Skill-Conditioned Gated Self-Distillation for LLM Reasoning
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866916056390434816 |
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| author | Huang, Jiazhen Chen, Xiao Luo, Xiao Dai, Yong Hu, Senkang Zhao, Yuzhi |
| author_facet | Huang, Jiazhen Chen, Xiao Luo, Xiao Dai, Yong Hu, Senkang Zhao, Yuzhi |
| contents | 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. Our code is available at https://github.com/walawalagoose/SGSD. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_28791 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Skill-Conditioned Gated Self-Distillation for LLM Reasoning Huang, Jiazhen Chen, Xiao Luo, Xiao Dai, Yong Hu, Senkang Zhao, Yuzhi Computation and Language Artificial Intelligence 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. Our code is available at https://github.com/walawalagoose/SGSD. |
| title | Skill-Conditioned Gated Self-Distillation for LLM Reasoning |
| topic | Computation and Language Artificial Intelligence |
| url | https://arxiv.org/abs/2605.28791 |