用细粒度验证发现大模型数学推理常错在过程而非答案
Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning
- 逐步检查解题过程，识别逻辑错误
- 在复杂问题上准确率显著优于传统方法
- 适合需要真实推理能力的模型评估与训练
以结果奖励的大语言模型在数学求解中表现优异，但其正确答案常依赖不合理的推理过程，即存在奖励滥用现象。我们构建了带有细粒度标注的MathOlympiadEval数据集，揭示了模型答案正确率与过程正确率之间存在显著差距。现有自动化评估方法（如LLM-as-a-judge）难以可靠检测此类推理缺陷。为此，我们提出ParaStepVerifier，一种针对数学解题过程的逐步验证方法，可精准识别错误推理步骤。实验证明，该方法在复杂多步问题上显著提升对错误解法的识别准确率，为实现真正具备数学推理能力的模型评估与训练提供了更可靠的路径。
原文摘要 · Abstract (English)
Outcome-rewarded Large Language Models (LLMs) have demonstrated remarkable success in mathematical problem-solving. However, this success often masks a critical issue: models frequently achieve correct answers through fundamentally unsound reasoning processes, a phenomenon indicative of reward hacking. We introduce MathOlympiadEval, a new dataset with fine-grained annotations, which reveals a significant gap between LLMs' answer correctness and their low process correctness. Existing automated methods like LLM-as-a-judge struggle to reliably detect these reasoning flaws. To address this, we propose ParaStepVerifier, a novel methodology for meticulous, step-by-step verification of mathematical solutions. ParaStepVerifier identifies incorrect reasoning steps. Empirical results demonstrate that ParaStepVerifier substantially improves the accuracy of identifying flawed solutions compared to baselines, especially for complex, multi-step problems. This offers a more robust path towards evaluating and training LLMs with genuine mathematical reasoning.
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