# What Should a Self-Teacher See? Privileged Context Design for On-Policy Self-Distillation

arXiv: https://arxiv.org/abs/2609.25623 · HTML: https://mlsanity.com/paper/2609.25623/

## Key facts

- Cited by 2 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 44 references that are in the map.
- First posted on arXiv 22 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, 30 of 39)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [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)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Distilling Step-by-Step! Outperforming Larger Language Models with Less Training Data and Smaller Model Sizes](https://mlsanity.com/paper/2305.02301/) (2023)
- [C-Eval: A Multi-Level Multi-Discipline Chinese Evaluation Suite for Foundation Models](https://mlsanity.com/paper/2305.08322/) (2023)
- [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)
- [Unifying distillation and privileged information](https://mlsanity.com/paper/1511.03643/) (2015)
- [ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoning](https://mlsanity.com/paper/2502.01100/) (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)
- [Learning by Distilling Context](https://mlsanity.com/paper/2209.15189/) (2022)
- [Privileged Information Distillation for Language Models](https://mlsanity.com/paper/2602.04942/) (2026)
- [Vision-OPD: Learning to See Fine Details for Multimodal LLMs via On-Policy Self-Distillation](https://mlsanity.com/paper/2605.18740/) (2026)
- [CRISP: Compressed Reasoning via Iterative Self-Policy Distillation](https://mlsanity.com/paper/2603.05433/) (2026)
- [Uni-OPD: Unifying On-Policy Distillation with a Dual-Perspective Recipe](https://mlsanity.com/paper/2605.03677/) (2026)
- [Rethinking On-Policy Self-Distillation for Thinking Models](https://mlsanity.com/paper/2607.05184/) (2026)
- [Linguistic Generalizability of Test-Time Scaling in Mathematical Reasoning](https://mlsanity.com/paper/2502.17407/) (2025)
- [AutoLogi: Automated Generation of Logic Puzzles for Evaluating Reasoning Abilities of Large Language Models](https://mlsanity.com/paper/2502.16906/) (2025)
- [Demystifying OPD: Length Inflation and Stabilization Strategies for Large Language Models](https://mlsanity.com/paper/2604.08527/) (2026)
- [Unmasking On-Policy Distillation: Where It Helps, Where It Hurts, and Why](https://mlsanity.com/paper/2605.10889/) (2026)

## Built on by (most cited first, 2 of 2)

- [Is Better Teacher Supervision Enough? Unlocking Student-side Learning in Multimodal On-Policy Distillation](https://mlsanity.com/paper/2609.39120/) (2026)
- [Better Supervision Is Nearby: Neighborhood On-Policy Self-Distillation](https://mlsanity.com/paper/2609.39687/) (2026)

## Abstract (arXiv)

More privileged information does not always make a better teacher. We study this tension in on-policy self-distillation (OPSD), where a self-teacher scores the student's own rollouts under privileged context, conventionally a complete reference solution that bundles the final answer with one particular reasoning path. Holding the student view and training fixed within each scale, we compare that default against three abstractions compiled offline, a named strategy, a method-independent framing, and a problem category, and against an answer-only control that keeps the destination but removes the path. In the primary runs on competition mathematics, the best intermediate contexts improve the in-domain peak mean over the full solution by 1.4 points at 4B and 1.6 at 8B, while storing an order of magnitude fewer hint tokens. Comparisons across three seeds also show positive mean gains for the framing and category contexts at both scales. Answer-only conditioning remains competitive in the primary runs, within 0.2 points of the full solution at these scales. The preferred context varies with student scale and task. Initial teacher-student KL does not order downstream performance. What a self-teacher should see is therefore not everything it could, but the level of abstraction its student can still act on.