Learning without Overwriting: A Theory of Self-Distillation and Supervised Fine-Tuning in Continual Reasoning
On-policy self-distillation (OPSD) of large language models (LLMs) has demonstrated the ability to improve reasoning capabilities while preserving previously acquired knowledge. Despite substantial empirical success, the dynamics of OPSD in continual reasoning remain incompletely understood. Modeling LLM reasoning as search over a directed acyclic graph, we provide a unified theoretical analysis of both the dynamics of post-training---OPSD and supervised fine-tuning (SFT) in continual learning---and the impact of pre-training on subsequent performance. Our findings establish three key insights with an optimization guarantee: (i) OPSD with hints from correct outputs enables continual learn...
| Authors | Shinichi Uemura, Taiji Suzuki |
|---|---|
| Primary category | cs.LG |
| Published | 4 October 2026 |
| Last updated at source | 4 October 2026 |
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