# Privileged Context as Drift in On-Policy Self-Distillation

arXiv: https://arxiv.org/abs/2610.07842 · HTML: https://mlsanity.com/paper/2610.07842/

## 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 36 of its 56 references that are in the map.
- First posted on arXiv 6 Oct 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 36)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [MiMo-V2-Flash Technical Report](https://mlsanity.com/paper/2601.02780/) (2026)
- [RL's Razor: Why Online Reinforcement Learning Forgets Less](https://mlsanity.com/paper/2509.04259/) (2025)
- [Big-Math: A Large-Scale, High-Quality Math Dataset for Reinforcement Learning in Language Models](https://mlsanity.com/paper/2502.17387/) (2025)
- [MOPD: Multi-Teacher On-Policy Distillation for Capability Integration in LLM Post-Training](https://mlsanity.com/paper/2606.30406/) (2026)
- [CRISP: Compressed Reasoning via Iterative Self-Policy Distillation](https://mlsanity.com/paper/2603.05433/) (2026)
- [Generalization in Deep Networks: The Role of Distance from Initialization](https://mlsanity.com/paper/1901.01672/) (2019)
- [Nemotron 3 Ultra: Open, Efficient Mixture-of-Experts Hybrid Mamba-Transformer Model for Agentic Reasoning](https://mlsanity.com/paper/2606.15007/) (2026)
- [GATES: Self-Distillation under Privileged Context with Consensus Gating](https://mlsanity.com/paper/2602.20574/) (2026)
- [OPSDL: On-Policy Self-Distillation for Long-Context Language Models](https://mlsanity.com/paper/2604.17535/) (2026)
- [Decoupling KL and Trajectories: A Unified Perspective for SFT, DAgger, Offline RL, and OPD in LLM Distillation](https://mlsanity.com/paper/2605.16826/) (2026)
- [On-Policy Self-Distillation without Any Supervision](https://mlsanity.com/paper/2608.06296/) (2026)
- [Rubric-Guided Self-Distillation: Post-Training Without Rubric Verifiers](https://mlsanity.com/paper/2606.12507/) (2026)
- [Anti-Self-Distillation for Reasoning RL via Pointwise Mutual Information](https://mlsanity.com/paper/2605.11609/) (2026)
- [Rethinking Reward Supervision: Rubric-Conditioned Self-Distillation](https://mlsanity.com/paper/2606.19327/) (2026)
- [Privileged Solutions or Context-Induced Teacher Behavior? Dissecting On-Policy Self-Distillation](https://mlsanity.com/paper/2608.09228/) (2026)
- [Reducing the Safety Tax in LLM Safety Alignment with On-Policy Self-Distillation](https://mlsanity.com/paper/2605.15239/) (2026)
- [HERO: Hindsight-Enhanced Reflection from Environment Observations for Agentic Self-Distillation](https://mlsanity.com/paper/2606.11559/) (2026)
- [Learning with Rare Success but Rich Feedback via Reflection-Enhanced Self-Distillation](https://mlsanity.com/paper/2605.12741/) (2026)
- [UniSD: Towards a Unified Self-Distillation Framework for Large Language Models](https://mlsanity.com/paper/2605.06597/) (2026)
- [Learning from Language Feedback via Variational Policy Distillation](https://mlsanity.com/paper/2605.15113/) (2026)
- [Localizing Credit at the Divergence: Path-Conditioned Self-Distillation for LLM Reasoning](https://mlsanity.com/paper/2606.15576/) (2026)
- [Latent On-Policy Self-Distillation](https://mlsanity.com/paper/2608.13040/) (2026)
- [MAIGO: Mitigating Lost-in-Conversation with History-Cleaned On-Policy Self-Distillation](https://mlsanity.com/paper/2605.27186/) (2026)
- [Context Distillation as Latent Memory Management](https://mlsanity.com/paper/2605.28889/) (2026)
- [Consensus as Privileged Context for Label-Free Self-Distillation](https://mlsanity.com/paper/2607.13643/) (2026)

## Abstract (arXiv)

On-policy self-distillation (OPSD) trains a language model to match a copy of itself conditioned on privileged context. Existing work varies what privileged context contains and how it is produced while also changing models, data, and training setups, making the effects of privileged context design difficult to isolate. Motivated by efforts in continual learning to reduce catastrophic forgetting, we study how the choice of privileged context affects policy drift. Specifically, we vary two axes: content (a demonstration, feedback, or rephrase) and source (external, self-generated with a verifier, or self-generated without a verifier). We train Qwen2.5-7B with OPSD across these nine combinations and three datasets, measuring target-task accuracy, prior-task retention, reverse KL from the base policy, and parameter-update geometry. Holding source fixed, changing content spans a wider median KL range than holding content fixed and changing source. The ratio between these ranges is 5.1× for per-token KL and 2.2× for per-sequence KL. Parameter-update geometry shows the same pattern: updates from adapters that share content are more closely aligned (mean cosine 0.571) than updates from adapters that share source (0.255). For continual learning, these findings suggest that privileged context should be treated as part of OPSD's stability design because it is associated with how far and in what direction the policy moves.