conductor(platonic_intelligence_kumar): Phase 3 OCR - 62 frames OCR'd via winsdk in 3.7s
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# OCR Results
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## frame_00001.jpg
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```
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The World is not Random
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```
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## frame_00002.jpg
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```
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Towards a Platonic Intelligence with
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Unified Factored Representations
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sae
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Good Adaptability
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Unified Factored
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Representation
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Open—Ended
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Search
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Identical
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output
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behavior
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Inputs
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Solves Task
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Function Space
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4
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Poor Adaptability
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Fractured Entangled
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Representation
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Conventional
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SGD
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Akarsh Kumar
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MIT CSAIL
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November 4, 2025
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1
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```
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## frame_00004.jpg
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```
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The World has Structure
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Real World
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```
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## frame_00008.jpg
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```
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(no text extracted)
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```
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## frame_00016.jpg
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```
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Intelligent Agents must capture this Structure
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```
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## frame_00017.jpg
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```
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Capturing Structure with AI
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```
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## frame_00019.jpg
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```
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Capturing Structure with AI
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• What about everything else?
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• Example: lighting invariance
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• How do you capture lighting invariance?
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Architecture
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Lighting
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Invariance
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6
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```
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## frame_00020.jpg
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```
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Capturing Structure with AI
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• What about everything else?
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• Example: lighting invariance
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• How do you capture lighting invariance?
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• We don't know
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• Solution: train on lots of data with SGD
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Architecture
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Lighting
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Invariance
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```
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## frame_00021.jpg
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```
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Does this Work?
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ChatGPT
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```
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## frame_00022.jpg
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```
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Hypothesis: Fractured Entangled Representations
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8
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```
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## frame_00023.jpg
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```
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Hypothesis: Fractured Entangled Representations
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• Conventional SGD training finds
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neural representations which are
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fractured and entangled
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output
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behavior
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Inputs
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Solves Task *
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Function S ace
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Fractured Entangled
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Representation
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Conventional
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SGD
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8
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```
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## frame_00024.jpg
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```
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Hypothesis: Fractured Entangled Representations
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• Conventional SGD training finds
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neural representations which are
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fractured and entangled
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• Doesn't capture the underlying
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regularities of the world
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• Position: Open-Ended Search
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may be the solution to learn
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unified and factored neural
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representations
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Unified Factored
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Representation
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Open—Ended
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Search
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Identical
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output
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behavior
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Inputs
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Solves Task
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Fractured Entangled
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Representation
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Conventional
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SGD
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Function S ace
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8
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```
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## frame_00025.jpg
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```
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Hypothesis: Fractured Entangled Representations
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• Conventional SGD training finds
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neural representations which are
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fractured and entangled
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• Doesn't capture the underlying
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regularities of the world
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• Position: Open-Ended Search
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may be the solution to learn
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unified and factored neural
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representations
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• Internal representation affects
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generalization, creativity, and
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continual learning
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Good Adaptability
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Unified Factored
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Representation
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Open—Ended
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Search
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Identical
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output
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behavior
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Inputs
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Solves Task *
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Function S ace
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Poor Adaptability
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Fractured Entangled
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Representation
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Conventional
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SGD
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8
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```
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## frame_00026.jpg
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```
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Compositional Pattern Producing Network
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(CPPN)
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```
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## frame_00027.jpg
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```
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Compositional Pattern Producing Network
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(CPPN)
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Toy domain to study neural representations: implicitly represent an image
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• Inspired by biological developmental process
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```
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## frame_00028.jpg
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```
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CPPNs are an Analogy
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```
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## frame_00029.jpg
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```
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Picbreeder!
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restart TilJtate
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SEjve
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11
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```
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## frame_00030.jpg
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```
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Picbreeder!
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• Evolve the underlying CPPNs
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restart
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11
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```
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## frame_00031.jpg
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```
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Picbreeder!
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• Online website for humans to breed images to
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their desire
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• Evolve the underlying CPPNs
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restart
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11
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```
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## frame_00032.jpg
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```
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Picbreeder!
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z. zzz
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• Online website for humans to breed images to
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their desire
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• Evolve the underlying CPPNs
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uzzzz
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zzzzz
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restart
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11
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```
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## frame_00033.jpg
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```
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Picbreeder!
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• Online website for humans to breed images to
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their desire
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• Evolve the underlying CPPNs
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restart
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11
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```
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## frame_00034.jpg
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```
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Picbreeder!
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• Online website for humans to breed images to
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their desire
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• Evolve the underlying CPPNs
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• No end goal, do whatever you want!
