少即是多令牌：通过难度感知思维链蒸馏实现高效数学推理
Less is More Tokens: Efficient Math Reasoning via Difficulty-Aware Chain-of-Thought Distillation
AI总结：
本研究提出难度感知思维链蒸馏框架，通过含难度匹配长度思维链的数据后训练，无需修改架构即可让模型动态调整推理深度，结合SFT与DPO实现简单题精简推理、难题保深度，缩短输出同时维持或提升性能。
摘要：
思维链推理虽然功能强大，但对于较简单的问题会产生不必要的冗长输出。我们提出了一种难度感知推理框架，教导模型根据问题复杂度动态调整推理深度。值得注意的是，我们证明无需任何架构修改即可赋予模型此类动态推理路径；我们仅需在精心策划的、包含与问题难度长度成正比的思维链轨迹的数据上进行后训练。我们的分析表明，通过监督微调（SFT）进行后训练主要捕捉推理长度和格式等模式，而直接偏好优化（DPO）则保持推理准确性，二者结合可缩短长度并维持或提升性能。定量指标和定性评估均证实，模型能够学会“按比例思考”，对简单问题进行最少推理，同时对复杂问题保持推理深度。
英文摘要：
Chain-of-thought reasoning, while powerful, can produce unnecessarily verbose output for simpler problems. We present a framework for difficulty-aware reasoning that teaches models to dynamically adjust reasoning depth based on problem complexity. Remarkably, we show that models can be endowed with such dynamic inference pathways without any architectural modifications; we simply post-train on data that is carefully curated to include chain-of-thought traces that are proportional in length to problem difficulty. Our analysis reveals that post-training via supervised fine-tuning (SFT) primarily captures patterns like reasoning length and format, while direct preference optimization (DPO) preserves reasoning accuracy, with their combination reducing length and maintaining or improving performance. Both quantitative metrics and qualitative assessments confirm that models can learn to "think proportionally", reasoning minimally on simple problems while maintaining depth for complex ones.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
