SkillEvoLean: Mutation-enhanced skill evolution for Lean provers

2026-10-01

AI Summary

This study addresses the stagnation of skill evolution in formal theorem proving caused by the absence of successful trajectories and the neglect of dynamically evolving reference knowledge. To overcome these limitations, we propose a mutation-enhanced skill self-evolution framework. By leveraging large language model agents and Monte Carlo Tree Search sampling, our method integrates progressive evolution with a verification feedback-driven, concept-oriented mutation mechanism. This enables the joint evolution of high-level strategies and mathematical concepts, effectively breaking the update bottleneck when no successful samples are available. Experimental results demonstrate that the proposed framework achieves a 100% success rate on MiniF2F and 90.6% on PutnamBench, while solving four problems each from the IMO and USAMO competitions, significantly outperforming existing baselines.

Abstract

Skill evolution offers a promising way to improve large language model agents without updating their parameters, but its use in formal theorem proving remains underexplored. Existing methods mainly target natural-language reasoning, improving skills by analyzing successful and failed trajectories and incrementally revising solving strategies. Although the Lean verifier provides reliable execution feedback, when all sampled trajectories fail, existing skill evolution methods lack successful trajectories from which to infer effective update directions. Furthermore, these methods also focus mainly on the root instruction file, thus underexploring the evolution of reference knowledge including mathematical concepts and proving techniques. To address these limitations, we propose a mutation-enhanced skill self-evolution framework for building skill-augmented Lean provers. The framework jointly evolves a high-level solving policy and its reference knowledge through progressive and mutation-based updates. Progressive evolution derives local improvements from successful and failed trajectories, while mutation is triggered when no complete proof can be generated, sampling mathematical concepts to produce and select new skill candidates under verifier feedback. We evaluate our method on MiniF2F, PutnamBench, the 2025 International Mathematical Olympiad (IMO 2025), and the 2026 USA Mathematical Olympiad (USAMO 2026). Under the same backbone model, trajectorysampling budget, and test-time compute, our method achieves proof success rates of 100.0%, 90.6%, 4/6, and 4/6, respectively, with GPT-5.5, outperforming the baseline methods. Further analysis shows that concept-guided mutation outperforms random-text-guided mutation by 6.9 and 8.2 percentage points on MiniF2F and PutnamBench, respectively, while solving one additional problem on both IMO 2025 and USAMO 2026.

Problem

• Skill evolution
• Formal theorem proving
• Lean prover
• Mutation
• Reference knowledge

Innovation

• Skill Evolution
• Mutation-enhanced Update
• Lean Theorem Proving
• Joint Policy-Knowledge Co-evolution
• Concept-guided Mutation