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

• URL: http://arxiv.org/abs/2505.13111v1
• Date: Mon, 19 May 2025 13:39:47 GMT
• Title: Why Knowledge Distillation Works in Generative Models: A Minimal Working Explanation
• Authors: Sungmin Cha, Kyunghyun Cho,
• Abstract summary: Knowledge distillation (KD) is a core component in the training and deployment of modern generative models.<n>We show that KD induces a trade-off between precision and recall in the student model.<n>Our analysis provides a simple and general explanation for the effectiveness of KD in generative modeling.
• Score: 53.30082523545212
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 proves especially beneficial in scenarios where sample quality outweighs diversity, such as instruction tuning or downstream generation. Our analysis provides a simple and general explanation for the effectiveness of KD in generative modeling.

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