Risk-Controlled Lean-as-Judge for Natural-Language Mathematical Reasoning
Lean is increasingly used to judge natural-language mathematical answers, but its signal is partial: many answers never formalize, and a failed proof may reflect an ill-typed statement or a missing library fact, not a wrong answer. On MATH-500 we show this signal is (i) sharply coverage-dependent, that is the proof-winning answer is correct 96% of the time at high proved coverage but 20% at low, and (ii) sparse and often unfaithful: a 7B autoformalizer proves a class for only 28% of problems, and a manual audit finds only approximately 43% of those proofs faithful. We propose COVCAL, a selector over Lean-trace diagnostics that certifies a finite-sample selective-risk bound on accepted ans...
| Authors | Pauline Bourigault, Xiaotong Ji, Matthieu Zimmer et al. |
|---|---|
| Primary category | cs.AI |
| Published | 27 May 2026 |
| Last updated at source | 27 May 2026 |
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