# What Shared Prefixes Hide: Trajectory Dropout for On-Policy Distillation

arXiv: https://arxiv.org/abs/2609.33455 · HTML: https://mlsanity.com/paper/2609.33455/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 27 of its 29 references that are in the map.
- First posted on arXiv 27 Sep 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, 27 of 27)

- [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)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [On-Policy Context Distillation for Language Models](https://mlsanity.com/paper/2602.12275/) (2026)
- [Fast and Effective On-policy Distillation from Reasoning Prefixes](https://mlsanity.com/paper/2602.15260/) (2026)
- [Not All Disagreement Is Learnable: Token Teachability in On-Policy Distillation](https://mlsanity.com/paper/2605.26844/) (2026)
- [Filter, Then Reweight: Rethinking Optimization Granularity in On-Policy Distillation](https://mlsanity.com/paper/2606.02684/) (2026)
- [Unmasking On-Policy Distillation: Where It Helps, Where It Hurts, and Why](https://mlsanity.com/paper/2605.10889/) (2026)
- [Prefix Teach, Suffix Fade: Local Teachability Collapse in Strong-to-Weak On-Policy Distillation](https://mlsanity.com/paper/2605.13643/) (2026)
- [Your Teacher Can't Help You Here: Combating Supervision Fidelity Decay in On-Policy Distillation](https://mlsanity.com/paper/2605.30833/) (2026)
- [ReflectionCoder: Learning from Reflection Sequence for Enhanced One-off Code Generation](https://mlsanity.com/paper/2405.17057/) (2024)
- [Token Weighting for Long-Range Language Modeling](https://mlsanity.com/paper/2503.09202/) (2025)
- [Bridging Reasoning Trajectories in On-Policy Distillation via Near-Future Guidance](https://mlsanity.com/paper/2606.00305/) (2026)
- [Dense Supervision, Sparse Updates: On the Sparsity and Geometry of On-Policy Distillation](https://mlsanity.com/paper/2606.13657/) (2026)
- [ReNIO: Reweighting Negative Trajectory Importance for LLM On-Policy Distillation](https://mlsanity.com/paper/2606.23104/) (2026)
- [Self-Supervised Visual On-Policy Distillation](https://mlsanity.com/paper/2608.14144/) (2026)
- [Hide to See: Reasoning-prefix Masking for Visual-anchored Thinking in VLM Distillation](https://mlsanity.com/paper/2605.11651/) (2026)
- [A Token-Level Analysis of Sampled-Token Reverse-KL On-Policy Distillation](https://mlsanity.com/paper/2608.25643/) (2026)
- [Beyond Length: Quantifying Long-Range Information for Long-Context LLM Pretraining Data](https://mlsanity.com/paper/2510.25804/) (2025)
- [Demystifying Training-Time Augmentation for Data-Constrained Language Model Pretraining](https://mlsanity.com/paper/2606.16246/) (2026)
- [Self-Boosting Vision-Language Models with Noisy Student On-Policy Self-Distillation](https://mlsanity.com/paper/2607.23125/) (2026)
- [Learning from Partial Chain-of-Thought via Truncated-Reasoning Self-Distillation](https://mlsanity.com/paper/2603.13274/) (2026)
- [Same Evidence, Different Answers: Canonical-Context On-Policy Distillation for Multi-Turn Language Models](https://mlsanity.com/paper/2605.30251/) (2026)
- [Masked Distillation: Internalizing the Chain-of-Thought in Language Models](https://mlsanity.com/paper/2607.22629/) (2026)
- [Adaptive FastOPD: Progress-Aware Rollout Horizon Expansion for Efficient On-Policy Distillation](https://mlsanity.com/paper/2607.29494/) (2026)

## Abstract (arXiv)

On-policy distillation (OPD) trains a student model on its own trajectories using dense token-level feedback from a stronger teacher model. Since each update is conditioned on the reasoning prefix already generated by the student, the prefix also shapes how effectively teacher feedback is converted into learning. We find that shared prefixes can lead to weak token-level updates, a phenomenon we call Prefix-Induced Supervision Attenuation (PISA). This attenuation arises in two common cases. (i) High student confidence can weaken corrective gradients even when the teacher disagrees. (ii) Tokens that rely on earlier reasoning can receive learning signals as weak as those for simple local continuations. To solve this problem, we propose Trajectory Dropout, a simple training-time intervention that exposes these weakened signals. The student first performs a standard full-context rollout to generate a complete trajectory. During training, we randomly drop a certain proportion of the student's reasoning trajectory, while the teacher continues to observe the complete trajectory for token-level supervision. This intervention strengthens corrections for overconfident predictions and introduces additional supervision at prefix-sensitive positions. Trajectory Dropout consistently improves average performance across teacher--student model pairs of different scales and six mathematical reasoning benchmarks, while also yielding gains on two out-of-domain benchmarks. It can also be flexibly integrated into existing OPD variants with negligible computational overhead, further improving their performance. These results demonstrate that Trajectory Dropout provides a simple mechanism for strengthening token-level supervision across model scales and OPD objectives.