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oosæ
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restart
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11
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```
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## frame_00035.jpg
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```
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What Do You Expect to Find?
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```
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## frame_00036.jpg
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```
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What People Actually Found!
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13
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```
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## frame_00037.jpg
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```
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Why Greatness Cannot be Planned
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• Many insights on the nature of search
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• Deception
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• Serendipity
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• Open-Endedness
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• Case studies:
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• Natural Evolution
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• Scientific Innovation
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Kenneth 0. Stanley • Joel Lehman
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Why Greatness
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Cannot Be Planned
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The Myth of the Objective
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@Springer
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14
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```
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## frame_00038.jpg
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```
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Picbreeder has Intriguing Properties
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Open-Ended
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```
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## frame_00039.jpg
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```
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Picbreeder has Intriguing Properties
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Open-Ended
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oäaua e
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ana
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16
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```
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## frame_00040.jpg
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```
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Picbreeder has Intriguing Properties
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Serendipitous Exaptation
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• When a trait evolved for one function but gets repurposed for another function
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Warmh
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Gliding
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17
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```
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## frame_00041.jpg
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```
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Picbreeder has Intriguing Properties
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Serendipitous Exaptation
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Stepping stone to the Teapot
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Stepping stone to the Skull
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Stepping stone to Jupiter
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Stepping stone to the Butterfly
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Stepping stone to the Penguin
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Stepping stone to the Lamp
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18
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```
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## frame_00042.jpg
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```
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Picbreeder has Intriguing Properties
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Emergence of Evolvability
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• Natural evolution has developed adaptable genotypes:
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• Canalization
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• Regularity
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Modularity
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• Symmetry
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• Certain axes of variation become more likely while
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others become impossible
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synurwtry
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synvnetry
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human
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19
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```
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## frame_00043.jpg
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```
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Picbreeder has Intriguing Properties
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Emergence of Evolvability
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Most Picbreeder images
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feature forms of canalization
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Mutating single genes of these images
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holistically affects distinct aspects of the image
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mutation in
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Nut.uon
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Mutation in
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ObJect Oni' Spatnght Only
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These images have a structurally organized
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(i.e. modular and hierarchical) genome
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Global Lighting
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genes
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Shadow Only
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Spotlight Only
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Some Picbreeder images
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show oor canalization
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Mutating single genes of these images
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affects none or many parts of the image
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»ut.uøn Mutation in Nuuuon in
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And
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These images have little structural
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organization in their genome
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genes
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Object Only
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genes
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genes
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Shadow And
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Object genes
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No Effect
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Global
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Distortion
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genes
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Dolphin Eye
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And Body
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genes
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These images have fit decendants
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These images have unfit decendants
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20
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```
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## frame_00045.jpg
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```
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Learning the Picbreeder Skull with SGD
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22
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```
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## frame_00046.jpg
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```
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Learning the Picbreeder Skull with SGD
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Picbreeder Skull
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22
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```
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## frame_00047.jpg
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```
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Learning the Picbreeder Skull with SGD
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• Let's train a conventional network to recreate the skull
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• Perfect reconstruction!
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Picbreeder Skull
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SGD Trainin
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SGD Skull
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22
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```
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## frame_00048.jpg
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```
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Layerization
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23
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```
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## frame_00049.jpg
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```
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Layerization
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• Convert everything to a universal architecture space: MLP
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sin(0)
