# Filter, Then Reweight: Rethinking Optimization Granularity in On-Policy Distillation

arXiv: https://arxiv.org/abs/2606.02684 · HTML: https://mlsanity.com/paper/2606.02684/

## Key facts

- Cited by 32 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 35 of its 48 references that are in the map.
- First posted on arXiv 1 Jun 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 35)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [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)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [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)
- [On-Policy Context Distillation for Language Models](https://mlsanity.com/paper/2602.12275/) (2026)
- [Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation](https://mlsanity.com/paper/2602.12125/) (2026)
- [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)
- [Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes](https://mlsanity.com/paper/2603.25562/) (2026)
- [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)
- [Skill-SD: Skill-Conditioned Self-Distillation for Multi-turn LLM Agents](https://mlsanity.com/paper/2604.10674/) (2026)
- [Scaling Reasoning Efficiently via Relaxed On-Policy Distillation](https://mlsanity.com/paper/2603.11137/) (2026)
- [Stable On-Policy Distillation through Adaptive Target Reformulation](https://mlsanity.com/paper/2601.07155/) (2026)
- [Fast and Effective On-policy Distillation from Reasoning Prefixes](https://mlsanity.com/paper/2602.15260/) (2026)
- [Uni-OPD: Unifying On-Policy Distillation with a Dual-Perspective Recipe](https://mlsanity.com/paper/2605.03677/) (2026)
- [TCOD: Exploring Temporal Curriculum in On-Policy Distillation for Multi-turn Autonomous Agents](https://mlsanity.com/paper/2604.24005/) (2026)
- [SCOPE: Signal-Calibrated On-Policy Distillation Enhancement with Dual-Path Adaptive Weighting](https://mlsanity.com/paper/2604.10688/) (2026)
- [HDPO: Hybrid Distillation Policy Optimization via Privileged Self-Distillation](https://mlsanity.com/paper/2603.23871/) (2026)
- [Video-OPD: Efficient Post-Training of Multimodal Large Language Models for Temporal Video Grounding via On-Policy Distillation](https://mlsanity.com/paper/2602.02994/) (2026)
- [Reinforcement-aware Knowledge Distillation for LLM Reasoning](https://mlsanity.com/paper/2602.22495/) (2026)
- [Lightning OPD: Efficient Post-Training for Large Reasoning Models with Offline On-Policy Distillation](https://mlsanity.com/paper/2604.13010/) (2026)
- [VOLD: Reasoning Transfer from LLMs to Vision-Language Models via On-Policy Distillation](https://mlsanity.com/paper/2510.23497/) (2025)
- [Demystifying OPD: Length Inflation and Stabilization Strategies for Large Language Models](https://mlsanity.com/paper/2604.08527/) (2026)
- [OPSDL: On-Policy Self-Distillation for Long-Context Language Models](https://mlsanity.com/paper/2604.17535/) (2026)
- [pi-Flow: Policy-Based Few-Step Generation via Imitation Distillation](https://mlsanity.com/paper/2510.14974/) (2025)

