Formalizing Numerical Analysis: An Agent Pipeline and Quality Audit Beyond Kernel Acceptance

While AI agents can now formalize advanced mathematics in Lean 4, relying solely on compiler acceptance hides critical semantic errors. This study introduces a rigorous three-dimensional framework to audit AI-generated formalizations, revealing that current metrics significantly overstate AI's mathematical accuracy.

Computer Science > Artificial Intelligence

Title:Formalizing Numerical Analysis: An Agent Pipeline and Quality Audit Beyond Kernel Acceptance

View PDF HTML (experimental)Abstract:Recent work has demonstrated that coding agents can formalize entire advanced mathematics textbooks in Lean 4, yet existing efforts concentrate on branches of mathematics already well-represented in mathlib and measure success solely through kernel acceptance. We address both limitations by applying a coding agent to formalize Numerical Methods for Ordinary Differential Equations, a textbook in numerical analysis that is largely absent from mathlib, stressing the agent's capacity to develop new theory from scratch. We further introduce a systematic, reproducible three-dimensional framework for evaluating the quality of agent-produced formalizations beyond compilation: semantic correctness, Mathlib reuse, and cross-file reuse via LLM-as-judge methods. Applying this framework to our own formalization and to the released outputs of RepoProver and M2F, we uncover recurring unfaithful formalization patterns, including incomplete multi-part statements, added weakening hypotheses, and parameter restrictions, that kernel acceptance entirely obscures. Our results suggest that compilation-based metrics substantially overstate formalization quality, and we provide a reproducible audit methodology to support more rigorous evaluation of future autoformalization systems.

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Source: arXiv cs.AI Recent

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