LLM Critics Help Catch Bugs in Mathematics: Towards a Better Mathematical Verifier with Natural Language Feedback
Bofei Gao, Zefan Cai, Runxin Xu, Peiyi Wang, Ce Zheng, Runji Lin, Keming Lu, Dayiheng Liu
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.
BibTeX
@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://aclanthology.org/2025.findings-acl.753/",
doi = "10.18653/v1/2025.findings-acl.753",
pages = "14588--14604",
ISBN = "979-8-89176-256-5"
}