# Learning to Foresee: Unveiling the Unlocking Efficiency of On-Policy Distillation

arXiv: https://arxiv.org/abs/2605.11739 · HTML: https://mlsanity.com/paper/2605.11739/

## Key facts

- Cited by 19 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 39 of its 52 references that are in the map.
- First posted on arXiv 12 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, 30 of 39)

- [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)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Instruction Tuning for Large Language Models: A Survey](https://mlsanity.com/paper/2308.10792/) (2023)
- [Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Space](https://mlsanity.com/paper/2203.14680/) (2022)
- [Dissecting Recall of Factual Associations in Auto-Regressive Language Models](https://mlsanity.com/paper/2304.14767/) (2023)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Layer by Layer: Uncovering Hidden Representations in Language Models](https://mlsanity.com/paper/2502.02013/) (2025)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models](https://mlsanity.com/paper/2505.24864/) (2025)
- [MiMo-V2-Flash Technical Report](https://mlsanity.com/paper/2601.02780/) (2026)
- [Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation](https://mlsanity.com/paper/2602.12125/) (2026)
- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)
- [Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes](https://mlsanity.com/paper/2603.25562/) (2026)
- [TIP: Token Importance in On-Policy Distillation](https://mlsanity.com/paper/2604.14084/) (2026)
- [The Art of Scaling Reinforcement Learning Compute for LLMs](https://mlsanity.com/paper/2510.13786/) (2025)
- [JustRL: Scaling a 1.5B LLM with a Simple RL Recipe](https://mlsanity.com/paper/2512.16649/) (2025)
- [Stabilizing Reinforcement Learning with LLMs: Formulation and Practices](https://mlsanity.com/paper/2512.01374/) (2025)

## Built on by (most cited first, 19 of 19)

- [Rethinking On-Policy Distillation of Large Language Models II: One Training Example](https://mlsanity.com/paper/2609.04172/) (2026)
- [On the Geometry of On-Policy Distillation](https://mlsanity.com/paper/2606.07082/) (2026)
- [Are Full Rollouts Necessary for On-Policy Distillation?](https://mlsanity.com/paper/2605.31490/) (2026)
- [H-OPD: Confidence Aware Heterogeneous Multi-Teacher Multimodal On-policy Distillation](https://mlsanity.com/paper/2607.02592/) (2026)
- [SAF-OPD: Stable Advantage Fusion for On-Policy Distillation](https://mlsanity.com/paper/2607.29209/) (2026)
- [Towards Understanding On-Policy Distillation through the Lens of Test-Time Scaling](https://mlsanity.com/paper/2608.11829/) (2026)
- [The Physics of Multi-Turn Long-Horizon Planning: From Pre-training to Post-training via Single- and Multi-Teacher On-Policy Agentic Distillation](https://mlsanity.com/paper/2607.24720/) (2026)
- [WDL-OPD: Weak-Driven On-Policy Distillation via Mixture-Constrained Co-Training](https://mlsanity.com/paper/2608.09447/) (2026)
- [GCPO: Diagnosing and Constraining Subspace Geometry in Rollout RL for LLMs](https://mlsanity.com/paper/2608.11674/) (2026)
- [Distillation as Probability Transport: Routed On-Policy Distillation](https://mlsanity.com/paper/2609.08337/) (2026)
- [ReDraft, Don't Just Distill: Reference-Driven Revision for Continual VLLM Post-Training](https://mlsanity.com/paper/2609.16639/) (2026)
- [Train4Merge: A Controlled Single-Teacher Study of RL vs. SFT Teachers for OPD-Based Model Merging](https://mlsanity.com/paper/2609.32303/) (2026)
- [Trapped by Their Own Rollouts: Understanding Aggregation--Rollout Feedback in Federated On-Policy Distillation](https://mlsanity.com/paper/2609.32573/) (2026)
- [USA: Update-aware SAM for Cross-domain On-Policy Disitllation of Language Agents](https://mlsanity.com/paper/2609.34225/) (2026)
- [Learning to Steer, Steering to See: Unveiling the Geometry of RLVR in Large Language Models via Trainable Vectors](https://mlsanity.com/paper/2609.34344/) (2026)
- [Look Before You Select: Rethinking Vocabulary Sparsification in On-Policy Distillation](https://mlsanity.com/paper/2609.34386/) (2026)
- [Learning to Revise Reasoning with Segment-wise On-Policy Distillation](https://mlsanity.com/paper/2610.02703/) (2026)
- [Flash-OPD: Fast On-Policy Distillation](https://mlsanity.com/paper/2610.06105/) (2026)
- [Why On-Policy Distillation Sometimes Fails: Vanishing Learning Signals](https://mlsanity.com/paper/2610.11247/) (2026)

## Abstract (arXiv)

On-policy distillation (OPD) has emerged as an efficient post-training paradigm for large language models. However, existing studies largely attribute this advantage to denser and more stable supervision, while the parameter-level mechanisms underlying OPD's efficiency remain poorly understood. In this work, we argue that OPD's efficiency stems from a form of ``foresight'': it establishes a stable update trajectory toward the final model early in training. This foresight manifests in two aspects. First, at the Module-Allocation Level, OPD identifies regions with low marginal utility and concentrates updates on modules that are more critical to reasoning. Second, at the Update-Direction Level, OPD exhibits stronger low-rank concentration, with its dominant subspaces aligning closely with the final update subspace early in training. Building on these findings, we propose EffOPD, a plug-and-play acceleration method that speeds up OPD by adaptively selecting an extrapolation step size and moving along the current update direction. EffOPD requires no additional trainable modules or complex hyperparameter tuning, and achieves an average training acceleration of 3× while maintaining comparable final performance. Overall, our findings provide a parameter-dynamics perspective for understanding the efficiency of OPD and offer practical insights for designing more efficient post-training methods for large language models.