Long chain-of-thought (CoT) trajectories provide rich supervision signals for distilling reasoning from teacher to student LLMs. However, both prior work and our experiments show that trajectories from stronger teachers do not necessarily yield better students, highlighting the importance of data-student suitability in distillation. Existing methods assess suitability primarily through student likelihood, favoring trajectories that align closely with the student model's current behavior but overlooking more informative ones. Addressing this, we propose Rank-Surprisal Ratio (RSR), a simple metric that captures both alignment and informativeness to assess the suitability of a reasoning trajectory. RSR is motivated by the observation that effective trajectories typically balance learning signal strength and behavioral alignment by combining low absolute probability with relatively high-ranked tokens under the student model. Concretely, RSR is defined as the ratio of a trajectory's average token-wise rank to its average negative log-likelihood, and is straightforward to compute and interpret. Across five student models and reasoning trajectories from 11 diverse teachers, RSR strongly correlates with post-training reasoning performance (average Spearman 0.86), consistently outperforming existing metrics. We further demonstrate its practical utility in both trajectory selection and teacher selection.

翻译：长链思维（CoT）轨迹为从教师大语言模型向学生大语言模型蒸馏推理能力提供了丰富的监督信号。然而，先前的研究以及我们的实验均表明，来自更强教师的轨迹并不一定能培养出更优秀的学生，这突显了数据与学生模型适配性在蒸馏过程中的重要性。现有方法主要通过学生模型的似然度来评估适配性，倾向于选择与学生模型当前行为高度对齐的轨迹，但可能忽略了更具信息量的轨迹。针对这一问题，我们提出了秩-惊异比（Rank-Surprisal Ratio, RSR），这是一个同时捕捉对齐性和信息量的简单度量，用于评估推理轨迹的适配性。RSR的提出基于一个观察：有效的推理轨迹通常能平衡学习信号的强度与行为对齐，其特点是在学生模型下，轨迹的平均绝对概率较低，但其构成令牌的相对排名却较高。具体而言，RSR定义为轨迹的平均令牌级排名与其平均负对数似然之比，计算和解释都较为直接。在涵盖五个学生模型和来自11位不同教师的推理轨迹的实验中，RSR与训练后的推理性能表现出强相关性（平均斯皮尔曼相关系数为0.86），并始终优于现有度量方法。我们进一步展示了RSR在轨迹选择和教师选择两个实际应用场景中的效用。