# TISD: On-Policy Self-Distillation with Trajectory Intervention

arXiv: https://arxiv.org/abs/2609.30878 · HTML: https://mlsanity.com/paper/2609.30878/

## Key facts

- Cited by 1 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 24 of its 28 references that are in the map.
- First posted on arXiv 25 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, 24 of 24)

- [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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (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)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [CodeRL: Mastering Code Generation through Pretrained Models and Deep Reinforcement Learning](https://mlsanity.com/paper/2207.01780/) (2022)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [VinePPO: Refining Credit Assignment in RL Training of LLMs](https://mlsanity.com/paper/2410.01679/) (2024)
- [RLEF: Grounding Code LLMs in Execution Feedback with Reinforcement Learning](https://mlsanity.com/paper/2410.02089/) (2024)
- [RLTF: Reinforcement Learning from Unit Test Feedback](https://mlsanity.com/paper/2307.04349/) (2023)
- [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)
- [Expanding the Capabilities of Reinforcement Learning via Text Feedback](https://mlsanity.com/paper/2602.02482/) (2026)
- [Do Not Let Low-Probability Tokens Over-Dominate in RL for LLMs](https://mlsanity.com/paper/2505.12929/) (2025)
- [GRPO-λ: Credit Assignment improves LLM Reasoning](https://mlsanity.com/paper/2510.00194/) (2025)
- [SelecTKD: Selective Token-Weighted Knowledge Distillation for LLMs](https://mlsanity.com/paper/2510.24021/) (2025)
- [Trajectory-Refined Distillation](https://mlsanity.com/paper/2606.08432/) (2026)
- [Teacher-Guided Policy Optimization for On-Policy Reasoning Distillation under Large Policy Divergence](https://mlsanity.com/paper/2605.13230/) (2026)
- [Bridging Reasoning Trajectories in On-Policy Distillation via Near-Future Guidance](https://mlsanity.com/paper/2606.00305/) (2026)
- [Rethinking Selective Knowledge Distillation](https://mlsanity.com/paper/2602.01395/) (2026)

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

- [From Existing Methods to New Research Ideas: Two Perspectives on Recursive Self-Improvement](https://mlsanity.com/paper/2610.14625/) (2026)

## Abstract (arXiv)

On-policy self-distillation (OPSD) provides dense teacher targets, but evaluates them only along student-sampled rollouts. When the privileged teacher favors an alternative action at a visited prefix, OPSD can provide a target for the branch decision but cannot supervise the successor contexts induced by that action unless the student samples it. This creates a training-time data-collection bottleneck and suggests a different role for teacher-student disagreement: proposing a trajectory branch rather than identifying a sufficient local repair. Our diagnostic framework using controlled token interventions reveals that a teacher-preferred token at peak disagreement can improve student continuation success, while its local corrective value is limited. Motivated by this finding, we introduce a simple branch-regenerate-distill algorithm, Trajectory-Intervention Self-Distillation (TISD). TISD forces a teacher-selected branch action, returns suffix generation to the student, and distills the full trajectory under the privileged-context-conditioned teacher. Across the coding models, TISD improves average Avg@4 over SDPO by 1.2 percentage points. Across the science domains, it improves average Avg@128 by 0.8 points under an equal-step budget and by 0.3 points under an equal-time budget. These results support teacher-guided branching as a way to expose useful successor contexts for self-distillation.