Exploring Reachability and Abstraction in Mathematical AI

Professor Swarat Chaudhuri from the University of Texas at Austin and visiting researcher at Google DeepMind discusses breakthroughs in AI reasoning, theorem proving, and mathematical discovery. Chaudhuri explains his groundbreaking work on COPRA (a GPT-based prover agent), shares insights on neurosymbolic approaches to AI.

Professor Swarat Chaudhuri:

https://www.cs.utexas.edu/~swarat/

SPONSOR MESSAGES:

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TOC:

[00:00:00] 0. Introduction / CentML ad, Tufa ad

1. AI Reasoning: From Language Models to Neurosymbolic Approaches

[00:02:27] 1.1 Defining Reasoning in AI

[00:09:51] 1.2 Limitations of Current Language Models

[00:17:22] 1.3 Neuro-symbolic Approaches and Program Synthesis

[00:24:59] 1.4 COPRA and In-Context Learning for Theorem Proving

[00:34:39] 1.5 Symbolic Regression and LLM-Guided Abstraction

2. AI in Mathematics: Theorem Proving and Concept Discovery

[00:43:37] 2.1 AI-Assisted Theorem Proving and Proof Verification

[01:01:37] 2.2 Symbolic Regression and Concept Discovery in Mathematics

[01:11:57] 2.3 Scaling and Modularizing Mathematical Proofs

[01:21:53] 2.4 COPRA: In-Context Learning for Formal Theorem-Proving

[01:28:22] 2.5 AI-driven theorem proving and mathematical discovery

3. Formal Methods and Challenges in AI Mathematics

[01:30:42] 3.1 Formal proofs, empirical predicates, and uncertainty in AI mathematics

[01:34:01] 3.2 Characteristics of good theoretical computer science research

[01:39:16] 3.3 LLMs in theorem generation and proving

[01:42:21] 3.4 Addressing contamination and concept learning in AI systems

REFS:

00:04:58 The Chinese Room Argument, https://plato.stanford.edu/entries/chinese-room/

00:11:42 Software 2.0, https://medium.com/@karpathy/software-2-0-a64152b37c35

00:11:57 Solving Olympiad Geometry Without Human Demonstrations, https://www.nature.com/articles/s41586-023-06747-5

00:13:26 Lean, https://lean-lang.org/

00:15:43 A General Reinforcement Learning Algorithm That Masters Chess, Shogi, and Go Through Self-Play, https://www.science.org/doi/10.1126/science.aar6404

00:19:24 DreamCoder (Ellis et al., PLDI 2021), https://arxiv.org/abs/2006.08381

00:24:37 The Lambda Calculus, https://plato.stanford.edu/entries/lambda-calculus/

00:26:43 Neural Sketch Learning for Conditional Program Generation, https://arxiv.org/pdf/1703.05698

00:28:08 Learning Differentiable Programs With Admissible Neural Heuristics, https://arxiv.org/abs/2007.12101

00:31:03 Symbolic Regression With a Learned Concept Library (Grayeli et al., NeurIPS 2024), https://arxiv.org/abs/2409.09359

00:41:30 Formal Verification of Parallel Programs, https://dl.acm.org/doi/10.1145/360248.360251

01:00:37 Training Compute-Optimal Large Language Models, https://arxiv.org/abs/2203.15556

01:18:19 Chain-of-Thought Prompting Elicits Reasoning in Large Language Models, https://arxiv.org/abs/2201.11903

01:18:42 Draft, Sketch, and Prove: Guiding Formal Theorem Provers With Informal Proofs, https://arxiv.org/abs/2210.12283

01:19:49 Learning Formal Mathematics From Intrinsic Motivation, https://arxiv.org/pdf/2407.00695

01:20:19 An In-Context Learning Agent for Formal Theorem-Proving (Thakur et al., CoLM 2024), https://arxiv.org/pdf/2310.04353

01:23:58 Learning to Prove Theorems via Interacting With Proof Assistants, https://arxiv.org/abs/1905.09381

01:39:58 An In-Context Learning Agent for Formal Theorem-Proving (Thakur et al., CoLM 2024), https://arxiv.org/pdf/2310.04353

01:42:24 Programmatically Interpretable Reinforcement Learning (Verma et al., ICML 2018), https://arxiv.org/abs/1804.02477