# What Does Privileged Information Add to On-Policy Self-Distillation?

arXiv: https://arxiv.org/abs/2609.20612 · HTML: https://mlsanity.com/paper/2609.20612/

## 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 24 of its 31 references that are in the map.
- First posted on arXiv 17 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)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Fine-Tuning Pretrained Language Models: Weight Initializations, Data Orders, and Early Stopping](https://mlsanity.com/paper/2002.06305/) (2020)
- [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)
- [Accounting for Variance in Machine Learning Benchmarks](https://mlsanity.com/paper/2103.03098/) (2021)
- [Does Knowledge Distillation Really Work?](https://mlsanity.com/paper/2106.05945/) (2021)
- [Have LLMs Advanced Enough? A Challenging Problem Solving Benchmark For Large Language Models](https://mlsanity.com/paper/2305.15074/) (2023)
- [Rethinking On-Policy Self-Distillation for Thinking Models](https://mlsanity.com/paper/2607.05184/) (2026)
- [Purified OPSD: On-Policy Self-Distillation Without Losing How to Think](https://mlsanity.com/paper/2607.02234/) (2026)
- [On-Policy Self-Distillation without Any Supervision](https://mlsanity.com/paper/2608.06296/) (2026)
- [Privileged, but Biased: How PI-Conditioned Teachers Break Self-Distillation](https://mlsanity.com/paper/2608.04794/) (2026)
- [Privileged Solutions or Context-Induced Teacher Behavior? Dissecting On-Policy Self-Distillation](https://mlsanity.com/paper/2608.09228/) (2026)
- [Is More Privileged Information Better? From Solution Traces to Problem-Solving Structure in Self-Distilled Reasoning](https://mlsanity.com/paper/2608.01589/) (2026)
- [Rethinking Privileged Information in On-Policy Self-Distillation](https://mlsanity.com/paper/2608.18271/) (2026)
- [PHF: Privileged Hidden Flow for On-Policy Self-Distillation](https://mlsanity.com/paper/2606.29340/) (2026)
- [ReNIO: Reweighting Negative Trajectory Importance for LLM On-Policy Distillation](https://mlsanity.com/paper/2606.23104/) (2026)
- [PAST: Privileged Adaptation from Complete Student Trajectories for On-Policy Self-Distillation](https://mlsanity.com/paper/2608.08726/) (2026)
- [The Role of Feedback Alignment in Self-Distillation](https://mlsanity.com/paper/2606.11173/) (2026)
- [Privileged Likelihood Is Not Automatically Value: Three Checks for Token Credit in On-Policy Self-Distillation](https://mlsanity.com/paper/2608.09263/) (2026)

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

- [When Clipping Reverses Correction: Failure Dynamics of Pointwise Forward-KL On-Policy Self-Distillation](https://mlsanity.com/paper/2609.38995/) (2026)
- [Does self-distillation improve reasoning?](https://mlsanity.com/paper/2610.18613/) (2026)

## Abstract (arXiv)

On-policy self-distillation (OPSD) lets a language model learn from a frozen copy of itself that sees an answer or a worked solution. Giving the teacher this extra information seems to offer the student more to learn, but how much does it add beyond distillation itself? To isolate that contribution, we construct AMPLE-Math, a reusable suite of 5,319 mathematical problems with six reasoning views that share the same answer, and compare each view with matched reference-free distillation. With a thinking-enabled teacher supervising direct-response rollouts, reference-free distillation accounts for much of Qwen3-1.7B's improvement under thinking-enabled evaluation, both in domain and on external benchmarks. Evidence for an additional reference benefit is modest in Qwen, strongest for a polished solution, whereas complete traces add two percentage points in SmolLM3-3B at step 50. These benefits depend on the student being trained. At the same checkpoint, replacing short direct-response rollouts with long thinking-enabled rollouts turns gains into losses in both families while the problems, references, and evaluation stay fixed. Teacher profiles and matched loss interventions in Qwen further show that changing token-level supervision can leave student behavior largely unchanged. Together, these findings suggest that OPSD can improve access to existing reasoning capabilities through parameters shared by direct-response and thinking-enabled inference. The value of a privileged reference is what it adds to this cross-mode transfer, not how much of the solution it reveals.