HEAL: Hindsight Entropy-Assisted Learning for Reasoning Distillation

arXiv:2603.10359v2 Announce Type: replace Abstract: Distilling reasoning capabilities from Large Reasoning Models (LRMs) into smaller models is typically constrained by the limitations of rejection sampling.

Standard methods treat the teacher as a static filter, discarding complex "corner-case" problems where the teacher fails to explore valid solutions independently, thereby creating an artificial "Teacher Ceiling" for the student. In this work, we propose Hindsight Entropy-Assisted Learning (HEAL), an RL-free framework designed to bridge this reasoning gap.

Drawing on the educational theory of the Zone of Proximal Development (ZPD), HEAL synergizes three core modules: (1) Guided Entropy-Assisted Repair (GEAR), an active intervention mechanism that detects critical reasoning breakpoints via entropy dynamics and injects targeted hindsight hints to repair broken trajectories; (2) Perplexity-Uncertainty Ratio Estimator (PURE), a ratio-based filtering heuristic that reduces high-anomaly shortcut-like rationales; and (3) Progressive Answer-guided Curriculum Evolution (PACE), a three-stage distillation strategy that organizes training from foundational alignment to hard-case adaptation.

Extensive experiments on multiple benchmarks demonstrate that HEAL significantly outperforms traditional SFT distillation and other baselines.