The recently released GPT-4 Code Interpreter has demonstrated remarkable
proficiency in solving challenging math problems, primarily attributed to its
ability to seamlessly reason with natural language, generate code, execute
code, and continue reasoning based on the execution output. In this paper, we
present a method to fine-tune open-source language models, enabling them to use
code for modeling and deriving math equations and, consequently, enhancing
their mathematical reasoning abilities. We propose a method of generating novel
and high-quality datasets with math problems and their code-based solutions,
referred to as MathCodeInstruct. Each solution interleaves natural language,
code, and execution results. We also introduce a customized supervised
fine-tuning and inference approach. This approach yields the MathCoder models,
a family of models capable of generating code-based solutions for solving
challenging math problems. Impressively, the MathCoder models achieve
state-of-the-art scores among open-source LLMs on the MATH (45.2%) and GSM8K
(83.9%) datasets, substantially outperforming other open-source alternatives.
Notably, the MathCoder model not only surpasses ChatGPT-3.5 and PaLM-2 on GSM8K
and MATH but also outperforms GPT-4 on the competition-level MATH dataset. The
dataset and models will be released at this https URL

我们提出了一种方法，通过对开源语言模型进行微调，使其能够使用代码进行建模，并推导出数学方程，从而增强其数学推理能力。我们介绍了一种生成包含数学问题和基于代码的解决方案的新颖高质量数据集的方法，称为 MathCodeInstruct。我们还引入了一种定制的有监督微调和推理方法。这种方法产生了 MathCoder 模型，一组能够生成基于代码的解决方案来解决具有挑战性的数学问题的模型。令人印象深刻的是，MathCoder 模型在 MATH（45.2％）和 GSM8K（83.9％）数据集上取得了开源语言模型的最新得分，远远超过其他开源方案。值得注意的是，MathCoder 模型不仅在 GSM8K 和 MATH 上超过了 ChatGPT-3.5 和 PaLM-2，还超过了 GPT-4 在竞争级别的 MATH 数据集上。数据集和模型将在此 URL 发布。