Which Reasoning Trajectories Teach Students to Reason Better? A Simple Metric of Informative Alignment

TL;DR

This paper introduces the Rank-Surprisal Ratio (RSR), a new metric that effectively assesses the informativeness and alignment of reasoning trajectories to improve student LLM training.

Contribution

The paper proposes RSR, a simple yet effective metric that outperforms existing measures in selecting informative reasoning trajectories for training student models.

Findings

RSR correlates strongly with reasoning performance (average Spearman 0.86).

RSR outperforms existing metrics in trajectory and teacher selection.

RSR is easy to compute and interpret across diverse models and trajectories.

Abstract

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.