用AI自动生成高难度数学题，提升模型推理能力
SAND-Math: Using LLMs to Generate Novel, Difficult and Useful Mathematics Questions and Answers
- 从零生成数学题，再通过难度提升机制增强复杂度
- 在AIME25上比次优数据集高17.85分，准确率提升至49.23%
- 适合训练数学推理大模型的研究者和开发者
大型语言模型在数学推理方面的需求持续增长，但性能受限于高质量复杂题目的稀缺。我们提出SAND-Math（合成新颖且困难的数学问题与解答），通过从零生成高质量题目，并引入新提出的‘难度爬升’步骤系统性提升题目复杂度。实验表明：(1) 用仅500样本的SAND-Math数据集微调强基线模型，在AIME25基准上比现有最优合成数据集高出17.85个百分点；(2) 经难度爬升后，平均题目难度从5.02升至5.98，对应AIME25准确率从46.38%提升至49.23%。完整生成流程、最终数据集及微调模型构成一个实用且可扩展的数学推理大模型构建工具包。
原文摘要 · Abstract (English)
The demand for Large Language Models (LLMs) at multiple scales, capable of sophisticated and sound mathematical reasoning, continues to grow. However, the development of performant mathematical LLMs is often bottlenecked by the scarcity of useful training data containing problems with significant complexity. We introduce \textbf{SAND-Math} (\textbf{S}ynthetic \textbf{A}ugmented \textbf{N}ovel and \textbf{D}ifficult Mathematics problems and solutions), a pipeline that addresses this by first synthesizing high-quality problems from scratch and then systematically elevating their complexity via a our newly proposed \textbf{Difficulty Hiking} step. We demonstrate the effectiveness of our approach through two key findings: \textbf{(1)} Augmenting a strong post-training baseline with a small 500-sample SAND-Math dataset significantly boosts performance, outperforming the next-best synthetic dataset by $\uparrow$ 17.85 absolute points on AIME25 benchmark. \textbf{(2)} In a dedicated ablation study, we show the effectiveness of our Difficulty Hiking process in increasing average problem difficulty from 5.02 to 5.98. This step consequently lifts AIME25 results from 46.38\% to 49.23\%. The full generation pipeline, final dataset, and a fine-tuned model form a practical and scalable toolkit for building capable and efficient mathematical reasoning LLMs.
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