# STEPS: Selective On-Policy Self-Distillation for Reasoning

arXiv: https://arxiv.org/abs/2605.10194 · HTML: https://mlsanity.com/paper/2605.10194/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 28 of its 36 references that are in the map.
- First posted on arXiv 11 May 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, 28 of 28)

- [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)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [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)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [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)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [GLM-5: from Vibe Coding to Agentic Engineering](https://mlsanity.com/paper/2602.15763/) (2026)
- [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)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [MiMo-V2-Flash Technical Report](https://mlsanity.com/paper/2601.02780/) (2026)
- [VinePPO: Refining Credit Assignment in RL Training of LLMs](https://mlsanity.com/paper/2410.01679/) (2024)
- [DistiLLM: Towards Streamlined Distillation for Large Language Models](https://mlsanity.com/paper/2402.03898/) (2024)
- [Self-Distilled RLVR](https://mlsanity.com/paper/2604.03128/) (2026)
- [TIP: Token Importance in On-Policy Distillation](https://mlsanity.com/paper/2604.14084/) (2026)
- [Why Does Self-Distillation (Sometimes) Degrade the Reasoning Capability of LLMs?](https://mlsanity.com/paper/2603.24472/) (2026)
- [The Art of Scaling Reinforcement Learning Compute for LLMs](https://mlsanity.com/paper/2510.13786/) (2025)
- [Privileged Information Distillation for Language Models](https://mlsanity.com/paper/2602.04942/) (2026)
- [Critical Tokens Matter: Token-Level Contrastive Estimation Enhances LLM's Reasoning Capability](https://mlsanity.com/paper/2411.19943/) (2024)
- [Unifying Group-Relative and Self-Distillation Policy Optimization via Sample Routing](https://mlsanity.com/paper/2604.02288/) (2026)
- [Learning Query-Specific Rubrics from Human Preferences for DeepResearch Report Generation](https://mlsanity.com/paper/2602.03619/) (2026)

## Built on by (most cited first, 16 of 16)

- [RLCSD: Reinforcement Learning with Contrastive On-Policy Self-Distillation](https://mlsanity.com/paper/2606.11709/) (2026)
- [CriPO: Enhancing Rubric-based RL via Self-Distillation](https://mlsanity.com/paper/2607.18082/) (2026)
- [SAF-OPD: Stable Advantage Fusion for On-Policy Distillation](https://mlsanity.com/paper/2607.29209/) (2026)
- [Matching Supervision to the Student's Learning Capacity: A Unified Framework for On-Policy Self-Distillation](https://mlsanity.com/paper/2608.08176/) (2026)
- [Restoring the Sweet Spot: Pass-Rate Weighted Self-Distillation for LLM Reasoning](https://mlsanity.com/paper/2605.27765/) (2026)
- [CoRT: Counterfactual Replay for Token-Level Rubric-Guided Policy Optimization](https://mlsanity.com/paper/2607.25659/) (2026)
- [1% of Tokens Can Be Enough: On Gradient Estimation in On-Policy Distillation](https://mlsanity.com/paper/2609.24432/) (2026)
- [On-Policy Distillation for LLM Safety: A Routing Approach to Template-Robust Realignment](https://mlsanity.com/paper/2607.27081/) (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)
- [VISTA: Verifier-Informed Student-to-Teacher Adaptation for On-Policy Self-Distillation](https://mlsanity.com/paper/2608.28306/) (2026)
- [Distillation as Probability Transport: Routed On-Policy Distillation](https://mlsanity.com/paper/2609.08337/) (2026)
- [Instruct, Not Answer: Using Instruction Privileges in On-Policy Context Distillation](https://mlsanity.com/paper/2609.32201/) (2026)
- [Beyond Prompt Count: How Data Shapes Transfer in On-Policy Distillation](https://mlsanity.com/paper/2609.37377/) (2026)
- [AdviSD: Learning to Advise Frontier LLMs via Targeted Multi-Turn Self-Distillation](https://mlsanity.com/paper/2609.38142/) (2026)
- [RELAY: Selective Self-Distillation with Adaptive Hand-off for Rubric-Based Reinforcement Learning](https://mlsanity.com/paper/2610.17623/) (2026)

## Abstract (arXiv)

On-policy self-distillation (OPSD) uses a model as its own teacher under privileged context, providing token-level supervision on the model's own reasoning trajectories. However, persistent all-token guidance can degrade training in our math RL setting. Such guidance may unnecessarily constrain non-critical tokens and reinforce biases induced by privileged information unavailable at inference. Motivated by these risks, we propose STEPS, a selective OPSD framework that controls the location, direction, and duration of distillation. STEPS identifies critical spans in student rollouts, applies forward KL to key spans or reverse KL to error spans, and gradually transitions to pure GRPO after a short distillation phase. Across four models from three families, STEPS improves mean accuracy over GRPO. On Qwen3-8B, it raises average accuracy across four math benchmarks and GPQA-Diamond by an absolute 2.76% with a strong annotator. Using the training policy as its own annotator yields an absolute mean gain of 1.90%, with an estimated 2.7% training-time overhead amortized over 300 steps. Controlled ablations support semantic span selection, class-specific KL directions, and the hand-off to GRPO. Together, these results support brief, targeted self-distillation as an efficient complement to reward-driven reasoning training.