Making deep learning perform real algorithms with Category Theory (Andrew Dudzik, Petar Velichkovich, Taco Cohen, Bruno Gavranović, Paul Lessard)
Show notes
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 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. --- TIMESTAMPS: 00:00:00 The Failure of LLM Addition & Physics 00:01:26 Tool Use vs Intrinsic Model Quality 00:03:07 Efficiency Gains via Internalization 00:04:28 Geometric Deep Learning & Equivariance 00:07:05 Limitations of Group Theory 00:09:17 Category Theory: Algebra with Colors 00:11:25 The Systematic Guide of Lego-like Math 00:13:49 The Alchemy Analogy & Unifying Theory 00:15:33 Information Destruction & Reasoning 00:18:00 Pathfinding & Monoids in Computation 00:20:15 System 2 Reasoning & Error Awareness 00:23:31 Analytic vs Synthetic Mathematics 00:25:52 Morphisms & Weight Tying Basics 00:26:48 2-Categories & Weight Sharing Theory 00:28:55 Higher Categories & Emergence 00:31:41 Compositionality & Recursive Folds 00:34:05 Syntax vs Semantics in Network Design 00:36:14 Homomorphisms & Multi-Sorted Syntax 00:39:30 The Carrying Problem & Hopf Fibrations Petar Veličković (GDM) https://petar-v.com/ 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/ --- REFERENCES: Model: [00:01:05] Veo https://deepmind.google/models/veo/ [00:01:10] Genie https://deepmind.google/blog/genie-3-a-new-frontier-for-world-models/ Paper: [00:04:30] Geometric Deep Learning Blueprint https://arxiv.org/abs/2104.13478 https://www.youtube.com/watch?v=bIZB1hIJ4u8 [00:16:45] AlphaGeometry https://arxiv.org/abs/2401.08312 [00:16:55] AlphaCode https://arxiv.org/abs/2203.07814 [00:17:05] FunSearch https://www.nature.com/articles/s41586-023-06924-6 [00:37:00] Attention Is All You Need https://arxiv.org/abs/1706.03762 [00:43:00] Categorical Deep Learning https://arxiv.org/abs/2402.15332
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