Towards Understanding Ensemble, Knowledge Distillation and Self-Distillation in Deep Learning

Zeyuan Allen-Zhu, Yuanzhi Li

TL;DR: We provide a theory to explain why ensemble and knowledge distillation work for Deep Learning. It matches practice well, while traditional theory such as boosting, random feature mappings or NTKs, cannot explain the same phenomena for DL.

Abstract:

We formally study how \emph{ensemble} of deep learning models can improve test accuracy, and how the superior performance of ensemble can be distilled into a single model using \emph{knowledge distillation}. We consider the challenging case where the ensemble is simply an average of the outputs of a few independently trained neural networks with the \emph{same} architecture, trained using the \emph{same} algorithm on the \emph{same} data set, and they only differ by the random seeds used in the initialization.

We show that ensemble/knowledge distillation in \emph{deep learning} works very differently from traditional learning theory (such as boosting or NTKs). We develop a theory showing that when data has a structure we refer to as ``multi-view'', then ensemble of independently trained neural networks can provably improve test accuracy, and such superior test accuracy can also be provably distilled into a single model. Our result sheds light on how ensemble works in deep learning in a way that is completely different from traditional theorems, and how the ``dark knowledge'' is hidden in the outputs of the ensemble and can be used in distillation.

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