# Internalize the Temperature: On-Policy Self-Distillation as Policy Reheater for Reinforcement Learning

arXiv: https://arxiv.org/abs/2606.00755 · HTML: https://mlsanity.com/paper/2606.00755/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 21 of its 28 references that are in the map.
- First posted on arXiv 30 May 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-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, 21 of 21)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [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)
- [SWIFT:A Scalable lightWeight Infrastructure for Fine-Tuning](https://mlsanity.com/paper/2408.05517/) (2024)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (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)
- [Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes](https://mlsanity.com/paper/2603.25562/) (2026)
- [f-Divergence Minimization for Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/2307.15190/) (2023)
- [Annealing Knowledge Distillation](https://mlsanity.com/paper/2104.07163/) (2021)
- [CRISP: Compressed Reasoning via Iterative Self-Policy Distillation](https://mlsanity.com/paper/2603.05433/) (2026)
- [BAPO: Stabilizing Off-Policy Reinforcement Learning for LLMs via Balanced Policy Optimization with Adaptive Clipping](https://mlsanity.com/paper/2510.18927/) (2025)
- [EDT: Improving Large Language Models' Generation by Entropy-based Dynamic Temperature Sampling](https://mlsanity.com/paper/2403.14541/) (2024)
- [Look Inward to Explore Outward: Learning Temperature Policy from LLM Internal States via Hierarchical RL](https://mlsanity.com/paper/2602.13035/) (2026)
- [On the Role of Temperature Sampling in Test-Time Scaling](https://mlsanity.com/paper/2510.02611/) (2025)
- [Temperature as a Meta-Policy: Adaptive Temperature in LLM Reinforcement Learning](https://mlsanity.com/paper/2602.11779/) (2026)

## Built on by (most cited first, 1 of 1)

- [Cool the Sampler, Not the Learner: Sampling Temperature Moves the Staleness Cliff of Importance-Corrected GRPO](https://mlsanity.com/paper/2609.36953/) (2026)

## Abstract (arXiv)

Reinforcement learning from verifiable rewards improves the reasoning ability of large language models, but often suffers from entropy collapse, in which increasingly concentrated policies reduce rollout diversity and useful learning signals. Existing remedies either constrain the RL objective (e.g., entropy regularization) or adjust sampling temperature during rollout collection, but these interventions remain external to the model parameters. We propose Temperature-Scaled On-Policy Self-Distillation (TS-OPSD), a lightweight policy reheating method that internalizes the exploratory effect of temperature into model parameters. Starting from an entropy-collapsed RL checkpoint, TS-OPSD constructs a self-teacher by applying high-temperature scaling to the model's own logits, then distills the resulting smoother distribution back into the student. This policy reheating requires no external teacher, privileged data, or additional inference cost. Experiments on Qwen3-4B-Base and Qwen3-8B-Base show that policy reheating yields a stronger initialization for continued RL than both standard continued RL and rollout-level temperature reheating. Further analyses show that TS-OPSD mainly reduces output sharpness while preserving intermediate representations, top candidate sets, and reasoning capability. These results suggest that entropy restoration can serve as a simple post-collapse intervention for extending reasoning-oriented RL.