用高效方法生成大量高难度数学题,提升模型推理能力。
ScaleDiff: Scaling Difficult Problems for Advanced Mathematical Reasoning
- 通过自适应思维模型单次前向传播筛选难题,降低计算成本。
- 训练专用生成器批量产出难题,使Qwen2.5-Math模型准确率达65.9%。
- 无需昂贵大模型教师,小模型也能学出强推理能力,适合资源有限者。
大型推理模型在复杂问题求解中表现优异,常得益于训练于高难度数学题。现有方法通过提示词生成题目,但存在计算成本高、提示复杂、题目难度有限等问题。为此,我们提出ScaleDiff,一种简单高效的难题规模化生成管道。该方法仅用一次前向传播,通过自适应思维模型识别难题,并自动切换“思考”与“不思考”模式。随后,基于筛选出的难题数据训练专用生成器DiffGen-8B,可大规模生成新难题,避免复杂提示及高昂API开销。将Qwen2.5-Math-7B-Instruct在ScaleDiff-Math数据集上微调后,相比原数据集性能提升11.3%,在AIME'24、AIME'25、HMMT-Feb'25、BRUMO'25和MATH500上平均准确率达65.9%,超越OpenThinker3等先进模型。该效果使用成本更低的Qwen3-8B作为教师模型实现,证明该管道可高效传递高级推理能力,且模型性能随难题数量增加呈明显上升趋势。代码已开源。
原文摘要 · Abstract (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.
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