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

TL;DR

This paper introduces Consequence-Based Utility, an oracle-free evaluation method for research-level math solutions, which improves ranking accuracy over existing models by testing solutions' utility in related questions.

Contribution

It proposes a novel consequence-based evaluation approach that outperforms reward models and LLM judges in ranking research-level math solutions without requiring an oracle.

Findings

Outperforms reward models and LLM judges in ranking quality

Improves accuracy metrics significantly on GPT-OSS-120B and GPT-OSS-20B

Maintains strong separation between correct and incorrect solutions even when solvers fail

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.