arXiv:2510.00732cs.AI2025-10被引 7

通过演化对称与难度生成新定理,提升数学证明模型鲁棒性。

EvolProver: Advancing Automated Theorem Proving by Evolving Formalized Problems via Symmetry and Difficulty

  • 基于抽象语法树和领域迁移,生成语义等价的对称问题变体
  • 设计进化指令生成多难度新定理,覆盖更广测试范围
  • 70亿参数模型在多个基准上刷新非推理类证明模型记录

用于形式化定理证明的大语言模型虽具潜力,但泛化能力差,对问题表述微小变化敏感。为解决此问题,本文提出一种新型数据增强流水线,从对称性和难度两方面提升模型鲁棒性。对称性方面,提出EvolAST(基于抽象语法树的语法对称生成)和EvolDomain(利用大模型跨数学领域翻译以实现语义对称);难度方面,提出EvolDifficulty,通过精心设计的进化指令引导大模型生成具有不同难度的新定理。使用演化数据训练出70亿参数的非推理型证明器EvolProver。该模型在FormalMATH-Lite上达到53.8% pass@32,超越所有同规模模型,包括基于推理的模型;并在MiniF2F-Test(69.8% pass@32)、Ineq-Comp-Seed(52.2% pass@32)和Ineq-Comp-Transformed(34.0% pass@32)上创下非推理模型新SOTA。消融实验进一步验证了数据增强的有效性。

原文摘要 · Abstract (English)

Large Language Models (LLMs) for formal theorem proving have shown significant promise, yet they often lack generalizability and are fragile to even minor transformations of problem statements. To address this limitation, we introduce a novel data augmentation pipeline designed to enhance model robustness from two perspectives: symmetry and difficulty. From the symmetry perspective, we propose two complementary methods: EvolAST, an Abstract Syntax Tree (AST) based approach that targets syntactic symmetry to generate semantically equivalent problem variants, and EvolDomain, which leverages LLMs to address semantic symmetry by translating theorems across mathematical domains. From the difficulty perspective, we propose EvolDifficulty, which uses carefully designed evolutionary instructions to guide LLMs in generating new theorems with a wider range of difficulty. We then use the evolved data to train EvolProver, a 7B-parameter non-reasoning theorem prover. EvolProver establishes a new state-of-the-art (SOTA) on FormalMATH-Lite with a 53.8% pass@32 rate, surpassing all models of comparable size, including reasoning-based models. It also sets new SOTA records for non-reasoning models on MiniF2F-Test (69.8% pass@32), Ineq-Comp-Seed (52.2% pass@32), and Ineq-Comp-Transformed (34.0% pass@32). Ablation studies further confirm our data augmentation pipeline's effectiveness across multiple benchmarks.

自动证明数据增强大模型形式化推理

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