Recursive Offline Distillation via Entropy Gain Sampling and Answer Mixing

Andrey Goncharov, Daniil Vyazhev, Simon Epanov, Alexey Zaytsev

Distillation of reasoning chains from Large Language Models (LLMs) into their smaller siblings is a standard training approach. Frequently, researchers do not have full access to a teacher model and its internal representations, which limits the resulting performance. We propose a recursive offline distillation method combining two components: entropy-based sampling for selective distillation and answer mixing. Specifically, for three open models (3-4B), at each epoch, we sample reasoning chains weighted by entropy difference with an auxiliary medium model (70-72B) and, next, supplement thinking traces with single-token ground truth answers. Our approach consistently outperforms naive distillation with comparable data budgets ($57.15 \pm 1.01$ vs 51.61 on average) and offers a much steeper learning curve. Additionally, we present a comparative analysis of methods to generate and normalize distillation traces.