# One Symptom, Three Levers: A Critical Review of On-Policy Self-Distillation

arXiv: https://arxiv.org/abs/2608.25936 · HTML: https://mlsanity.com/paper/2608.25936/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 56 of its 62 references that are in the map.
- First posted on arXiv 26 Aug 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)
- 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 56)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Born Again Neural Networks](https://mlsanity.com/paper/1805.04770/) (2018)
- [RMA: Rapid Motor Adaptation for Legged Robots](https://mlsanity.com/paper/2107.04034/) (2021)
- [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)
- [Policy Distillation](https://mlsanity.com/paper/1511.06295/) (2015)
- [Learning by Cheating](https://mlsanity.com/paper/1912.12294/) (2019)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [Unifying distillation and privileged information](https://mlsanity.com/paper/1511.03643/) (2015)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [RL's Razor: Why Online Reinforcement Learning Forgets Less](https://mlsanity.com/paper/2509.04259/) (2025)
- [Entropy-Aware On-Policy Distillation of Language Models](https://mlsanity.com/paper/2603.07079/) (2026)
- [Self-Distillation Amplifies Regularization in Hilbert Space](https://mlsanity.com/paper/2002.05715/) (2020)
- [DistiLLM: Towards Streamlined Distillation for Large Language Models](https://mlsanity.com/paper/2402.03898/) (2024)
- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)
- [Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Data](https://mlsanity.com/paper/2404.01413/) (2024)
- [OctoThinker: Mid-training Incentivizes Reinforcement Learning Scaling](https://mlsanity.com/paper/2506.20512/) (2025)
- [Why Does Self-Distillation (Sometimes) Degrade the Reasoning Capability of LLMs?](https://mlsanity.com/paper/2603.24472/) (2026)
- [A Sober Look at Progress in Language Model Reasoning: Pitfalls and Paths to Reproducibility](https://mlsanity.com/paper/2504.07086/) (2025)
- [Reasoning or Memorization? Unreliable Results of Reinforcement Learning Due to Data Contamination](https://mlsanity.com/paper/2507.10532/) (2025)
- [MOPD: Multi-Teacher On-Policy Distillation for Capability Integration in LLM Post-Training](https://mlsanity.com/paper/2606.30406/) (2026)

## Abstract (arXiv)

On-policy distillation trains a language model on its own generations while a teacher scores them token by token. It combines the dense supervision of imitation learning with the on-policy sampling of reinforcement learning. But it requires a second, larger model to act as teacher. On-Policy Self-Distillation (OPSD) removes that cost. The teacher is the model itself, conditioned on privileged information the student will not have at test time, such as a reference solution, a plan, or environment feedback. The teacher is no stronger than the student, only better informed. Early results were promising, with accuracy comparable to reinforcement learning at a fraction of the generated tokens. But the same asymmetry that produces the signal also biases it. One failure mode now dominates the field: collapse, the progressive narrowing of the set of reasoning paths the model can produce. Collapse is not specific to OPSD, though privileged information aggravates it. This review treats collapse as a symptom governed by three levers: (i) where the signal is applied, that is, how tokens are weighted; (ii) what the teacher is shown, that is, the nature of the privileged information; and (iii) when the signal changes, that is, the teacher's dynamics and the decay of guidance. We restrict our scope to mathematical reasoning, where the method originated and where its failure modes are best documented. We report no new experiments. The contribution is structural: a shared vocabulary for phenomena named differently across papers, and a clear line between what is settled and what is still disputed.