AutoIP：用 AI 智能体在 Lean 中形式化反问题经典理论
Formalizing inverse problems in the age of AI: possibilities, pitfalls, and an invitation
AI 导读
研究者发布 AutoIP，一个由 AI 智能体自动形式化的 Lean 库，涵盖经典线性正则化理论及其泛函分析基础，证明由机器校验。人的核心任务转为审核形式化陈述与自然语言表述是否一致，审阅者无需阅读证明。作者指出风险主要在陈述而非证明，并以一个假设条件比原表述更严格教材定理为例，邀请反问题社区扩展该库。
正文 · 原文
Abstract:Proof assistants such as Lean check mathematical proofs down to the axioms, and AI agents have recently made writing such proofs cheap. We describe AutoIP, a Lean library in which classical linear regularization theory, together with the functional analysis it rests on, has been autoformalized by AI agents. A machine-checked proof certifies only the formal statement it proves, so the remaining human task is to confirm that each formal statement says what was intended. We organize the library around this task: a reviewer compares the formal statements with their natural-language counterparts and never needs to read a proof. Our experience is that the risks lie in the statements rather than in the proofs, and that simple automated tests on the statements can expose problems even in the established literature. We illustrate this with a textbook theorem whose hypothesis is more restrictive than asserted. We invite the inverse problems community to extend and build on the library.
| Subjects: | Artificial Intelligence (cs.AI) |
| MSC classes: | 68V20, 47A52 |
| Cite as: | arXiv:2611.06962 [cs.AI] |
| (or arXiv:2611.06962v1 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2611.06962 arXiv-issued DOI via DataCite |
Submission history
From: Lauri Oksanen [view email]
[v1]
Wed, 4 Nov 2026 08:30:31 UTC (21 KB)
来源：arXiv cs.AI · arxiv.org