Despite recent progress in improving the mathematical reasoning ability of large language models(LLMs), solving competition-level math problems without the use of external tools remains challenging for open-source LLMs. In this work, we introduce the MMIQC dataset, a mixture of processed web data and synthetic question-response pairs, to equip base models with better mathematical reasoning skills. Mistral-7B-MMIQC, the model obtained by fine-tuning Mistral-7B(arXiv:2310.06825) on MMIQC, achieves 36.0\% accuracy on MATH(arXiv:2103.03874), 5.8\% higher than the previous (model size $\sim$7B) SOTA. Our experiments also show that a large part of the improvement attributes to our novel augmentation method IQC(Iterative Question Composing), where we iteratively ask an LLM to compose new questions from the given seed problems and do rejection sampling from another LLM. MMIQC has now been released on https://huggingface.co/datasets/Vivacem/MMIQC.

翻译：尽管近期在提升大型语言模型（LLMs）的数学推理能力方面取得了进展，但对于开源LLMs而言，在不借助外部工具的情况下解决竞赛级数学问题仍具有挑战性。在本工作中，我们引入了MMIQC数据集，该数据集融合了经过处理的网络数据与合成的问答对，旨在为基座模型赋予更强大的数学推理能力。通过在MMIQC上微调Mistral-7B（arXiv:2310.06825）得到的Mistral-7B-MMIQC模型，在MATH（arXiv:2103.03874）基准上实现了36.0%的准确率，较之前（模型规模约7B）的最优结果提升了5.8%。实验进一步表明，性能提升的很大一部分归功于我们提出的新型增强方法——迭代问题组合（IQC），该方法通过迭代方式引导LLM根据给定的种子问题生成新问题，并利用另一LLM进行拒绝采样。目前MMIQC已发布于https://huggingface.co/datasets/Vivacem/MMIQC。