Failure Profiling and Reachable Trajectory Selection for Reasoning Distillation

Yijun Zhu, Jianxin Wang, Chengchao Shen

Training smaller language models on reasoning solutions generated by a larger teacher model is the prevailing approach for transferring mathematical reasoning capabilities. However, the student tends to overfit the output distribution of the teacher and generalizes poorly when its own behavior at inference time deviates from the training data. Recent methods attempt to bridge this gap by incorporating error data, yet the corrective trajectories still reflect the reasoning patterns of the teacher, which the student cannot reliably reproduce, leaving the distribution mismatch largely unresolved. We propose a method, Failure Profiling and Reachable Trajectory Selection (FPRT), built on the insight that effective training data should be jointly determined by what the student fails on and what it can realistically learn. Our method first profiles the failure behavior of the student on each problem through repeated sampling, characterizing it in terms of error rate and error consistency to reveal qualitatively distinct failure modes. Each mode demands a fundamentally different training signal. The diagnosed mode then guides candidate generation from the teacher via distinct prompting…