Despite the advancements in large language models (LLMs) for mathematical reasoning, solving competition-level math problems remains a significant challenge, especially for open-source LLMs without external tools. We introduce the MMIQC dataset, comprising a mixture of processed web data and synthetic question-response pairs, aimed at enhancing the mathematical reasoning capabilities of base language models. Models fine-tuned on MMIQC consistently surpass their counterparts in performance on the MATH benchmark across various model sizes. Notably, Qwen-72B-MMIQC achieves a 45.0% accuracy, exceeding the previous open-source state-of-the-art by 8.2% and outperforming the initial version GPT-4 released in 2023. Extensive evaluation results on Hungarian high school finals suggest that such improvement can generalize to unseen data. Our ablation study on MMIQC reveals that a large part of the improvement can be attributed to our novel augmentation method, Iterative Question Composing (IQC), which involves iteratively composing new questions from seed problems using an LLM and applying rejection sampling through another LLM. The MMIQC dataset is available on the HuggingFace hub at https://huggingface.co/datasets/Vivacem/MMIQC. Our code is available at https://github.com/iiis-ai/IterativeQuestionComposing.

翻译：尽管大型语言模型（LLMs）在数学推理方面取得了进展，但解决竞赛级数学问题仍然是一项重大挑战，尤其是对于未使用外部工具的开源LLMs。我们引入了MMIQC数据集，该数据集包含处理后的网络数据与合成问答对的混合，旨在提升基础语言模型的数学推理能力。基于MMIQC微调的模型在MATH基准测试中，在不同模型规模下均持续超越其对应模型。值得注意的是，Qwen-72B-MMIQC实现了45.0%的准确率，比此前开源最佳模型高出8.2%，并优于2023年发布的初始版GPT-4。在匈牙利高中毕业考试上的广泛评估结果表明，此类改进可泛化至未见数据。我们对MMIQC的消融研究发现，大部分改进归功于我们提出的新型增强方法——迭代式问题组合（IQC），该方法通过一个LLM从种子问题迭代式地组合新问题，并利用另一个LLM进行拒绝采样。MMIQC数据集可在HuggingFace平台获取：https://huggingface.co/datasets/Vivacem/MMIQC。我们的代码已开源：https://github.com/iiis-ai/IterativeQuestionComposing。