On the Generalization of Knowledge Distillation: An Information-Theoretic View

Fuente: arXiv
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Main Authors: Li, Bingying, He, Haiyun
Format: Preprint
Published: 2026
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author Li, Bingying
He, Haiyun
author_facet Li, Bingying
He, Haiyun
contents Knowledge distillation is widely used to improve generalization in practice, yet its theoretical understanding remains elusive. In the standard distillation setting, a teacher model provides soft predictions to guide the training of a student model. We model teacher and student training as coupled stochastic processes and introduce a distillation divergence, defined as the Kullback-Leibler divergence between these two stochastic kernels. Within this framework, we derive two generalization bounds for the student model relative to the teacher's generalization gap: an upper bound under a sub-Gaussian assumption via algorithmic stability, and a lower bound under a central condition with sharper dependence on the distillation divergence. We further develop a loss-sharpness-aware bound with an explicit tightness regime, showing that the teacher's local flatness can strictly tighten the bound. Additionally, in a linear Gaussian case study, the distillation divergence admits an interpretable decomposition into bias, variance, and rank-bottleneck costs, yielding practical guidance for distillation design.
format Preprint
id arxiv_https___arxiv_org_abs_2605_13143
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle On the Generalization of Knowledge Distillation: An Information-Theoretic View
Li, Bingying
He, Haiyun
Information Theory
Machine Learning
Knowledge distillation is widely used to improve generalization in practice, yet its theoretical understanding remains elusive. In the standard distillation setting, a teacher model provides soft predictions to guide the training of a student model. We model teacher and student training as coupled stochastic processes and introduce a distillation divergence, defined as the Kullback-Leibler divergence between these two stochastic kernels. Within this framework, we derive two generalization bounds for the student model relative to the teacher's generalization gap: an upper bound under a sub-Gaussian assumption via algorithmic stability, and a lower bound under a central condition with sharper dependence on the distillation divergence. We further develop a loss-sharpness-aware bound with an explicit tightness regime, showing that the teacher's local flatness can strictly tighten the bound. Additionally, in a linear Gaussian case study, the distillation divergence admits an interpretable decomposition into bias, variance, and rank-bottleneck costs, yielding practical guidance for distillation design.
title On the Generalization of Knowledge Distillation: An Information-Theoretic View
topic Information Theory
Machine Learning
url https://arxiv.org/abs/2605.13143