# Respecting Self-Uncertainty in On-Policy Self-Distillation for Efficient LLM Reasoning

arXiv: https://arxiv.org/abs/2605.13255 · HTML: https://mlsanity.com/paper/2605.13255/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 25 of its 29 references that are in the map.
- First posted on arXiv 13 May 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, 25 of 25)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [OLMo: Accelerating the Science of Language Models](https://mlsanity.com/paper/2402.00838/) (2024)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [Chain of Draft: Thinking Faster by Writing Less](https://mlsanity.com/paper/2502.18600/) (2025)
- [Entropy-Aware On-Policy Distillation of Language Models](https://mlsanity.com/paper/2603.07079/) (2026)
- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)
- [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)
- [AceReason-Nemotron: Advancing Math and Code Reasoning through Reinforcement Learning](https://mlsanity.com/paper/2505.16400/) (2025)
- [CRISP: Compressed Reasoning via Iterative Self-Policy Distillation](https://mlsanity.com/paper/2603.05433/) (2026)
- [Selective Reflection-Tuning: Student-Selected Data Recycling for LLM Instruction-Tuning](https://mlsanity.com/paper/2402.10110/) (2024)
- [Embarrassingly Simple Self-Distillation Improves Code Generation](https://mlsanity.com/paper/2604.01193/) (2026)
- [GATES: Self-Distillation under Privileged Context with Consensus Gating](https://mlsanity.com/paper/2602.20574/) (2026)
- [Reinforcement-aware Knowledge Distillation for LLM Reasoning](https://mlsanity.com/paper/2602.22495/) (2026)
- [PACED: Distillation and On-Policy Self-Distillation at the Frontier of Student Competence](https://mlsanity.com/paper/2603.11178/) (2026)

## Built on by (most cited first, 23 of 23)

- [RLCSD: Reinforcement Learning with Contrastive On-Policy Self-Distillation](https://mlsanity.com/paper/2606.11709/) (2026)
- [On-Policy Self-Distillation without Any Supervision](https://mlsanity.com/paper/2608.06296/) (2026)
- [Look Ahead Before You Distill: Future Trajectory Validation of Teacher Guidance for Agentic On-Policy Distillation](https://mlsanity.com/paper/2608.01953/) (2026)
- [Mismatch Matters: On-Policy Distillation Beyond Token Agreement](https://mlsanity.com/paper/2608.09836/) (2026)
- [Rethinking Privileged Information in On-Policy Self-Distillation](https://mlsanity.com/paper/2608.18271/) (2026)
- [H2SD: Hybrid Hindsight Self-Distillation](https://mlsanity.com/paper/2607.18955/) (2026)
- [A Formula-Driven Survey and Research Agenda for On-Policy Distillation](https://mlsanity.com/paper/2606.22793/) (2026)
- [DemoPSD: Disagreement-Modulated Policy Self-Distillation](https://mlsanity.com/paper/2607.02502/) (2026)
- [Lightning OPD 2.0: Mitigating Style Bias in Cross-Teacher On-Policy Distillation for Large Reasoning Models](https://mlsanity.com/paper/2607.28449/) (2026)
- [Trust the Right Teacher: Quality-Aware Self-Distillation for GUI Grounding](https://mlsanity.com/paper/2606.18101/) (2026)
- [Matching Supervision to the Student's Learning Capacity: A Unified Framework for On-Policy Self-Distillation](https://mlsanity.com/paper/2608.08176/) (2026)
- [Trust Is Not Enough: Influence Calibration for On-Policy Self-Distillation in Agentic RL](https://mlsanity.com/paper/2608.14945/) (2026)
- [1% of Tokens Can Be Enough: On Gradient Estimation in On-Policy Distillation](https://mlsanity.com/paper/2609.24432/) (2026)
- [Self-Distillation Policy Optimization via Visual Feedback: Bridging Code and Visual Artifacts](https://mlsanity.com/paper/2606.10334/) (2026)
- [Overcoming Scaling Limits in On-Policy Self-Distillation for LLM Reasoning](https://mlsanity.com/paper/2609.37915/) (2026)
- [The Hitchhiker's Guide to Agentic AI: From Foundations to Systems](https://mlsanity.com/paper/2606.24937/) (2026)
- [RP-OPSD: Reasoning-Pivot-Guided On-Policy Self-Distillation for Multilingual Reasoning Transfer](https://mlsanity.com/paper/2608.06347/) (2026)
- [SR-OPSD: Self-Referenced On-Policy Self-Distillation](https://mlsanity.com/paper/2608.09745/) (2026)
- [Aha-Flow Distillation: Flow Markers Matter in LLM Reasoning](https://mlsanity.com/paper/2609.07036/) (2026)
- [UOPD: Uncertainty-Aware Intervention for On-Policy Distillation of Multi-Turn Agents](https://mlsanity.com/paper/2609.34036/) (2026)
- [Reward-Aligned Reweighting for On-Policy Distillation](https://mlsanity.com/paper/2609.35517/) (2026)
- [E2-OPSD: Taming Entropy Overshoot in On-Policy Self-Distillation](https://mlsanity.com/paper/2610.05048/) (2026)
- [Learning from Self-Generated Responses: Reliability--Uncertainty Self-Distillation for Reasoning](https://mlsanity.com/paper/2610.19176/) (2026)

## Abstract (arXiv)

On-policy self-distillation trains a reasoning model on its own rollouts while a teacher, often the same model conditioned on privileged context, provides dense token-level supervision. Existing objectives typically weight the teacher's token-level signal uniformly across a chain-of-thought sequence, despite substantial variation in the entropy of the teacher's predictive distribution. We propose EGRSD (Entropy-Guided Reinforced Self-Distillation), which unifies token-level updates through three signals: a reward-grounded direction, a teacher-student likelihood-ratio magnitude, and the proposed teacher-entropy confidence gate that down-weights high-entropy token positions while maintaining a nonzero lower bound on every token weight. We further introduce CL-EGRSD, a causal-lookahead variant that distinguishes sustained high-entropy spans from transient high-entropy positions whose following context rapidly becomes low entropy. Experiments with Qwen3-4B and Qwen3-8B in thinking mode show that EGRSD and CL-EGRSD advance the accuracy-length frontier among the compared trainable methods.