Judging What We Cannot Solve: A Consequence-Based Approach for Oracle-Free Evaluation of Research-Level Math

• URL: http://arxiv.org/abs/2602.06291v1
• Date: Fri, 06 Feb 2026 01:10:28 GMT
• Title: Judging What We Cannot Solve: A Consequence-Based Approach for Oracle-Free Evaluation of Research-Level Math
• Authors: Guijin Son, Donghun Yang, Hitesh Laxmichand Patel, Hyunwoo Ko, Amit Agarwal, Sunghee Ahn, Kyong-Ha Lee, Youngjae Yu,
• Abstract summary: We propose Consequence-Based Utility, an oracle-free evaluator that scores each candidate by testing its value as an in-context exemplar in solving related questions.<n>Our approach is evaluated on an original set of research-level math problems, each paired with one expert-written solution and nine LLM-generated solutions.<n> Notably, Consequence-Based Utility consistently outperforms reward models, generative reward models, and LLM judges on ranking quality.
• Score: 21.001217194182995
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recent progress in reasoning models suggests that generating plausible attempts for research-level mathematics may be within reach, but verification remains a bottleneck, consuming scarce expert time. We hypothesize that a meaningful solution should contain enough method-level information that, when applied to a neighborhood of related questions, it should yield better downstream performance than incorrect solutions. Building on this idea, we propose \textbf{Consequence-Based Utility}, an oracle-free evaluator that scores each candidate by testing its value as an in-context exemplar in solving related yet verifiable questions. Our approach is evaluated on an original set of research-level math problems, each paired with one expert-written solution and nine LLM-generated solutions. Notably, Consequence-Based Utility consistently outperforms reward models, generative reward models, and LLM judges on ranking quality. Specifically, for GPT-OSS-120B, it improves Acc@1 from 67.2 to 76.3 and AUC from 71.4 to 79.6, with similarly large AUC gains on GPT-OSS-20B (69.0 to 79.2). Furthermore, compared to LLM-Judges, it also exhibits a larger solver-evaluator gap, maintaining a stronger correct-wrong separation even on instances where the underlying solver often fails to solve.

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