MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models

Longhui Yu, Weisen Jiang, Han Shi, Jincheng YU, Zhengying Liu, Yu Zhang, James Kwok, Zhenguo Li, Adrian Weller, Weiyang Liu

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Keywords: Large Language Model; Mathematical Reasoning

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TL;DR: Bootstrap the mathematical questions in multiple perspectives and then finetune a powerful LLM

Abstract: Large language models (LLMs) have pushed the limits of natural language understanding and exhibited excellent problem-solving ability. Despite the great success, most existing open-source LLMs (\eg, LLaMA-2) are still far away from satisfactory for solving mathematical problems due to the complex reasoning procedures. To bridge this gap, we propose \emph{MetaMath}, a finetuned language model that specializes in mathematical reasoning. Specifically, we start by bootstrapping mathematical questions by rewriting the question from multiple perspectives, which results in a new dataset called MetaMathQA. Then we finetune the LLaMA-2 models on MetaMathQA. Experimental results on two popular benchmarks (\ie, GSM8K and MATH) for mathematical reasoning demonstrate that MetaMath outperforms a suite of open-source LLMs by a significant margin. Our MetaMath-7B model achieves $66.5\%$ on GSM8K and $19.8\%$ on MATH, exceeding the state-of-the-art models of the same size by $11.5\%$ and $8.7\%$. Particularly, MetaMath-70B achieves an accuracy of $82.3\%$ on GSM8K, slightly better than GPT-3.5-Turbo. We release the MetaMathQA dataset, the MetaMath models with different model sizes and the training code for public use.

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Primary Area: representation learning for computer vision, audio, language, and other modalities

Submission Number: 4520