MuMath-Code: Combining Tool-Use Large Language Models with Multi-perspective Data Augmentation for Mathematical Reasoning

• URL: http://arxiv.org/abs/2405.07551v1
• Date: Mon, 13 May 2024 08:32:19 GMT
• Title: MuMath-Code: Combining Tool-Use Large Language Models with Multi-perspective Data Augmentation for Mathematical Reasoning
• Authors: Shuo Yin, Weihao You, Zhilong Ji, Guoqiang Zhong, Jinfeng Bai,
• Abstract summary: This work includes new math questions via multi-perspective data augmenting methods and then synthesize code-nested solutions to them. Open Large Language Models (LLMs) that integrate with external Python interpreters have significantly enhanced mathematical reasoning capabilities. We propose a two-stage training strategy: In Stage-1, we finetune Llama-2 on pure CoT data to get an intermediate model, which then is trained on the code-nested data in Stage-2 to get the resulting MuMath-Code.
• Score: 11.426127461122908
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The tool-use Large Language Models (LLMs) that integrate with external Python interpreters have significantly enhanced mathematical reasoning capabilities for open-source LLMs, while tool-free methods chose another track: augmenting math reasoning data. However, a great method to integrate the above two research paths and combine their advantages remains to be explored. In this work, we firstly include new math questions via multi-perspective data augmenting methods and then synthesize code-nested solutions to them. The open LLMs (i.e., Llama-2) are finetuned on the augmented dataset to get the resulting models, MuMath-Code ($\mu$-Math-Code). During the inference phase, our MuMath-Code generates code and interacts with the external python interpreter to get the execution results. Therefore, MuMath-Code leverages the advantages of both the external tool and data augmentation. To fully leverage the advantages of our augmented data, we propose a two-stage training strategy: In Stage-1, we finetune Llama-2 on pure CoT data to get an intermediate model, which then is trained on the code-nested data in Stage-2 to get the resulting MuMath-Code. Our MuMath-Code-7B achieves 83.8 on GSM8K and 52.4 on MATH, while MuMath-Code-70B model achieves new state-of-the-art performance among open methods -- achieving 90.7% on GSM8K and 55.1% on MATH. Extensive experiments validate the combination of tool use and data augmentation, as well as our two-stage training strategy. We release the proposed dataset along with the associated code for public use.

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