SHADOWBENCH: Toward Reliable Automatic Evaluation of Semantic Alignment in Autoformalization

Abstract:Autoformalization translates informal mathematical theorems into code for proof assistants such as Lean. A central challenge is that current evaluation metrics can accept type-correct but misaligned statements or reject correct statements written in a different formulation. Inspired by Pass@$k$, we propose SA-Pass (*Semantic Alignment Pass*), which tests formal statements using auxiliary statements called *shadows* that characterize the intended statement. A generated statement receives full credit only when it compiles, implies each shadow (forward check), and is implied by their conjunction (backward check). We instantiate SA-Pass in ShadowBench, a Lean 4 full autoformalization benchmark of 178 postgraduate- to research-level problems spanning eight mathematical areas. Claude Code (Opus 4.8) with Numina-Lean-Agent reaches $61.8\%$ compile rate and $11.2\%$ SA-Pass. Across outputs generated by six agentic configurations, SA-Pass achieves $98.8\%$ binary agreement with expert judgments. An early version of ShadowBench served as the benchmark for Track 4 of the ICML 2026 AI4Math Challenge.

Computation and Language (cs.CL); Artificial Intelligence (cs.AI)

arXiv:2608.29270 [cs.CL]

(or arXiv:2608.29270v1 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2608.29270 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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