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do
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cos(O)
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bias
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dx
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lio
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itie
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-Afia
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lin
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ReLO •
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tanh
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23
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```
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## frame_00050.jpg
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```
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Layerization
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• Convert everything to a universal architecture space: MLP
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• Existence proof of Picbreeder solution MLP weight space
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e
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DLI
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Neuron
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24
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```
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## frame_00051.jpg
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```
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Picbreeder Skull
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Unified Factored Representation
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e
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Neuron
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ssgg
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anon
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25
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```
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## frame_00052.jpg
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```
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SGD Skull
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Fractured Entangled Representation
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Zigle
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aaaa
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Neuron
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26
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```
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## frame_00053.jpg
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```
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Picbreeder Skull
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Unified Factored Representation
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Controls Mouth Opening
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Controls Eye Winking
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Controls Eye Width
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Controls Jaw Width
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Sweeping Weight Value
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SGD Skull
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Fractured Entangled Representation
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Sweeping Weight Value
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27
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```
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## frame_00054.jpg
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```
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Picbreeder Butterfly
|
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Unified Factored Representation
|
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Neuron
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ooaa
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28
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```
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## frame_00055.jpg
|
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```
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SGD Butterfly
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Fractured Entangled Representation
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Neuron
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29
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```
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## frame_00056.jpg
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```
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Picbreeder Butterfly
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Unified Factored Representation
|
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Controls Wing Area
|
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Controls Color
|
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Converts Butterfly to Fly
|
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Controls Vertical Shape
|
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Sweeping Weight Value
|
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SGD Butterfly
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Fractured Entangled Representation
|
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Aw= —1
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Sweeping Weight Value
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30
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```
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## frame_00057.jpg
|
||||
|
||||
```
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Picbreeder Apple
|
||||
Unified Factored Representation
|
||||
Neuron
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nannæg••
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31
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```
|
||||
|
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## frame_00058.jpg
|
||||
|
||||
```
|
||||
SGD Apple
|
||||
Fractured Entangled Representation
|
||||
ooose•n
|
||||
oec
|
||||
Cloe
|
||||
D •BRA
|
||||
x yd 1
|
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Neuron
|
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32
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```
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|
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## frame_00059.jpg
|
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|
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```
|
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Picbreeder Apple
|
||||
Unified Factored Representation
|
||||
Controls Stem Angle
|
||||
ooooo
|
||||
Controls Apple Size
|
||||
Cleans Background
|
||||
ooooo
|
||||
Removes Stem
|
||||
AYI/ = +1
|
||||
Sweeping Weight Value
|
||||
SGD Apple
|
||||
Fractured Entangled Representation
|
||||
ecoe
|
||||
Controls Apple Size
|
||||
= Cleans Background
|
||||
ooooe
|
||||
Aw = +1
|
||||
Sweeping Weight Value
|
||||
33
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```
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## frame_00060.jpg
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||||
|
||||
```
|
||||
How does this Apply to LLMs?
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34
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```
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|
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## frame_00061.jpg
|
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|
||||
```
|
||||
FER In LLMs
|
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Evidence in GPT-3
|
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Example 1:
|
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Me: I have 3 pencils, 2 pens, and 4 erasers. How many things do I
|
||||
have?
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GPT-3: You have 9 things. [always correct]
|
||||
Example 2:
|
||||
Me: I have 3 chickens, 2 ducks, and 4 geese. How many things do I
|
||||
have?
|
||||
GPT-3: You have 10 animals total. [always incorrect]
|
||||
35
|
||||
```
|
||||
|
||||
## frame_00062.jpg
|
||||
|
||||
```
|
||||
GSM-Symbolic: Understanding the Limitations of
|
||||
Mathematical Reasoning in Large Language Models
|
||||
Iman Mirzadeht Keivan Alizadeh Hooman Shahrokhi*
|
||||
Samy Bengio Mehrdad Farajtabart
|
||||
Oncel Tuzel
|
||||
Apple
|
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Abstract
|
||||
Recent advancements in Large Language Models (LLMs) have sparked interest in their formal
|
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reasoning capabilities, particularly in mathematics. The GSM8K benchmark is widely used
|
||||
to assess the mathematical reasoning of models on grade-school-level questions. While the
|
||||
performance of LLMs on GSM8K has significantly improved in recent years, it remains unclear
|
||||
whether their mathematical reasoning capabilities have genuinely advanced, raising questions
|
||||
about the reliability of the reported metrics. To address these concerns, we conduct a large-
|
||||
scale study on several state-of-the-art open and closed models. To overcome the limitations of
|
||||
existing evaluations, we introduce GSM-Symbolic, an improved benchmark created from symbolic
|
||||
templates that allow for the generation of a diverse set of questions. GSM-SymboIic enables
|
||||
more controllable evaluations, providing key insights and more reliable metrics for measuring the
|
||||
reasoning capabilities of models.Our findings reveal that LLMs exhibit noticeable variance when
|
||||
responding to different instantiations of the same question. Specifically, the performance of all
|
||||
models declines when only the numerical values in the question are altered in the GSM-Symbolic
|
||||
benchmark. Furthermore, we investigate the fragility of mathematical reasoning in these models
|
||||
and demonstrate that their performance significantly deteriorates as the number of clauses in
|
||||
a question increases. We hypothesize that this decline is due to the fact that current LLMs
|
||||
are not capable of genuine logical reasoning; instead, they attempt to replicate the reasoning
|
||||
steps observed in their training data. When we add a single clause that appears relevant to the
|
||||
question, we observe significant performance drops (up to 65%) across all state-of-the-art models,
|
||||
even though the added clause does not contribute to the reasoning chain needed to reach the
|
||||
final answer. Overall, our work provides a more nuanced understanding of LLMs' capabilities
|
||||
and limitations in mathematical reasoning.
