Why Knowledge Distillation Works in Generative Models: A Minimal Working Explanation

Sungmin Cha, Kyunghyun Cho

Keywords: LLMs, Generative Model, Knowledge Distillation

TL;DR: We propose a minimal working explanation of knowledge distillation in generative models, demonstrating that it induces a precision-recall trade-off where the student concentrates on high-likelihood regions at the expense of diversity.

Abstract: Knowledge distillation (KD) is a core component in the training and deployment of modern generative models, particularly large language models (LLMs). While its empirical benefits are well documented---enabling smaller student models to emulate the performance of much larger teachers---the underlying mechanisms by which KD improves generative quality remain poorly understood. In this work, we present a minimal working explanation of KD in generative modeling. Using a controlled simulation with mixtures of Gaussians, we demonstrate that distillation induces a trade-off between precision and recall in the student model. As the teacher distribution becomes more selective, the student concentrates more probability mass on high-likelihood regions at the expense of coverage---a behavior modulated by a single entropy-controlling parameter. We then validate this effect in a large-scale language modeling setup using the SmolLM2 family of models. Empirical results reveal the same precision-recall dynamics observed in simulation, where precision corresponds to sample quality and recall to distributional coverage. This precision-recall trade-off in LLMs is found to be especially beneficial in scenarios where sample quality is more important than diversity, such as instruction tuning or downstream generation. Our analysis provides a simple and general explanation for the effectiveness of KD in generative modeling.

Primary Area: Deep learning (e.g., architectures, generative models, optimization for deep networks, foundation models, LLMs)

Submission Number: 12367