HEAL: Hindsight Entropy-Assisted Learning for Reasoning Distillation

TL;DR

HEAL is a novel framework that enhances reasoning distillation from large models to smaller ones by actively repairing reasoning trajectories and filtering genuine breakthroughs, leading to superior performance.

Contribution

HEAL introduces a new RL-free distillation framework with three modules that improve reasoning transfer by active intervention, filtering, and curriculum evolution.

Findings

HEAL outperforms traditional SFT distillation on multiple benchmarks.

HEAL effectively repairs reasoning trajectories using entropy dynamics.

HEAL's curriculum strategy accelerates reasoning skill transfer.

Abstract

Distilling reasoning capabilities from Large Reasoning Models (LRMs) into smaller models is typically constrained by the limitation 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 rigorous filtering protocol that decouples genuine cognitive breakthroughs from spurious shortcuts; and (3) Progressive Answer-guided Curriculum Evolution (PACE), a three-stage distillation strategy that organizes training from foundational alignment to frontier breakthrough. Extensive experiments on multiple benchmarks demonstrate that HEAL significantly outperforms traditional SFT distillation and other baselines.