Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning

Jiaxing Guo; Wenjie Yang; Shengzhong Zhang; Tongshan Xu; Lun Du; Da Zheng; Zengfeng Huang

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arXiv · 2506.06877

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning

Jiaxing Guo·Wenjie Yang·Shengzhong Zhang·Tongshan Xu·Lun Du·Da Zheng·Zengfeng Huang

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Abstract

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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Jiaxing Guo, Wenjie Yang, Shengzhong Zhang, Tongshan Xu, Lun Du, Da Zheng, Zengfeng Huang. 2025-06-07. Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning. https://arxiv.org/abs/2506.06877

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