|
||||
36
|
||||
```
|
||||
|
||||
## frame_00063.jpg
|
||||
|
||||
```
|
||||
Reasoning or Reciting? Exploring the Capabilities and Limitations of
|
||||
Language Models Through Counterfactual Tasks
|
||||
Zhaofeng Wue Linlu Qiue Alexis Rosse EkinAkyürekC Boyuan Chene
|
||||
Bailin Wange Najoung Kima Jacob Andrease Yoon Kim
|
||||
e MIT O Boston University
|
||||
zfw@csail.mit.edu
|
||||
G PT-4
|
||||
Performance
|
||||
Default
|
||||
Counterfactual
|
||||
Spatial
|
||||
COO Of
|
||||
Arithmetic
|
||||
Drawing
|
||||
Draw a
|
||||
Code Exec.
|
||||
pytim
|
||||
L"bo". "nb"l
|
||||
"bo"l
|
||||
Chord Fingering
|
||||
play C
|
||||
a guitar
|
||||
Code Gen.
|
||||
Sort list by the
|
||||
second c
|
||||
in
|
||||
Note in Melody
|
||||
The 4th note of
|
||||
Twinkle Twinkle
|
||||
in C major
|
||||
in Ai
|
||||
Basic Syntax
|
||||
Find the main
|
||||
subject and verb
|
||||
think 'MS
|
||||
(they. think)
|
||||
(they, 'hink)
|
||||
IS the move
|
||||
TX are Y, Y are Z.
|
||||
Are X Z?
|
||||
SET Game
|
||||
Rule:
|
||||
or
|
||||
•hap..
|
||||
Figure 1: GPT-4's performance on the default version of various tasks (blue) and counterfactual counterparts
|
||||
The shown results use O-shot chain-of-thought prompting (54; GPT-4 consistently
|
||||
orange
|
||||
and substantially underperforms on counterfactual variants compared to default task instantiations.
|
||||
37
|
||||
```
|
||||
|
||||
## frame_00068.jpg
|
||||
|
||||
```
|
||||
On the Biology of a Large Language Model
|
||||
We investigate the internal mechanisms used by Claude 3.5 Haiku — Anthropic's lightweight
|
||||
production model — in a variety of contexts, using our circuit tracing methodology.
|
||||
add —57
|
||||
95
|
||||
sum = _5
|
||||
add _9
|
||||
Inputs near 30 make this
|
||||
early feature fire
|
||||
-30
|
||||
calc :
|
||||
36
|
||||
calc :
|
||||
Hover to see
|
||||
visualizations!
|
||||
Example
|
||||
low precision
|
||||
features
|
||||
_6
|
||||
36
|
||||
36+59=
|
||||
sum —92
|
||||
-40 + -50
|
||||
5-
|
||||
-59
|
||||
sum =
|
||||
-36 + -60
|
||||
59
|
||||
59
|
||||
Exam mod O
|
||||
eat ures
|
||||
_9
|
||||
Ull
|
||||
Sum Features
|
||||
The model has finally computed information
|
||||
about the sum: its value mod 10, mod 100,
|
||||
and its approximate magnitude.
|
||||
Lookup Table Features
|
||||
The model has stored information about
|
||||
particular pairs of input properties. They take
|
||||
input from the original addends (via attention)
|
||||
and the Add Function features. Operand plots
|
||||
ssibly with repetition (modular) or
|
||||
are points.
|
||||
smearing (tw•preciston)
|
||||
Add Function Features
|
||||
The model separately determines the ones
|
||||
digit Of the number to be added and its
|
||||
approximate magnitude. Operand plots show
|
||||
vertical or horizontal stripes,
|
||||
Input Features
|
||||
The model has features specific to the ones
|
||||
digit and Io the approximate magnitude, at
|
||||
various scales.
|
||||
Most computation
|
||||
takes place on the
|
||||
•zu token
|
||||
38
|
||||
```
|
||||
|
||||
## frame_00069.jpg
|
||||
|
||||
```
|
||||
Scaling helps... but in what way?
