# Distill Skills into Weights, Not Prompts: Abstract Skills as Privileged Signals for On-Policy Self-Distillation

arXiv: https://arxiv.org/abs/2608.09826 · HTML: https://mlsanity.com/paper/2608.09826/

## Key facts

- Cited by 5 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 34 references that are in the map.
- First posted on arXiv 10 Aug 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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [On the Efficacy of Knowledge Distillation](https://mlsanity.com/paper/1910.01348/) (2019)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [Unifying distillation and privileged information](https://mlsanity.com/paper/1511.03643/) (2015)
- [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)
- [Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes](https://mlsanity.com/paper/2603.25562/) (2026)
- [SoK: Agentic Skills -- Beyond Tool Use in LLM Agents](https://mlsanity.com/paper/2602.20867/) (2026)
- [The Invisible Leash: Why RLVR May or May Not Escape Its Origin](https://mlsanity.com/paper/2507.14843/) (2025)
- [SKILL0: In-Context Agentic Reinforcement Learning for Skill Internalization](https://mlsanity.com/paper/2604.02268/) (2026)
- [Skill-SD: Skill-Conditioned Self-Distillation for Multi-turn LLM Agents](https://mlsanity.com/paper/2604.10674/) (2026)
- [Self-Distillation Zero: Self-Revision Turns Binary Rewards into Dense Supervision](https://mlsanity.com/paper/2604.12002/) (2026)
- [A Comprehensive Survey on Knowledge Distillation](https://mlsanity.com/paper/2503.12067/) (2025)
- [Knowledge Distillation on Graphs: A Survey](https://mlsanity.com/paper/2302.00219/) (2023)
- [Learning with privileged information via adversarial discriminative modality distillation](https://mlsanity.com/paper/1810.08437/) (2018)
- [OPSDL: On-Policy Self-Distillation for Long-Context Language Models](https://mlsanity.com/paper/2604.17535/) (2026)
- [Efficient Multivariate Time Series Forecasting via Calibrated Language Models with Privileged Knowledge Distillation](https://mlsanity.com/paper/2505.02138/) (2025)
- [Generalized Knowledge Distillation via Relationship Matching](https://mlsanity.com/paper/2205.01915/) (2022)

## Built on by (most cited first, 5 of 5)

- [E2-OPSD: Taming Entropy Overshoot in On-Policy Self-Distillation](https://mlsanity.com/paper/2610.05048/) (2026)
- [Privileged Context as Drift in On-Policy Self-Distillation](https://mlsanity.com/paper/2610.07842/) (2026)
- [Hindsight Structured Advice Distillation: Steering Executor Agents with Advisors Trained on Their Failures and Task Characteristics](https://mlsanity.com/paper/2610.13000/) (2026)
- [Self-Distillation with Verbal Regularization](https://mlsanity.com/paper/2610.16354/) (2026)
- [Explore with Memory, Learn without It: In-Context Exploration and Self-Distillation for LLM Reasoning](https://mlsanity.com/paper/2610.17734/) (2026)

## Abstract (arXiv)

Reinforcement learning with verifiable rewards yields no group-relative signal when rollout groups are uniformly correct or uniformly wrong, which account for 63.0-68.0% of groups in our experiments. We propose SKALD (Skill-Anchored Latent Distillation), an on-policy self-distillation framework that uses two context views of the same Qwen3-Base model: a question-only student and a teacher conditioned on an abstract, explicit-answer-filtered skill card. The student is trained on its own prefixes, transferring the skill-induced advantage into shared parameters without privileged input at test time. To stabilize context-induced distribution mismatch, SKALD employs an annealed exponentially tilted objective that downweights teacher-preferred tokens with very low student likelihood; as the tilt vanishes, it converges to teacher cross-entropy and recovers the forward-KL student gradient. An empirical gate activates distillation only when verified rollouts estimate a positive teacher advantage. Across five held-out mathematics benchmarks, SKALD improves overall avg@8 over GRPO by +2.46, +4.85, and +12.01 at 0.6B, 1.7B, and 4B, respectively. At 1.7B, zero-variance-only distillation recovers 84.7% of the full gain, while SKALD remains +4.06 above FLOP-matched GRPO and exceeds contextual skill exposure by +3.77. These results show that abstract skills provide dense supervision where group-relative rewards become uninformative.