待翻译：Cost-Effective Automated Judging of Natural-Language Mathematical Proofs

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--> [Submitted on 29 May 2026] Title:Cost-Effective Automated Judging of Natural-Language Mathematical Proofs View a PDF of the paper titled Cost-Effective Automated Judging of Natural-Language Mathematical Proofs, by Benjamin Grayzel View PDF HTML (experimental) Abstract:Grading natural-language mathematical proofs is a recurring cost in evaluating math-reasoning systems, and frontier LLM judges are expensive. We ask whether cheap open-weight models can serve as reliable judges given a candidate proof, a ground-truth proof, and a human-grading rubric. On a 200-instance validation sample of IMO-GradingBench, three cheap judges (GPT-OSS 120B, DeepSeek-V4 Flash, Gemma-4 31B) agree with human pass/fail decisions at rates statistically indistinguishable from Claude Opus 4.7 and Gemini 3.1 Pro, at up to $100\times$ lower cost. We had expected a majority vote of the three to be the best budget option; it matched the frontier but did not improve on its strongest member. Extending to the full 1000-instance benchmark and exploring consensus rules, we found that requiring unanimous agreement (all-three-pass) reaches the highest pass-agreement and precision and, on four replicate runs, the smallest run-to-run spread. The headline finding is that cheap judges are competitive with the frontier at one to two orders of magnitude lower cost; as a deployable default we recommend all-three-pass, with the caveat that this rule was identified post-hoc and warrants independent replication. Comments: 7 pages, 5 figures, 4 tables Subjects: Computation and Language (cs.CL); Artificial Intelligence (cs.AI); Machine Learning (cs.LG) Cite as: arXiv:2608.00004 [cs.CL] (or arXiv:2608.00004v1 [cs.CL] for this version) https://doi.org/10.48550/arXiv.2608.00004 arXiv-issued DOI via DataCite Submission history From: Benjamin Grayzel [view email] [v1] Fri, 29 May 2026 17:22:57 UTC (250 KB) Full-text links: Access Paper: View a PDF of the paper titled Cost-Effective Automated Judging of Natural-Language Mathematical Proofs, by Benjamin Grayzel View PDF HTML (experimental) TeX Source view license Current browse context: cs.CL new | recent | 2026-08 Change to browse by: cs cs.AI cs.LG References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)