arXiv:2604.23712cs.LGcs.AI2026-04

用奥运数学模型迁移优化领域,提升证明效率。

OptProver: Bridging Olympiad and Optimization through Continual Training in Formal Theorem Proving

论文配图:OptProver: Bridging Olympiad and Optimization through Continual Training in Formal Theorem Proving
图 1 · 摘自论文原文
  • 从奥数模型出发,通过专家迭代和偏好学习缓解领域差异。
  • 在新基准上达到同类模型最优的通过率,且不遗忘通用证明能力。
  • 适合研究形式化证明与跨领域迁移的学者参考。

当前形式化定理证明主要聚焦于奥数级数学问题,而本科阶段的优化领域尚未得到充分关注。优化作为机器学习、运筹学和科学计算的基础,依赖领域特定的形式化(如凸性、最优性条件、算法分析),导致现有证明器无法直接迁移。我们提出 OptProver,一种从奥数模型成功迁移到本科优化领域的训练模型。其方法包括:大规模优化相关数据的专家迭代构建;引入结合困惑度加权与无效步骤惩罚的特殊偏好学习目标,引导搜索走向高效路径。为支持严谨评估,我们构建了基于 Lean 4 的新型优化定理证明基准。在该基准上,OptProver 在同等规模模型中实现最优的 Pass@1 与 Pass@32 性能,同时保持通用定理证明任务上的竞争力,证明了有效迁移且无灾难性遗忘。

原文摘要 · Abstract (English)

Recent advances in formal theorem proving have focused on Olympiad-level mathematics, leaving undergraduate domains largely unexplored. Optimization, fundamental to machine learning, operations research, and scientific computing, remains underserved by existing provers. Its reliance on domain-specific formalisms (convexity, optimality conditions, and algorithmic analysis) creates significant distribution shift, making naive domain transfer ineffective. We present OptProver, a trained model that achieves robust transfer from Olympiad to undergraduate optimization. Starting from a strong Olympiad-level prover, our pipeline mitigates distribution shift through two key innovations. First, we employ large-scale optimization-focused data curation via expert iteration. Second, we introduce a specialized preference learning objective that integrates perplexity-weighted optimization with a mechanism to penalize valid but non-progressing proof steps. This not only addresses distribution shifts but also guides the search toward efficient trajectories. To enable rigorous evaluation, we construct a novel benchmark in Lean 4 focused on optimization. On this benchmark, OptProver achieves state-of-the-art Pass@1 and Pass@32 among comparably sized models while maintaining competitive performance on general theorem-proving tasks, demonstrating effective domain transfer without catastrophic forgetting.

形式化证明优化迁移学习

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