## Built on by (most cited first, 30 of 32)

- [Mismatch Matters: On-Policy Distillation Beyond Token Agreement](https://mlsanity.com/paper/2608.09836/) (2026)
- [A Formula-Driven Survey and Research Agenda for On-Policy Distillation](https://mlsanity.com/paper/2606.22793/) (2026)
- [What Matters in On-Policy Distillation? A Perspective on Data Efficiency and Data Selection](https://mlsanity.com/paper/2609.05198/) (2026)
- [When Teachers Mislead: Spurious-Signal-Aware On-Policy Distillation](https://mlsanity.com/paper/2608.03632/) (2026)
- [When Top-K Misses the Decision: Tool-Call Drift in Multi-Teacher On-Policy Distillation](https://mlsanity.com/paper/2607.07050/) (2026)
- [Every Coin Has Two Sides: On the Dual Nature of Generalization in On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2608.16647/) (2026)
- [Beyond Teacher Likelihood: Group-Calibrated On-Policy Distillation for Long-Context Reasoning](https://mlsanity.com/paper/2608.19181/) (2026)
- [Matching Supervision to the Student's Learning Capacity: A Unified Framework for On-Policy Self-Distillation](https://mlsanity.com/paper/2608.08176/) (2026)
- [ReOrder-OPD:Reliability-Aware Prompt Ordering for On-Policy Distillation](https://mlsanity.com/paper/2608.10905/) (2026)
- [Better Starts, Better Ends: Bootstrapped Iterative Self-Reasoning Distillation for Compressed Reasoning](https://mlsanity.com/paper/2607.15736/) (2026)
- [D3-MOPD: Dynamic Domain ScheDuling for Efficient Multi-Teacher Distillation](https://mlsanity.com/paper/2608.24987/) (2026)
- [SnapBench: Benchmarking Snap-and-Ask Multimodal Retrieval for Mobile Interactions](https://mlsanity.com/paper/2608.29607/) (2026)
- [Teacher Should Think Ahead: Adaptive Continuations for Reliable On-Policy Distillation](https://mlsanity.com/paper/2609.22254/) (2026)
- [Distill What You Trust: Reliability-Aware Multi-Teacher On-Policy Distillation](https://mlsanity.com/paper/2609.23697/) (2026)
- [Influence-Directed Distillation: Solving the Diversity Bottleneck in Sampled-Token On-Policy Distillation](https://mlsanity.com/paper/2608.29846/) (2026)
- [Gradients Know What Outcomes Don't: Unlocking Reinforcement Learning for LLM Reasoning with Gradient-Aligned Rewards](https://mlsanity.com/paper/2609.03342/) (2026)
- [Blockwise Policy-Drift Gating for On-Policy Distillation](https://mlsanity.com/paper/2606.24084/) (2026)
- [AlphaG-OPD: Reliability-Gated Sibling Counterfactuals for On-Policy Distillation in Symbolic Alpha Factor Discovery](https://mlsanity.com/paper/2608.01303/) (2026)
- [SciLENS: RL-Driven Autonomous Agents for Scientific Localized Evidence Navigation and Synthesis](https://mlsanity.com/paper/2609.03338/) (2026)
- [KuaiRP Series Role-playing Models Technical Report](https://mlsanity.com/paper/2609.11127/) (2026)
- [Trajectory Learnability for Offline On-Policy Distillation with Imperfect Teachers](https://mlsanity.com/paper/2609.18321/) (2026)
- [Dense Is Not Enough: Hierarchical Supervision Allocation for Long-Horizon On-Policy Distillation](https://mlsanity.com/paper/2609.33409/) (2026)
- [What Shared Prefixes Hide: Trajectory Dropout for On-Policy Distillation](https://mlsanity.com/paper/2609.33455/) (2026)
- [DuoOPD: Learning from Joint Teacher-Student Outcomes for Multi-Task On-Policy Distillation](https://mlsanity.com/paper/2609.33711/) (2026)
- [Look Before You Select: Rethinking Vocabulary Sparsification in On-Policy Distillation](https://mlsanity.com/paper/2609.34386/) (2026)
- [On-Policy or Off-Policy Learning? A Systematic Study of Distillation Dynamics](https://mlsanity.com/paper/2609.35259/) (2026)
- [Reward-Aligned Reweighting for On-Policy Distillation](https://mlsanity.com/paper/2609.35517/) (2026)
- [REVO: Rollout-Efficient Off-Policy Distillation via Variance-Guided Reuse](https://mlsanity.com/paper/2609.37500/) (2026)
- [RISED: RubrIcs for agentic multi-environment Selection and sElf-Distillation](https://mlsanity.com/paper/2610.00979/) (2026)
- [DIAL-OPD: Learning More from Fewer Tokens in On-Policy Distillation](https://mlsanity.com/paper/2610.11659/) (2026)

## Abstract (arXiv)

On-Policy distillation (OPD) in large language models is shifting from full-trace KL supervision toward more selective training paradigms. Recent OPD methods increasingly focus on selecting which trajectories to learn from, which tokens are most informative, and which supervision signals are most reliable. Motivated by this trend, we rethink optimization granularity of OPD and propose fireicon FiRe-OPD (Filter, then Reweight), which jointly adjusts supervision signals at both trajectory and token levels. In details, FiRe-OPD first filters trajectories to remove low-quality rollout samples, and then applies soft reweighting within the retained trajectories to emphasize informative tokens. Compared with hard token selection, FiRe-OPD leverages a soft-weighting mechanism to effectively mitigate information loss and enhance optimization stability, thereby achieving finer-grained OPD optimization. We validate the effectiveness of FiRe-OPD across strong-to-weak, single-teacher, and multi-teacher settings, and demonstrate its superiority over recent token-level OPD methods ( (e.g., +6.25 on AIME 2024 in strong-to-weak, +18.81 on Miner in multi-teacher). Our code is available at https://github.com/YuYingLi0/FiRe-OPD.