ScaleDiff：为高级数学推理扩展难题规模

ScaleDiff: Scaling Difficult Problems for Advanced Mathematical Reasoning

September 25, 2025

作者: Qizhi Pei, Zhuoshi Pan, Honglin Lin, Xin Gao, Yu Li, Zinan Tang, Conghui He, Rui Yan, Lijun Wu

cs.AI

摘要

大规模推理模型（LRMs）在解决复杂问题方面展现了卓越的能力，通常得益于在具有挑战性的数学问题上的训练，这些问题能够激发复杂的推理过程。近期研究探索了通过提示专有模型或大规模开源模型，从种子数据或内在数学概念中自动合成数学问题的方法。然而，由于高昂的计算/API成本、提示的复杂性以及生成问题难度有限，这些方法的扩展仍面临挑战。为克服这些限制，我们提出了ScaleDiff，一个简单而有效的流程，旨在规模化创建高难度问题。我们利用自适应思维模型，仅需一次前向传播即可高效地从现有数据集中识别出难题，该模型能够感知问题难度并自动在“思考”与“非思考”模式间切换。随后，我们在这些筛选出的难题数据上训练了一个专门的难题生成器（DiffGen-8B），它能够大规模生成新的难题，无需复杂的逐实例提示及其伴随的高昂API成本。在ScaleDiff-Math数据集上微调Qwen2.5-Math-7B-Instruct，相比原始数据集实现了11.3%的性能显著提升，并在AIME'24、AIME'25、HMMT-Feb'25、BRUMO'25和MATH500上取得了65.9%的平均准确率，超越了近期如OpenThinker3等强大的LRMs。值得注意的是，这一性能是通过成本效益高的Qwen3-8B模型作为教师实现的，表明我们的流程能够有效转移高级推理能力，而无需依赖更大、更昂贵的教师模型。此外，我们观察到随着难题数量的增加，模型在困难基准测试上的性能呈现出明显的扩展现象。代码见：https://github.com/QizhiPei/ScaleDiff。

English

Large Reasoning Models (LRMs) have shown impressive capabilities in complex problem-solving, often benefiting from training on difficult mathematical problems that stimulate intricate reasoning. Recent efforts have explored automated synthesis of mathematical problems by prompting proprietary models or large-scale open-source models from seed data or inherent mathematical concepts. However, scaling up these methods remains challenging due to their high computational/API cost, complexity of prompting, and limited difficulty level of the generated problems. To overcome these limitations, we propose ScaleDiff, a simple yet effective pipeline designed to scale the creation of difficult problems. We efficiently identify difficult problems from existing datasets with only a single forward pass using an adaptive thinking model, which can perceive problem difficulty and automatically switch between "Thinking" and "NoThinking" modes. We then train a specialized difficult problem generator (DiffGen-8B) on this filtered difficult data, which can produce new difficult problems in large scale, eliminating the need for complex, per-instance prompting and its associated high API costs. Fine-tuning Qwen2.5-Math-7B-Instruct on the ScaleDiff-Math dataset yields a substantial performance increase of 11.3% compared to the original dataset and achieves a 65.9% average accuracy on AIME'24, AIME'25, HMMT-Feb'25, BRUMO'25, and MATH500, outperforming recent strong LRMs like OpenThinker3. Notably, this performance is achieved using the cost-efficient Qwen3-8B model as a teacher, demonstrating that our pipeline can effectively transfer advanced reasoning capabilities without relying on larger, more expensive teacher models. Furthermore, we observe a clear scaling phenomenon in model performance on difficult benchmarks as the quantity of difficult problems increases. Code: https://github.com/QizhiPei/ScaleDiff.