|
||||
Scaling Laws for Neural Language Models
|
||||
2024
|
||||
10—9
|
||||
L = (Cmin/2.3 •
|
||||
10-7
|
||||
10-5
|
||||
10-3
|
||||
10—1
|
||||
Compute
|
||||
PF-days, non-embedding
|
||||
4.2
|
||||
3.9
|
||||
3.6
|
||||
3.3
|
||||
3.0
|
||||
2.7
|
||||
101
|
||||
L = (0/5.4
|
||||
108
|
||||
Dataset Size
|
||||
tokens
|
||||
Kaplan et al. (2020)
|
||||
5.6
|
||||
4.8
|
||||
3.2
|
||||
2.4
|
||||
109
|
||||
105
|
||||
L = (N18.8 •
|
||||
107
|
||||
Parameters
|
||||
non-embedding
|
||||
109
|
||||
39
|
||||
```
|
||||
|
||||
## frame_00070.jpg
|
||||
|
||||
```
|
||||
Scaling helps... but in what way?
|
||||
Platonic Representation Hypothesis
|
||||
The Platonic Representation Hypothesis
|
||||
Neural networks, trained with different objectives
|
||||
on different data and modalities, are converging to a
|
||||
shared statistical model of reality in their representa-
|
||||
tion spaces.
|
||||
z
|
||||
x
|
||||
Img
|
||||
A red sphere next to
|
||||
ft ext
|
||||
Huh et al. (2020)
|
||||
40
|
||||
```
|
||||
|
||||
## frame_00071.jpg
|
||||
|
||||
```
|
||||
Scaling helps... but in what way?
|
||||
41
|
||||
```
|
||||
|
||||
## frame_00072.jpg
|
||||
|
||||
```
|
||||
What could be better?
|
||||
42
|
||||
```
|
||||
|
||||
## frame_00073.jpg
|
||||
|
||||
```
|
||||
What could be better?
|
||||
• Complexification (ex: morphogenesis, etc.)
|
||||
• Builds regularities on top of other regularities (bottom up)
|
||||
• Emergence
|
||||
• Adaptability
|
||||
• Pressures the learned regularities to be robust to environmental changes
|
||||
• Representation must capture axes of variation which "carve nature at its joints"
|
||||
• Serendipity (order matters for learning!)
|
||||
• Much higher chance of finding a useful learning curriculum
|
||||
• What learning paradigm captures all of these? Open-Endedness!
|
||||
Function Space
|
||||
FER
|
||||
olution Space
|
||||
of Skull
|
||||
UFR
|
||||
: Open—Ended
|
||||
Search
|
||||
Conventional
|
||||
SGD
|
||||
42
|
||||
```
|
||||
|
||||
## frame_00074.jpg
|
||||
|
||||
```
|
||||
Is this a Platonic Intelligence?
|
||||
Space of Forms
|
||||
Real World
|
||||
Intelligent Agents
|
||||
Unified Factored
|
||||
Representation
|
||||
43
|
||||
```
|
||||
|
||||
## frame_00075.jpg
|
||||
|
||||
```
|
||||
Is this a Platonic Intelligence?
|
||||
Aspirational Ideal
|
||||
Unified Factored
|
||||
Representation
|
||||
Instantiation
|
||||
Fractured Entangled
|
||||
Representation
|
||||
44
|
||||
```
|
||||
|
||||
## frame_00076.jpg
|
||||
|
||||
```
|
||||
Collaborators
|
||||
Jeff Clune
|
||||
UBC
|
||||
Vector Institute
|
||||
Joel Lehman
|
||||
University of Oxford
|
||||
Kenneth Stanley
|
||||
Lila Sciences
|
||||
UBC
|
||||
45
|
||||
```
|
||||
|
||||
## frame_00077.jpg
|
||||
|
||||
```
|
||||
Thank You!
|
||||
46
|
||||
```
|
||||
|
||||
## frame_00081.jpg
|
||||
|
||||
```
|
||||
Thanh You!
|
||||
```
|
||||
|
||||
## frame_00082.jpg
|
||||
|
||||
```
|
||||
(no text extracted)
|
||||
```
|
||||
+2
@@ -0,0 +1,2 @@
|
||||
Phase 2 Keyframes for C:\projects\manual_slop\conductor\tracks\video_analysis_platonic_intelligence_kumar_20260621\artifacts\video.mp4
|
||||
OK: kept 62 frames
|
||||
+2
@@ -0,0 +1,2 @@
|
||||
Phase 3 OCR for C:\projects\manual_slop\conductor\tracks\video_analysis_platonic_intelligence_kumar_20260621\artifacts\frames (winsdk)
|
||||
OK: OCR'd 62 frames in 3.7s
|
||||
Reference in New Issue
Block a user