让数学证明机器人自我进化,边改代码边练题,越练越强。
Self-Modifying Lean Proof Agents with Verifier-Grounded Benchmark Coevolution

- Agent自我修改工作流,通过验证闭环不断迭代
- 自适应难度升级,最高解题率达45.1%
- 适合研究自动推理与智能体自演化的学者
设计高效的Lean证明代理是形式化数学推理的核心挑战。除了构建更强的证明器,近期工作更关注Lean流程:代理如何分解证明任务、使用工具与编译器反馈、诊断失败、修复证明并维护结构化证明上下文。受代码级自演化智能体启发,我们探索这些流程能否被演化而非手工设计。本文提出一个自演化Lean证明代理,其小规模固定可信运行时包裹完全可变的工作空间:证明流程、提示词和工具。不同于多数在固定外部基准上优化的系统,本系统同时演化代理与基准。每代之间,表现最佳的代理(冠军)通过“掌握阈值课程更新”引入更难证明任务,仅当当前水平已掌握后才提升难度;并通过单锚点校准,将冠军重跑于新基准以保持评分可比性。所有演化均在基于Lean的验证闭环内进行:无论代理如何自我重写,只有生成可被Lean验证的证明才算成功,且每次尝试必须输出机器可读的Lean基础证明上下文,其表示可演化但根基始终受控。我们在15代活跃演化中对比了该系统与固定基准基线,在保留的miniF2F测试集上,最佳共演化代理达到45.1%的解题率,优于种子模型的12.7%和最优固定基准代理的32.0%,表明基于验证器的自演化能有效提升Lean证明工作流。
原文摘要 · Abstract (English)
Designing effective Lean proof agents is a central challenge in formal mathematical reasoning. Beyond building stronger provers, recent work emphasizes the workflow around Lean: how an agent decomposes proof obligations, uses tools and compiler feedback, diagnoses failures, repairs proofs, and maintains structured proof context. Motivated by code-level self-evolving agents, we study whether such workflows can be evolved rather than hand-designed. We present a self-evolving Lean proof agent in which a small fixed, trusted runtime wraps a fully mutable workspace: the proof workflow, prompts, and tools. Unlike most self-evolving systems, which optimize against a fixed external benchmark, our system coevolves the agent and its benchmark. Between generations, the highest-scoring agent (the champion) revises the active task distribution through a mastery-throttled curriculum update that introduces harder proof obligations only after the current level is mastered, and a single-anchor recalibration re-runs the champion on the updated benchmark to keep scores comparable as difficulty rises. All evolution stays inside a Lean-grounded verification loop: however the agent rewrites itself, a success counts only when its behavior yields Lean-verified proofs under a trusted snapshot, and each attempt must emit a machine-readable, Lean-grounded proof context whose representation may evolve but whose groundedness is enforced. We run the coevolving trajectory and a fixed-benchmark baseline for 15 active generations and compare them on a held-out miniF2F test split. The best coevolving agent reaches a 45.1% held-out solve rate, versus 12.7% for the seed and 32.0% for the best fixed-benchmark agent, showing that verifier-grounded self-evolution can improve Lean proof workflows under a coevolving benchmark.
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