@inproceedings{gao-etal-2025-llm-critics,
    title = "{LLM} Critics Help Catch Bugs in Mathematics: Towards a Better Mathematical Verifier with Natural Language Feedback",
    author = "Gao, Bofei  and
      Cai, Zefan  and
      Xu, Runxin  and
      Wang, Peiyi  and
      Zheng, Ce  and
      Lin, Runji  and
      Lu, Keming  and
      Liu, Dayiheng  and
      Zhou, Chang  and
      Xiao, Wen  and
      Liu, Tianyu  and
      Chang, Baobao",
    editor = "Che, Wanxiang  and
      Nabende, Joyce  and
      Shutova, Ekaterina  and
      Pilehvar, Mohammad Taher",
    booktitle = "Findings of the Association for Computational Linguistics: ACL 2025",
    month = jul,
    year = "2025",
    address = "Vienna, Austria",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/display_plenaries/2025.findings-acl.753/",
    pages = "14588--14604",
    ISBN = "979-8-89176-256-5",
    abstract = "In recent progress, mathematical verifiers have achieved success in mathematical reasoning tasks by validating the correctness of solutions generated by policy models. However, existing verifiers are trained with binary classification labels, which are not informative enough for the model to accurately assess the solutions. To mitigate the aforementioned insufficiency of binary labels, we introduce step-wise natural language feedback as rationale labels, that is, the correctness of each step and the detailed explanations. In this paper, we propose Math-Minos, a natural language feedback-enhanced verifier by constructing automatically generated training data and a two-stage training paradigm for effective training and efficient inference. Our experiments reveal that a small set of natural language feedback can significantly boost the performance of the verifier in both verification and reinforcement learning and also significantly alleviates the data-demanding problems of the reward model with an over 700{\%} data efficiency improvement."
}