# E2-OPSD: Taming Entropy Overshoot in On-Policy Self-Distillation

arXiv: https://arxiv.org/abs/2610.05048 · HTML: https://mlsanity.com/paper/2610.05048/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 43 of its 47 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## Placed in

- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 30 of 43)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [A General Language Assistant as a Laboratory for Alignment](https://mlsanity.com/paper/2112.00861/) (2021)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [Reinforcement learning](https://mlsanity.com/paper/2405.10369/) (2024)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoning](https://mlsanity.com/paper/2502.01100/) (2025)
- [On-Policy Context Distillation for Language Models](https://mlsanity.com/paper/2602.12275/) (2026)
- [Entropy-Aware On-Policy Distillation of Language Models](https://mlsanity.com/paper/2603.07079/) (2026)
- [DistiLLM: Towards Streamlined Distillation for Large Language Models](https://mlsanity.com/paper/2402.03898/) (2024)
- [MiniLLM: On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2306.08543/) (2023)
- [Learning by Distilling Context](https://mlsanity.com/paper/2209.15189/) (2022)
- [Self-Distilled RLVR](https://mlsanity.com/paper/2604.03128/) (2026)
- [Why Does Self-Distillation (Sometimes) Degrade the Reasoning Capability of LLMs?](https://mlsanity.com/paper/2603.24472/) (2026)
- [Self-Distillation Zero: Self-Revision Turns Binary Rewards into Dense Supervision](https://mlsanity.com/paper/2604.12002/) (2026)
- [Rethinking Kullback-Leibler Divergence in Knowledge Distillation for Large Language Models](https://mlsanity.com/paper/2404.02657/) (2024)
- [Rethinking Entropy Interventions in RLVR: An Entropy Change Perspective](https://mlsanity.com/paper/2510.10150/) (2025)
- [RLCSD: Reinforcement Learning with Contrastive On-Policy Self-Distillation](https://mlsanity.com/paper/2606.11709/) (2026)
- [QuestA: Expanding Reasoning Capacity in LLMs via Question Augmentation](https://mlsanity.com/paper/2507.13266/) (2025)
- [Rethinking On-Policy Self-Distillation for Thinking Models](https://mlsanity.com/paper/2607.05184/) (2026)

## Abstract (arXiv)

On-policy self-distillation (OPSD) provides dense token-level supervision without a second model: one network acts as teacher with the reference solution and as student with only the problem. We identify a specific failure mode of this recipe. During training, student token entropy rises past the teacher's and remains elevated, a pattern we call entropy overshoot. We trace it to both sides of distillation. The reference-conditioned teacher is confident along its answer-directed reasoning path, but this confidence transfers poorly to student-generated prefixes, making its supervision overly tied to answer-specific cues rather than reusable reasoning patterns; meanwhile, the forward KL used by OPSD continually diffuses the student's predictive distribution without pulling it back. We introduce E2-OPSD to address both causes. Exemplar-guided teaching replaces the current answer with a retrieved solved neighboring problem, providing transferable reasoning guidance without revealing the destination and better matching student-reachable states. Entropy-aware distillation uses the student-teacher entropy gap to determine the direction and strength of each token's correction. E2-OPSD improves math reasoning by up to 4.3 points in mean@16 over OPSD, while out-of-domain evaluations show gains over the corresponding base models of up to 4.9 points in mean@16 and 5.5 points in pass@8. Despite these gains, E2-OPSD remains simple, requiring no additional forward passes or networks. Code repo: https://github.com/orionfei/E2-OPSD.