HEAL: Hindsight Entropy-Assisted Learning for Reasoning Distillation
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arXiv
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| Autores principales: | , , , , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910048646594560 |
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| author | Zhang, Wenjing Yan, Jiangze Huang, Jieyun Shen, Yi Shi, Shuming Chen, Ping Wang, Ning Liu, Zhaoxiang Wang, Kai Lian, Shiguo |
| author_facet | Zhang, Wenjing Yan, Jiangze Huang, Jieyun Shen, Yi Shi, Shuming Chen, Ping Wang, Ning Liu, Zhaoxiang Wang, Kai Lian, Shiguo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10359 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | HEAL: Hindsight Entropy-Assisted Learning for Reasoning Distillation Zhang, Wenjing Yan, Jiangze Huang, Jieyun Shen, Yi Shi, Shuming Chen, Ping Wang, Ning Liu, Zhaoxiang Wang, Kai Lian, Shiguo Artificial Intelligence Machine Learning 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. |
| title | HEAL: Hindsight Entropy-Assisted Learning for Reasoning Distillation |
| topic | Artificial Intelligence Machine Learning |
| url | https://arxiv.org/abs/2603.10359 |