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HEAL: Hindsight Entropy-Assisted Learning for Reasoning Distillation

arXiv:2603.10359v1 Announce Type: new 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 bre

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Wenjing Zhang, Jiangze Yan, Jieyun Huang, Yi Shen, Shuming Shi, Ping Chen, Ning Wang, Zhaoxiang Liu, Kai Wang, Shiguo Lian · · 1 min read · 17 views
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arXiv:2603.10359v1 Announce Type: new 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.

Executive Summary

This study, titled HEAL: Hindsight Entropy-Assisted Learning for Reasoning Distillation, proposes a novel framework for distilling reasoning capabilities from Large Reasoning Models (LRMs) into smaller models. The authors tackle the limitation of rejection sampling by introducing three core modules: Guided Entropy-Assisted Repair (GEAR), Perplexity-Uncertainty Ratio Estimator (PURE), and Progressive Answer-guided Curriculum Evolution (PACE). Through extensive experiments on multiple benchmarks, the study demonstrates that HEAL outperforms traditional SFT distillation and other baselines. The proposed framework has significant implications for the development of more efficient and effective reasoning systems. While the study makes substantial contributions to the field, its practical applications and scalability remain to be explored. The research has the potential to revolutionize the way we approach reasoning distillation and has far-reaching implications for artificial intelligence and machine learning.

Key Points

  • ▸ HEAL proposes a novel framework for distilling reasoning capabilities from LRMs into smaller models.
  • ▸ The framework consists of three core modules: GEAR, PURE, and PACE.
  • ▸ HEAL outperforms traditional SFT distillation and other baselines on multiple benchmarks.

Merits

Strength in Addressing the 'Teacher Ceiling' Problem

HEAL effectively tackles the limitation of rejection sampling by introducing a novel framework that synergizes three core modules to address the 'Teacher Ceiling' problem.

Efficient and Effective Reasoning System

The proposed framework has the potential to develop more efficient and effective reasoning systems by distilling reasoning capabilities from LRMs into smaller models.

Demerits

Scalability and Practical Applications

The study's practical applications and scalability remain to be explored, limiting the framework's immediate impact and adoption.

Dependence on Complex Mathematical Frameworks

The framework's reliance on complex mathematical concepts, such as entropy dynamics and perplexity-uncertainty ratio estimation, may create barriers to adoption and understanding.

Expert Commentary

The HEAL framework represents a significant advancement in the field of reasoning distillation. By introducing a novel framework that synergizes three core modules, the authors provide a more efficient and effective approach to distilling reasoning capabilities from LRMs into smaller models. However, the study's practical applications and scalability remain to be explored, and the framework's reliance on complex mathematical concepts may create barriers to adoption and understanding. Nevertheless, the study's findings have far-reaching implications for artificial intelligence and machine learning, and its potential to revolutionize the development of more efficient and effective reasoning systems is substantial.

Recommendations

  • ✓ Future research should focus on exploring the practical applications and scalability of the HEAL framework.
  • ✓ The development of simplified or more accessible versions of the framework may help to increase its adoption and understanding.

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