Go to ICLR 2026 Workshop VerifAI-2 homepageJudging What We Cannot Solve: A Consequence-Based Approach for Oracle-Free Evaluation of Research-Level Math
Track: long paper (up to 8 pages)
Keywords: math, verifier
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 stronger correct–wrong separation even on instances the underlying solver often fails to solve
Anonymization: This submission has been anonymized for double-blind review via the removal of identifying information such as names, affiliations, and identifying URLs.
Presenter: ~Guijin_Son1
Format: Yes, the presenting author will definitely attend in person because they attending ICLR for other complementary reasons.
Funding: No, the presenting author of this submission does *not* fall under ICLR’s funding aims, or has sufficient alternate funding.
Submission Number: 27
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