.560> another\nother things. Um there's also another\nother things. Um there's also another perspective\nperspective\nperspective uh<01:05:58.600> you<01:05:58.680> know,<01:05:58.760> the<01:05:58.840> more<01:05:58.960> classical<01:06:00.000> uh\nuh you know, the more classical uh\nuh you know, the more classical uh learning<01:06:00.320> theory<01:06:00.560> perspective<01:06:01.160> of<01:06:01.920> uh\nlearning theory perspective of uh\nlearning theory perspective of uh the<01:06:02.760> size<01:06:03.000> of<01:06:03.080> your<01:06:03.160> hypothesis<01:06:03.600> space<01:06:04.400> you\nthe size of your hypothesis space you\nthe size of your hypothesis space you want<01:06:04.880> to<01:06:05.000> be<01:06:05.120> small<01:06:06.359> um\nwant to be small um\nwant to be small um given<01:06:08.560> uh<01:06:08.880> all<01:06:09.040> things<01:06:09.240> being<01:06:09.440> equal<01:06:09.840> because\ngiven uh all things being equal because\ngiven uh all things being equal because then<01:06:10.600> you<01:06:11.160> will<01:06:11.280> have<01:06:11.440> less<01:06:11.640> overfitting,<01:06:12.280> you\nthen you will have less overfitting, you\nthen you will have less overfitting, you can<01:06:12.600> make<01:06:12.760> generalization<01:06:13.240> bounds.<01:06:14.120> So,<01:06:14.600> you\ncan make generalization bounds. So, you\ncan make generalization bounds. So, you know,<01:06:14.760> I<01:06:14.800> think<01:06:14.960> there's<01:06:15.120> a<01:06:15.200> bit<01:06:15.359> of<01:06:15.480> interplay\nknow, I think there's a bit of interplay\nknow, I think there's a bit of interplay between<01:06:16.200> those<01:06:16.400> two.<01:06:16.760> Um\nbetween those two. Um\nbetween those two. Um uh\nuh\nuh and<01:06:19.200> and<01:06:19.400> and<01:06:19.520> random<01:06:19.720> information.\nand and and random information.\nand and and random information. Um\nUm\nUm Yeah,<01:06:23.280> I<01:06:23.800> I<01:06:24.560> uh<01:06:25.000> I<01:06:25.080> don't<01:06:25.240> have<01:06:25.400> anything<01:06:26.200> uh\nYeah, I I uh I don't have anything uh\nYeah, I I uh I don't have anything uh very<01:06:27.040> uh\nvery uh\nvery uh yeah,<01:06:29.520> very<01:06:30.480> very<01:06:30.800> useful<01:06:31.080> to<01:06:31.200> say,<01:06:31.440> but<01:06:31.600> I<01:06:31.720> I\nyeah, very very useful to say, but I I\nyeah, very very useful to say, but I I think<01:06:32.040> it<01:06:32.120> would<01:06:32.240> be<01:06:32.440> Yeah,<01:06:32.640> any<01:06:32.960> any<01:06:33.160> more\nthink it would be Yeah, any any more\nthink it would be Yeah, any any more specific<01:06:33.760> questions<01:06:34.120> about<01:06:34.320> from<01:06:34.480> the<01:06:34.760> ARC\nspecific questions about from the ARC\nspecific questions about from the ARC AGI<01:06:35.640> pattern<01:06:35.880> like<01:06:36.120> anything\nAGI pattern like anything\nAGI pattern like anything specific<01:06:38.400> about<01:06:38.600> that<01:06:38.800> that<01:06:38.920> you<01:06:39.000> think<01:06:39.600> might\nspecific about that that you think might\nspecific about that that you think might Uh<01:06:40.640> so<01:06:40.960> so<01:06:41.200> so<01:06:41.440> they<01:06:41.640> they<01:06:41.760> actually<01:06:42.120> also<01:06:42.440> use\nUh so so so they they actually also use\nUh so so so they they actually also use a<01:06:43.280> a<01:06:43.320> neural<01:06:43.600> network<01:06:44.520> to<01:06:44.720> to<01:06:44.840> represent<01:06:45.320> the\na a neural network to to represent the\na a neural network to to represent the P.<01:06:45.760> So<01:06:46.120> actually<01:06:46.560> the<01:06:46.760> P<01:06:47.200> the<01:06:47.359> computation<01:06:47.880> of\nP. So actually the P the computation of\nP. So actually the P the computation of P<01:06:48.280> is<01:06:48.480> bounded.<01:06:49.560> And<01:06:50.560> the<01:06:50.920> the<01:06:51.040> introduce<01:06:51.880> some\nP is bounded. And the the introduce some\nP is bounded. And the the introduce some variational<01:06:52.840> way<01:06:53.160> to<01:06:53.520> to<01:06:54.280> to<01:06:54.680> optimize<01:06:55.200> the\nvariational way to to to optimize the\nvariational way to to to optimize the size<01:06:55.800> of<01:06:55.960> P,<01:06:56.359> like<01:06:56.600> the<01:06:56.960> number<01:06:57.320> of<01:06:57.440> bit.