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The researchers proposed an Optimal Path Selection (OPD) method based on data selection, aimed at improving the training efficiency of large language models. This method uses only 8 difficult samples to enable student models with parameters between 1.5B and 7B to reach the baseline performance level on a 17K dataset. The analysis showed that the effectiveness of this strategy is not driven by high token entropy, but rather by the fact that difficult samples naturally generate longer CoT paths. These long CoT paths help students maintain alignment with the teacher during long-term reasoning processes and learn key thinking patterns such as reflection. Experimental verification demonstrated that this method can even train using “unsolvable” samples that completely exceed the capabilities of the teacher model, and it is effective for all sampled samples in one-shot settings.
本文提出一种基于数据选择的上策蒸馏（OPD）方法，仅使用 8 个困难样本即可使 1.5B 至 7B 参数量学生模型达到 17K 数据集基线的性能。研究首先发现 1-shot OPD 在所有采样样本上均有效，且困难样本能带来更优的性能提升；其次分析表明，学生模型的改进并非由高 token 熵驱动，而是由困难问题自然生成的更长思维链（CoT）路径驱动。长 CoT 有助于在长期推理中保持与教师的对齐并学习反思等关键思维模式。基于此，该方法仅选择困难样本进行训练，甚至能利用完全超出教师能力的“无解”样本。实验验证了该数据选择策略的有效性。