MetaMath：为大型语言模型自动生成数学问题

摘要

大型语言模型（LLMs）推动了自然语言理解的极限，并展现出出色的问题解决能力。尽管取得了巨大成功，大多数现有的开源LLMs（如LLaMA-2）在解决数学问题方面仍然远未令人满意，这是由于复杂的推理过程。为了弥补这一差距，我们提出了MetaMath，这是一个专门用于数学推理的微调语言模型。具体而言，我们通过从多个角度重写问题来引导数学问题，而无需额外知识，从而产生了一个名为{MetaMathQA}的新数据集。然后我们在MetaMathQA上对LLaMA-2模型进行微调。在两个流行的数学推理基准测试（即GSM8K和MATH）上的实验结果表明，MetaMath在性能上明显优于一系列开源LLMs。我们的MetaMath-7B模型在GSM8K上达到了66.4%，在MATH上达到了19.4%，超过了相同规模的最先进模型11.5%和8.7%。特别地，{MetaMath-70B}在{GSM8K}上实现了82.3%的准确率，略优于{GPT-3.5-Turbo}。我们发布了{MetaMathQA}数据集，以及不同模型规模的{MetaMath}模型和训练代码，供公众使用。

English

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 problem due to the complex reasoning procedures. To bridge this gap, we propose MetaMath, a fine-tuned language model that specializes in mathematical reasoning. Specifically, we start by bootstrapping mathematical questions by rewriting the question from multiple perspectives without extra knowledge, which results in a new dataset called {MetaMathQA}. Then we fine-tune 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 66.4% on GSM8K and 19.4% 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.

MetaMath：为大型语言模型自动生成数学问题

MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models

摘要

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