5600亿参数模型用智能工具强化学习,让AI自动证明数学定理。
LongCat-Flash-Prover: Advancing Native Formal Reasoning via Agentic Tool-Integrated Reinforcement Learning

- 分三步解决形式化推理:自动命题、草图生成、完整证明。
- 仅用72次推理就达97.1%通过率,复杂题库中达41.5%成功率。
- 适合研究形式化验证与自动化证明的学者,开源可用。
我们提出 LongCat-Flash-Prover,一个5600亿参数的开源混合专家(MoE)模型,通过智能体工具集成推理(TIR)推进 Lean4 中的原生形式化推理。将任务分解为自动形式化、草图生成和证明三个独立能力,设计混合专家迭代框架扩展高质量轨迹。采用分层重要性采样策略优化(HisPO),通过梯度掩码缓解策略过时与训练推理差异问题。引入定理一致性和合法性检测机制,防止奖励滥用。大量评估显示,该模型在开放权重模型中达到新SOTA:MiniF2F-Test通过率达97.1%(每题仅72次推理预算);在更难的ProverBench上解决70.8%,PutnamBench上解决41.5%(每题不超过220次尝试),显著优于现有开源基线。
原文摘要 · Abstract (English)
We introduce LongCat-Flash-Prover, a flagship 560-billion-parameter open-source Mixture-of- Experts (MoE) model that advances Native Formal Reasoning in Lean4 through agentic tool-integrated reasoning (TIR). We decompose the native formal reasoning task into three independent formal capabilities, i.e., auto-formalization, sketching, and proving. To facilitate these capabilities, we propose a Hybrid-Experts Iteration Framework to expand high-quality task trajectories, including generating a formal statement based on a given informal problem, producing a whole-proof directly from the statement, or a lemma-style sketch. During agentic RL, we present a Hierarchical Importance Sampling Policy Optimization (HisPO) algorithm, which aims to stabilize the MoE model training on such long-horizon tasks. It employs a gradient masking strategy that accounts for the policy staleness and the inherent train-inference engine discrepancies at both sequence and token levels. Additionally, we also incorporate theorem consistency and legality detection mechanisms to eliminate reward hacking issues. Extensive evaluations show that our LongCat-Flash-Prover sets a new state-of-the-art for open-weights models in both auto-formalization and theorem proving. Demonstrating remarkable sample efficiency, it achieves a 97.1% pass rate on MiniF2F-Test using only 72 inference budget per problem. On more challenging benchmarks, it solves 70.8% of ProverBench and 41.5% of PutnamBench with no more than 220 attempts per problem, significantly outperforming existing open-weights baselines.
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