形式化定理证明一直门槛高、成本高，Goedel-Architect 用蓝图+精炼策略大幅提升效率，做数学证明或形式化验证的团队值得关注，开源且成本极低。
Goedel-Architect 是一个基于 Lean 4 的智能体框架，通过生成和精炼“蓝图”（定义和引理的依赖图）来简化形式化定理证明。它先根据自然语言证明生成蓝图，然后并行证明每个引理节点，失败节点会驱动全局蓝图精炼，避免了传统递归分解的低效循环。使用开源模型 DeepSeek-V4-Flash 作为骨干，在 MiniF2F-test 上达到 99.2% pass@1，在 PutnamBench 上达到 75.6% pass@1。结合自然语言证明引导，可解决更难的题目，如 IMO 2025 的 4/6 和 Putnam 2025 的 11/12。该框架在开源管道中实现了最先进性能，且成本比同类开源方案低 500 倍。
Goedel-Architect: Streamlining Formal Theorem Proving with Blueprint Generation and Refinement
We introduce Goedel-Architect, an agentic framework for formal theorem proving in Lean 4 centered on blueprint generation and refinement. A blueprint is a dependency graph of definitions and lemmas that builds up to the main theorem. First, Goedel-Architect generates a blueprint of formally stated definitions and lemmas, along with declared dependencies. This blueprint is optionally guided by a natural language proof. Then, a tool-equipped Lean prover component closes each open lemma node in parallel using relevant dependencies. Failed lemmas in turn drive refinement of the global blueprint. This strategy contrasts with other mainstream approaches which use recursive lemma decomposition, and can inefficiently loop on dead-end strategies. Using the open-weight DeepSeek-V4-Flash (284B-A13B) as the backbone, Goedel-Architect attains 99.2% pass@1 on MiniF2F-test and 75.6% pass@1 on PutnamBench. With an optional natural-language proof seeding the initial blueprint on the harder problems, we additionally close the remaining two MiniF2F-test problems (reaching 100%), lift PutnamBench to 88.8% (597/672), and solve 4/6 on IMO 2025, 11/12 on Putnam 2025, and 3/6 on USAMO 2026. This represents state-of-the-art performance for an open-source pipeline at a price point up to 500x less than comparable open-source pipelines.
- Pandaily06-06 07:35原文