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

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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.

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arXiv AI
Jun 12

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

arXiv:2606. 12594v1 Announce Type: new Abstract: Modern Lean theorem provers achieve strong performance only with substantial training and inference compute, driven in part by scarce verified proof data and the long reasoning traces of formal proof search, making both supervised fine-tuning (SFT) and sampling expensive.

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
arXiv Computation and Language
Sep 24

Towards Efficient Reasoning: Learning Causal Shortcuts for Diffusion Language Models

The paper introduces Causal Shortcut Learning (CSL), a framework that identifies token chains—called causal shortcuts—that guide Diffusion Language Models (DLMs) toward correct reasoning paths. By extracting these shortcuts and applying parallel prioritized masking during training, CSL improves both convergence speed and generation accuracy. Experiments on several reasoning benchmarks and two base models show CSL outperforms existing SFT-variant baselines, achieving an average 1.92% improvement over SFT-only models and up to 4.20% on MATH-500.

By Dian Jin, Kairong Han, Baohong Li, Xinpeng Dong, Zijing Hu, Nuanqiao Shan, Fei Wu, Kun Kuang