We often think of Large Language Models (LLMs) as all-knowing, but as the team reveals, they still struggle with the logic of a second-grader. Why can’t ChatGPT reliably add large numbers? Why does it "hallucinate" the laws of physics? The answer lies in the architecture. This episode explores how *Category Theory* —an ultra-abstract branch of mathematics—could provide the "Periodic Table" for neural networks, turning the "alchemy" of modern AI into a rigorous science.
In this deep-dive exploration, *Andrew Dudzik*, *Petar Velichkovich*, *Taco Cohen*, *Bruno Gavranović*, and *Paul Lessard* join host *Tim Scarfe* to discuss the fundamental limitations of today’s AI and the radical mathematical framework that might fix them.
TRANSCRIPT:
https://app.rescript.info/public/share/LMreunA-BUpgP-2AkuEvxA7BAFuA-VJNAp2Ut4MkMWk
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Key Insights in This Episode:
*The "Addition" Problem:* *Andrew Dudzik* explains why LLMs don't actually "know" math—they just recognize patterns. When you change a single digit in a long string of numbers, the pattern breaks because the model lacks the internal "machinery" to perform a simple carry operation.
*Beyond Alchemy:* deep learning is currently in its "alchemy" phase—we have powerful results, but we lack a unifying theory. Category Theory is proposed as the framework to move AI from trial-and-error to principled engineering. []
*Algebra with Colors:* To make Category Theory accessible, the guests use brilliant analogies—like thinking of matrices as *magnets with colors* that only snap together when the types match. This "partial compositionality" is the secret to building more complex internal reasoning. []
*Synthetic vs. Analytic Math:* *Paul Lessard* breaks down the philosophical shift needed in AI research: moving from "Analytic" math (what things are made of) to "Synthetic" math []
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Why This Matters for AGI
If we want AI to solve the world's hardest scientific problems, it can't just be a "stochastic parrot." It needs to internalize the rules of logic and computation. By imbuing neural networks with categorical priors, researchers are attempting to build a future where AI doesn't just predict the next word—it understands the underlying structure of the universe.
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TIMESTAMPS:
The Failure of LLM Addition & Physics
Tool Use vs Intrinsic Model Quality
Efficiency Gains via Internalization
Geometric Deep Learning & Equivariance
Limitations of Group Theory
Category Theory: Algebra with Colors
The Systematic Guide of Lego-like Math
The Alchemy Analogy & Unifying Theory
Information Destruction & Reasoning
Pathfinding & Monoids in Computation
System 2 Reasoning & Error Awareness
Analytic vs Synthetic Mathematics
Morphisms & Weight Tying Basics
2-Categories & Weight Sharing Theory
Higher Categories & Emergence
Compositionality & Recursive Folds
Syntax vs Semantics in Network Design
Homomorphisms & Multi-Sorted Syntax
The Carrying Problem & Hopf Fibrations
Petar Veličković (GDM)
Paul Lessard
https://www.linkedin.com/in/paul-roy-lessard/
Bruno Gavranović
https://www.brunogavranovic.com/
Andrew Dudzik (GDM)
https://www.linkedin.com/in/andrew-dudzik-222789142/
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REFERENCES:
Model:
[] Veo
https://deepmind.google/models/veo/
[] Genie
https://deepmind.google/blog/genie-3-a-new-frontier-for-world-models/
Paper:
[] Geometric Deep Learning Blueprint
https://arxiv.org/abs/2104.13478
https://www.youtube.com/watch?v=bIZB1hIJ4u8
[] AlphaGeometry
https://arxiv.org/abs/2401.08312
[] AlphaCode
https://arxiv.org/abs/2203.07814
[] FunSearch
https://www.nature.com/articles/s41586-023-06924-6
[] Attention Is All You Need
https://arxiv.org/abs/1706.03762
[] Categorical Deep Learning
