Machine Learning Street Talk (MLST)

Category theory: the "Final Boss" of Deep Learning (Andrew Dudzik, Petar Velichkovich, Taco Cohen, Bruno Gavranović, Paul Lessard)

22 Dec 2025

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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---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. [00:13:49]* *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. [00:09:17]* *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 [00:23:41]---Why This Matters for AGIIf 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.---TIMESTAMPS:00:00:00 The Failure of LLM Addition & Physics00:01:26 Tool Use vs Intrinsic Model Quality00:03:07 Efficiency Gains via Internalization00:04:28 Geometric Deep Learning & Equivariance00:07:05 Limitations of Group Theory00:09:17 Category Theory: Algebra with Colors00:11:25 The Systematic Guide of Lego-like Math00:13:49 The Alchemy Analogy & Unifying Theory00:15:33 Information Destruction & Reasoning00:18:00 Pathfinding & Monoids in Computation00:20:15 System 2 Reasoning & Error Awareness00:23:31 Analytic vs Synthetic Mathematics00:25:52 Morphisms & Weight Tying Basics00:26:48 2-Categories & Weight Sharing Theory00:28:55 Higher Categories & Emergence00:31:41 Compositionality & Recursive Folds00:34:05 Syntax vs Semantics in Network Design00:36:14 Homomorphisms & Multi-Sorted Syntax00:39:30 The Carrying Problem & Hopf FibrationsPetar Veličković (GDM)https://petar-v.com/Paul Lessardhttps://www.linkedin.com/in/paul-roy-lessard/Bruno Gavranovićhttps://www.brunogavranovic.com/Andrew Dudzik (GDM)https://www.linkedin.com/in/andrew-dudzik-222789142/---REFERENCES:Model:[00:01:05] Veohttps://deepmind.google/models/veo/[00:01:10] Geniehttps://deepmind.google/blog/genie-3-a-new-frontier-for-world-models/Paper:[00:04:30] Geometric Deep Learning Blueprinthttps://arxiv.org/abs/2104.13478https://www.youtube.com/watch?v=bIZB1hIJ4u8[00:16:45] AlphaGeometryhttps://arxiv.org/abs/2401.08312[00:16:55] AlphaCodehttps://arxiv.org/abs/2203.07814[00:17:05] FunSearchhttps://www.nature.com/articles/s41586-023-06924-6[00:37:00] Attention Is All You Needhttps://arxiv.org/abs/1706.03762[00:43:00] Categorical Deep Learninghttps://arxiv.org/abs/2402.15332

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Machine Learning Street Talk (MLST)

Category theory: the "Final Boss" of Deep Learning (Andrew Dudzik, Petar Velichkovich, Taco Cohen, Bruno Gavranović, Paul Lessard)

This episode hasn't been transcribed yet

Other episodes from Machine Learning Street Talk (MLST)

Abstraction & Idealization: AI's Plato Problem [Mazviita Chirimuuta]

Why Every Brain Metaphor in History Has Been Wrong [SPECIAL EDITION]

Adversarial Examples and Data Modelling - Andrew Ilyas (MIT)

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