ChatGLM-Math: Improving Math Problem-Solving in Large Language Models with a Self-Critique Pipeline

TL;DR

This paper introduces a Self-Critique pipeline that enhances large language models' mathematical problem-solving abilities while maintaining language skills, using a feedback-based training approach with a dedicated critique model.

Contribution

The work presents a novel Self-Critique pipeline that improves LLMs' math skills through self-generated feedback and fine-tuning, outperforming larger models.

Findings

Significant improvement in mathematical problem-solving accuracy.

Maintains or enhances language capabilities.

Outperforms larger baseline models.

Abstract

Large language models (LLMs) have shown excellent mastering of human language, but still struggle in real-world applications that require mathematical problem-solving. While many strategies and datasets to enhance LLMs' mathematics are developed, it remains a challenge to simultaneously maintain and improve both language and mathematical capabilities in deployed LLM systems.In this work, we tailor the Self-Critique pipeline, which addresses the challenge in the feedback learning stage of LLM alignment. We first train a general Math-Critique model from the LLM itself to provide feedback signals. Then, we sequentially employ rejective fine-tuning and direct preference optimization over the LLM's own generations for data collection. Based on ChatGLM3-32B, we conduct a series of experiments on both academic and our newly created challenging dataset, MathUserEval. Results show that our pipeline significantly enhances the LLM's mathematical problem-solving while still improving its language ability, outperforming LLMs that could be two times larger. Related techniques have been deployed to ChatGLM\footnote{\url{https://chatglm.cn}}, an online serving LLM. Related evaluation dataset and scripts are released at \url{https://github.com/THUDM/ChatGLM-Math}.