# On-Policy Distillation Teaches New Skills but Not New Knowledge

arXiv: https://arxiv.org/abs/2610.09639 · HTML: https://mlsanity.com/paper/2610.09639/

## 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 10 of its 34 references that are in the map.
- First posted on arXiv 7 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, 10 of 10)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [Olmo 3](https://mlsanity.com/paper/2512.13961/) (2025)
- [Demystifying On-Policy Distillation: Roles, Pathologies, and Regulations](https://mlsanity.com/paper/2607.13399/) (2026)
- [Does On-Policy Distillation Really Distill? From Noisy Teacher to Self-Improvement](https://mlsanity.com/paper/2608.31046/) (2026)
- [Towards Understanding On-Policy Distillation through the Lens of Test-Time Scaling](https://mlsanity.com/paper/2608.11829/) (2026)

## Abstract (arXiv)

On-policy distillation (OPD) strengthens language-model reasoning, yet whether students acquire new factual knowledge or compositional skill for multi-step reasoning remains unknown. We separate these capabilities using a controlled synthetic framework that measures the student's initial capabilities and independently controls the teacher's additional facts, compositional skill, or both. Across four models from three families, reverse-KL OPD reliably transfers compositional skill across unseen reasoning structures, but transfers minimal factual knowledge. Decoupling the distillation recipe reveals the source of this asymmetry: replacing reverse KL with forward KL restores factual transfer, whereas student rollouts specifically improve the execution of multi-step reasoning. Experiments on recent factual QA and competition mathematics show a similar asymmetry under reverse-KL OPD, yielding notable reasoning gains without factual memory expansion. Together, these results demonstrate that on-policy distillation does not expand a model's parametric knowledge, but instead teaches it to organize and compose the knowledge it already possesses.