LEAP:用智能体框架为形式数学增强大语言模型
LEAP: Supercharging LLMs for Formal Mathematics with Agentic Frameworks
Po-Nien Kung, Linfeng Song, Dawsen Hwang, Jinsung Yoon, Chun-Liang Li, Simone Severini, Mirek Olšák, Edward Lockhart 等 13 位作者
AI 速读 基于摘要
LEAP 是一个智能体框架,让通用基础模型通过与 Lean 编译器持续交互,把非形式化推理转化为可机械验证的形式化证明,并在 2025 年 Putnam 竞赛与自建 Lean-IMO-Bench 上取得作者报告的高求解率。
cs.AI
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Large Language Models (LLMs) exhibit strong informal mathematical reasoning but struggle to generate mechanically verifiable proofs in formal languages like Lean. We present LEAP, an agentic framework that enables general-purpose foundation models to achieve state-of-the-art performance on automated formal theorem proving. LEAP leverages foundation model capabilities, such as informal reasoning, instruction following, and iterative self-refinement. By decomposing complex problems into smaller units, the system bridges formal proof construction with informal blueprints through continuous interaction with the Lean compiler. To provide a rigorous evaluation beyond increasingly saturated benchmarks, we introduce Lean-IMO-Bench, a benchmark of IMO-style problems formalized in Lean, with short statements yet highly non-routine and multi-step proofs across a wide range of difficulty levels. Empirically, on the latest 2025 Putnam Competition, an annual mathematics competition for undergraduate students in North America, LEAP solves all 12 problems, matching recent breakthroughs by frontier formal mathematical models. On Lean-IMO-Bench, LEAP boosts the one-shot formal solve rate of general-purpose LLMs from below 10% to 70%, notably surpassing the 48% benchmark set by a specialized, gold-medal-caliber IMO system. Furthermore, we demonstrate LEAP's research-level utility by autonomously formalizing complex proofs for open combinatorial challenges, including a verified proof for a key subproblem in Knuth's Hamiltonian decomposition of even-order Cayley graphs.