LARK: Learnability-Grounded Trajectory Selection for Efficient Reasoning Distillation 文章

arXiv:2605.30651v1 Announce Type: cross Abstract: We study trajectory selection for reasoning distillation, where teacher-generated reasoning trajectories are selectively used as supervision for a student model. Existing methods rely on heuristics such as trajectory quality or model confidence, but they often overlook whether a trajectory is learnable by the student. In this paper, we present LARK, a learnability-grounded method for reasoning trajectory selection. LARK selects trajectories that the student can learn efficiently while preserving the generalization of the full training distribution. At the core of LARK is a learnability factor $\rho$, which characterizes the rate at which the student's training loss decreases. To estimate this rate efficiently and maintain generalization, we introduce a learnability proxy and a $\chi^2$-regularized selection policy that balances learnability and distributional coverage, both with strong theoretical guarantees on their estimation error.