# Skill-Conditioned Gated Self-Distillation for LLM Reasoning

arXiv: https://arxiv.org/abs/2605.28791 · HTML: https://mlsanity.com/paper/2605.28791/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 0 of its 55 references that are in the map.
- First posted on arXiv 27 May 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)
- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Built on by (most cited first, 6 of 6)

- [Agent Skills Matter: Inferring Proprietary Skills from Execution Trajectories](https://mlsanity.com/paper/2607.25560/) (2026)
- [Who Teaches Which Token? Verifier-Gated Multi-Expert On-Policy Distillation for Scientific Reasoning](https://mlsanity.com/paper/2609.15404/) (2026)
- [From Scoring to Acting: Outcome-Verified Comparative Self-Distillation for LLM Agents](https://mlsanity.com/paper/2607.27937/) (2026)
- [RP-OPSD: Reasoning-Pivot-Guided On-Policy Self-Distillation for Multilingual Reasoning Transfer](https://mlsanity.com/paper/2608.06347/) (2026)
- [SeOPD: Self-Evolving LLMs via Online Policy Distillation from Self-Generated Chain-of-Thought](https://mlsanity.com/paper/2609.33181/) (2026)
- [Which Skill to Distill? SGUID: Selecting a Compact Skill Bank for Model-Skill Co-Evolution](https://mlsanity.com/paper/2610.12367/) (2026)

## Abstract (arXiv)

On-policy self-distillation (SD) improves LLM reasoning by using teacher-side privileged information (PI) to turn sparse verifier outcomes into dense token-level supervision. Existing methods usually assume trusted PI, such as reference answers or successful traces. We ask whether PI can instead come from an experience-derived skill bank, where retrieved skills are compact and reusable but may also be irrelevant or misleading. We propose Skill-Conditioned Gated Self-Distillation (SGSD), which formulates skill-based SD as teacher hypothesis validation rather than unconditional imitation. SGSD retrieves skill-mistake pairs, constructs a multi-teacher pool, and lets all skill-conditioned teachers score the same plain-prompt student rollout. The verifier validates each teacher's polarity: supporting a success or suppressing a failure gives positive supervision, while the opposite stance is reversed. A robust gated objective then distills informative teacher-student disagreements while suppressing uncertain or extreme signals. Experiments on multiple mathematical reasoning benchmarks show that SGSD consistently improves over GRPO and remains competitive with answer-conditioned OPSD under a weaker PI assumption. For example, on Qwen3-1.7B, SGSD outperforms GRPO by 6.2% and OPSD by 1.7% on average on AIME24, AIME25, and HMMT25.