arXiv:2506.07047cs.AI2025-06被引 15

让AI从自然语言直接证明定理,突破传统依赖人工形式化瓶颈。

Mathesis: Towards Formal Theorem Proving from Natural Languages

  • 用强化学习构建自动形式化引擎,将口语化问题转为可验证数学命题。
  • 在高考数学题库上达到18%准确率,端到端系统表现超越现有方法。
  • 首次实现从自然语言到正式证明的全流程自动化,适合数学教育与科研应用。

大型语言模型在形式推理方面展现出巨大潜力,但大多数基于LLM的定理证明器长期受限于需专家编写的形式化输入,难以应用于自然语言表达的真实问题。本文提出Mathesis,首个端到端处理非正式问题陈述的定理证明流程。其核心贡献包括:Mathesis-Autoformalizer,首个采用强化学习提升自然语言问题形式化能力的自动形式化工具,辅以新颖的LeanScorer框架实现细粒度的形式化质量评估;以及Mathesis-Prover,从形式化语句生成正式证明。为评估端到端形式化定理证明的实际应用性,我们引入了Gaokao-Formal,一个包含488道中国高考数学难题的基准数据集。实验表明,Mathesis在各组件设计上均经过充分验证,其自动形式化模块在Gaokao-Formal上的通过率相比最佳基线提升22%;完整系统在MiniF2F上取得64%准确率(pass@32),并在Gaokao-Formal上达到18%的领先水平。

原文摘要 · Abstract (English)

Recent advances in large language models show strong promise for formal reasoning. However, most LLM-based theorem provers have long been constrained by the need for expert-written formal statements as inputs, limiting their applicability to real-world problems expressed in natural language. We tackle this gap with Mathesis, the first end-to-end theorem proving pipeline processing informal problem statements. It contributes Mathesis-Autoformalizer, the first autoformalizer using reinforcement learning to enhance the formalization ability of natural language problems, aided by our novel LeanScorer framework for nuanced formalization quality assessment. It also proposes a Mathesis-Prover, which generates formal proofs from the formalized statements. To evaluate the real-world applicability of end-to-end formal theorem proving, we introduce Gaokao-Formal, a benchmark of 488 complex problems from China's national college entrance exam. Our approach is carefully designed, with a thorough study of each component. Experiments demonstrate Mathesis's effectiveness, with the autoformalizer outperforming the best baseline by 22% in pass-rate on Gaokao-Formal. The full system surpasses other model combinations, achieving 64% accuracy on MiniF2F with pass@32 and a state-of-the-art 18% on Gaokao-Formal.

定理证明自然语言强化学习数学推理

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