Which Reasoning Trajectories Teach Students to Reason Better? A Simple Metric of Informative Alignment
Authors: name: Yuming Yang, name: Mingyoung Lai, name: Wanxu Zhao, name: Xiaoran Fan, name: Zhiheng Xi, name: Mingqi Wu, name: Chiyue Huang, name: Jun Zhao, name: Haijun Lv, name: Jian Tong, name: Yunhua Zhou, name: Yicheng Zou, name: Qipeng Guo, name: Tao Gui, name: Qi Zhang, name: Xuanjing Huang
Organization: Fudan University

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 closely align with the 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 combine low absolute probability with relatively high-ranked tokens under the student model, balancing learning signal strength and behavioral alignment. 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 performance (average Spearman 0.86), outperforming existing metrics. We further demonstrate its practical utility in both trajectory selection and teacher selection.