<01:06:58.120> It's\nsize of P, like the number of bit. It's\nsize of P, like the number of bit. It's basically<01:06:59.200> injecting<01:06:59.800> noise<01:07:00.280> to<01:07:00.440> your\nbasically injecting noise to your\nbasically injecting noise to your parameter<01:07:01.000> space<01:07:01.440> so<01:07:01.600> you<01:07:01.720> can<01:07:01.920> explicitly\nparameter space so you can explicitly\nparameter space so you can explicitly compute<01:07:04.080> the<01:07:04.240> the\ncompute the the\ncompute the the number<01:07:05.400> of<01:07:05.560> bits<01:07:05.960> in<01:07:06.120> your<01:07:06.280> model.<01:07:07.040> So<01:07:07.240> in<01:07:07.440> that\nnumber of bits in your model. So in that\nnumber of bits in your model. So in that way\nway\nway you<01:07:09.240> you<01:07:09.440> are<01:07:09.800> you<01:07:09.960> can<01:07:10.400> optimize<01:07:11.080> the<01:07:11.320> the\nyou you are you can optimize the the\nyou you are you can optimize the the size<01:07:11.920> of<01:07:12.040> P<01:07:12.400> and<01:07:12.760> your<01:07:12.960> residual<01:07:13.520> loss\nsize of P and your residual loss\nsize of P and your residual loss together.<01:07:15.280> So<01:07:15.880> so<01:07:16.160> I<01:07:16.320> just<01:07:16.520> feel<01:07:16.760> maybe<01:07:17.359> maybe\ntogether. So so I just feel maybe maybe\ntogether. So so I just feel maybe maybe the<01:07:17.800> the<01:07:17.920> method<01:07:18.280> can<01:07:18.480> directly<01:07:19.440> uh<01:07:19.800> combine\nthe the method can directly uh combine\nthe the method can directly uh combine into<01:07:20.680> your<01:07:20.840> method<01:07:21.240> and<01:07:21.720> you<01:07:21.920> don't<01:07:22.160> need<01:07:22.480> like\ninto your method and you don't need like\ninto your method and you don't need like uh\nuh\nuh something<01:07:24.240> like<01:07:25.040> uh<01:07:25.520> uh\nsomething like uh uh\nsomething like uh uh uh<01:07:26.840> you<01:07:26.920> don't<01:07:27.120> need<01:07:27.359> something<01:07:27.720> like<01:07:28.280> teacher\nuh you don't need something like teacher\nuh you don't need something like teacher student<01:07:29.760> way<01:07:30.040> to<01:07:30.240> to<01:07:30.359> measure<01:07:30.760> measure<01:07:31.240> that\nstudent way to to measure measure that\nstudent way to to measure measure that and<01:07:31.680> directly<01:07:32.080> optimize<01:07:32.560> the<01:07:32.680> model.<01:07:33.160> Yeah,\nand directly optimize the model. Yeah,\nand directly optimize the model. Yeah, that<01:07:34.040> that's<01:07:34.240> possible.<01:07:34.680> I<01:07:34.800> think<01:07:35.200> yeah,<01:07:35.320> it\nthat that's possible. I think yeah, it\nthat that's possible. I think yeah, it would<01:07:35.440> be<01:07:35.520> interesting<01:07:35.960> exploring<01:07:36.320> both\nwould be interesting exploring both\nwould be interesting exploring both different<01:07:36.840> coding<01:07:37.080> strategies<01:07:37.560> here.<01:07:38.359> Um\ndifferent coding strategies here. Um\ndifferent coding strategies here. Um and<01:07:39.240> then<01:07:39.440> so<01:07:39.560> both<01:07:39.840> both<01:07:40.040> versions,\nand then so both both versions,\nand then so both both versions, basically<01:07:41.120> both<01:07:41.440> take<01:07:41.640> our<01:07:41.760> sequential<01:07:42.160> code,\nbasically both take our sequential code,\nbasically both take our sequential code, maybe<01:07:42.760> test<01:07:43.000> it<01:07:43.120> out<01:07:43.359> in<01:07:43.760> in<01:07:43.880> that<01:07:44.040> setting,\nmaybe test it out in in that setting,\nmaybe test it out in in that setting, right?<01:07:45.080> Uh<01:07:45.240> and<01:07:45.440> then<01:07:45.600> take<01:07:45.840> the<01:07:45.920> codes<01:07:46.160> that\nright? Uh and then take the codes that\nright? Uh and then take the codes that they're<01:07:46.440> doing<01:07:46.800> and<01:07:46.960> then<01:07:47.080> use<01:07:47.240> it<01:07:47.359> here,<01:07:47.720> see\nthey're doing and then use it here, see\nthey're doing and then use it here, see if<01:07:47.960> we<01:07:48.040> get<01:07:48.160> better<01:07:48.359> codes.<01:07:48.960> I<01:07:49.040> think<01:07:49.240> both\nif we get better codes. I think both\nif we get better codes. I think both both<01:07:49.800> directions<01:07:50.120> would<01:07:50.200> be<01:07:50.280> good.",
+ "fetched_at": "2026-06-21T20:52:22Z",
+ "source": "yt-dlp-vtt"
+}
\ No newline at end of file
diff --git a/conductor/tracks/video_analysis_entropy_epiplexity_20260621/artifacts/video.log b/conductor/tracks/video_analysis_entropy_epiplexity_20260621/artifacts/video.log
new file mode 100644
index 00000000..f7b20f79
--- /dev/null
+++ b/conductor/tracks/video_analysis_entropy_epiplexity_20260621/artifacts/video.log
@@ -0,0 +1,10 @@
+# yt-dlp log
+# url: https://youtu.be/_U8AwUq_aJQ
+# output: video.mp4
+# returncode: 0
+
+stdout:
+
+
+stderr:
+