Formalizing Numerical Analysis: An Agent Pipeline and Quality Audit Beyond Kernel Acceptance
Quick Answer
This study formalizes Numerical Methods for Ordinary Differential Equations using a coding agent in Lean 4, addressing gaps in existing mathlib.
Quick Take
This study formalizes Numerical Methods for Ordinary Differential Equations using a coding agent in Lean 4, addressing gaps in existing mathlib. A new evaluation framework reveals that traditional kernel acceptance metrics overstate formalization quality, uncovering issues like incomplete statements and added hypotheses.
Key Points
- Formalization focuses on a textbook largely absent from existing mathlib resources.
- Introduces a three-dimensional framework to evaluate formalization quality beyond kernel acceptance.
- Identifies recurring issues in formalizations, such as incomplete statements and added hypotheses.
- Suggests that compilation-based metrics significantly overstate the quality of formalizations.
- Provides a reproducible audit methodology for evaluating future autoformalization systems.
Paper Resources
Article Content
From source RSS / original summaryarXiv:2606. 14000v1 Announce Type: new 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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