Summary
A new method verifies Lean formalizations of mathematics by combining LLM-based semantic review with mechanical numerical and vacuity checks, moving beyond purely LLM-judged faithfulness. The approach provides checkable feedback and catches errors that LLM judges miss. Integrated with the authors' Extract-Verify-Proof autoformalization pipeline, it was used to build the Formalized Library of Mathematical Functions (FLMF), a partial formalization of the NIST Digital Library of Mathematical Functions (DLMF). Evaluated on three labeled datasets, the method achieved the lowest accepted-error rate — the fraction of incorrect statements accepted by the verifier — among all compared methods. Expert review also uncovered translation and source-text defects in the existing datasets. Paper by Anna Mei and Michael R. Douglas, arXiv:2610.20573, with open-source code released on GitHub.
Paper Overview
Field: Machine Learning
Authors: Anna Mei, Michael R. Douglas
Released: 2026-10-14
arXiv: 2610.20573
Summary
The authors introduce a novel method for verifying Lean formalizations that goes beyond LLM-judged faithfulness. Unlike most verification methods, which rely on LLMs or trained models, their approach combines LLM-based semantic review with mechanical numerical and vacuity checks, providing checkable feedback and detecting errors missed by LLM judges.
The method is applied, together with the authors' Extract-Verify-Proof autoformalization pipeline, to construct the Formalized Library of Mathematical Functions (FLMF) — a partial formalization of the NIST Digital Library of Mathematical Functions (DLMF).
Key Results
- On three labeled datasets, the method achieves the lowest accepted-error rate among the evaluated verification methods, where the accepted-error rate is measured as the fraction of incorrect statements accepted by the method.
- Expert review of the results identified translation and source-text defects in the existing datasets.
- The code is open source: https://github.com/annamei1/FLMF-Ch7ErrFunc-Release.git
*Auto-collected on 2026-10-16.*
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