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arXiv 2602.03061cs.LGcs.AImath.STstat.MEstat.MLstat.TH
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评估LLMs在不知道答案时的性能:通过比较信号进行数学推理的统计评估

Evaluating LLMs When They Do Not Know the Answer: Statistical Evaluation of Mathematical Reasoning via Comparative Signals

Rutgers University(罗格斯大学);Shanghai Jiao Tong University(上海交通大学)

Zihan Dong, Zhixian Zhang, Yang Zhou, Can Jin, Ruijia Wu, Linjun Zhang

AI总结:

本文提出一种统计高效的方法,通过结合标准结果与成对比较信号,提升LLM数学推理能力评估的准确性和稳定性。

摘要:

评估LLM中的数学推理能力受到基准数据量有限和模型固有随机性的影响,导致准确性估计高方差和跨平台排名不稳定。在困难问题上,LLM可能无法生成正确最终答案,但仍然能提供可靠的成对比较信号,表明两个候选解决方案中哪个更好。我们利用这一观察,设计了一个统计上高效的评估框架,结合标准标记结果与通过让模型判断辅助推理链获得的成对比较信号。将这些比较信号视为控制变量,我们开发了一种基于高效影响函数(EIF)的半参数估计器,适用于辅助推理链被观察的场景。这产生了一个一步估计器,实现了半参数效率界,保证了严格方差减少,且在原理上允许渐近正态性以进行不确定性量化。在模拟中,我们的一步估计器显著提高了排名准确性,随着模型输出噪声增长,收益增加。在GPQA Diamond、AIME 2025和GSM8K上的实验进一步展示了更精确的性能估计和更可靠的模型排名,特别是在小样本情况下,传统评估相当不稳定。

英文摘要:

Evaluating mathematical reasoning in LLMs is constrained by limited benchmark sizes and inherent model stochasticity, yielding high-variance accuracy estimates and unstable rankings across platforms. On difficult problems, an LLM may fail to produce a correct final answer, yet still provide reliable pairwise comparison signals indicating which of two candidate solutions is better. We leverage this observation to design a statistically efficient evaluation framework that combines standard labeled outcomes with pairwise comparison signals obtained by having models judge auxiliary reasoning chains. Treating these comparison signals as control variates, we develop a semiparametric estimator based on the efficient influence function (EIF) for the setting where auxiliary reasoning chains are observed. This yields a one-step estimator that achieves the semiparametric efficiency bound, guarantees strict variance reduction over naive sample averaging, and admits asymptotic normality for principled uncertainty quantification. Across simulations, our one-step estimator substantially improves ranking accuracy, with gains increasing as model output noise grows. Experiments on GPQA Diamond, AIME 2025, and GSM8K further demonstrate more precise performance estimation and more reliable model rankings, especially in small-sample regimes where conventional evaluation is pretty unstable.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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