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

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 (e.g., Llama-2) are finetuned on the augmented dataset to get the resulting models, MuMath-Code (µ-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: https://github.com/ youweihao-tal/MuMath-Code.