arXiv Machine Learning By Thomas Chen, Zhiyuan Li

A Theoretical Framework for Self-Play Theorem Proving Algorithms

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arXiv:2606. 01861v1 Announce Type: new Abstract: Self-play, a type of training algorithm that enables a model to self-improve, has recently shown promising empirical results in the context of formal theorem proving using Large Language Models (LLMs).

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arXiv Machine Learning
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Scaling Self-Play with Self-Guidance

arXiv:2604. 20209v2 Announce Type: replace Abstract: LLM self-play algorithms are notable in that, in principle, nothing bounds their learning: a Conjecturer model creates problems for a Solver, and both improve together.

By Luke Bailey, Kaiyue Wen, Kefan Dong, Tatsunori Hashimoto, Tengyu Ma
arXiv AI
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Learning to Discover Interesting Mathematics

The paper introduces a method for evaluating the intrinsic interestingness of mathematical theorems by comparing the length of their proofs to the length of their statements. It trains a 27B language model to predict proof difficulty, enabling the generation and selection of more interesting theorems while significantly reducing overlap with existing Mathlib. The approach allows iterative expansion of a self‑building, machine‑verified mathematical library guided by quantifiable metrics.

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Diffusion-Proof: Recipe for Formal Theorem Proving Beyond Auto-Regressive Generation

Enhancing the formal math reasoning capabilities of Large Language Models (LLMs) has become a key focus in both mathematical and computer science communities in recent years. While significant progress has been made in using state-of-the-art Auto-Regressive (AR) LLMs for formal theorem proving, these models suffer from inherent limitations.

arXiv AI
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Pythagoras-Prover: Advancing Efficient Formal Proving via Augmented Lean Formalisation

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By Joshua Ong Jun Leang, Zheng Zhao, Mihaela C\u{a}t\u{a}lina Stoian, Qiyuan Xu, Haonan Li, Wenda Li, Shay B. Cohen, Eleonora Giunchiglia