Towards Understanding Knowledge Distillation

TL;DR

This paper provides the first theoretical insights into knowledge distillation, demonstrating how data geometry, optimization bias, and monotonicity influence the convergence and success of distillation in linear classifiers.

Contribution

It offers the first theoretical analysis of knowledge distillation, deriving a generalization bound and identifying key factors affecting its effectiveness.

Findings

Data geometry influences convergence speed.

Gradient descent finds favorable minima in distillation.

Expected risk decreases with larger training sets.

Abstract

Knowledge distillation, i.e., one classifier being trained on the outputs of another classifier, is an empirically very successful technique for knowledge transfer between classifiers. It has even been observed that classifiers learn much faster and more reliably if trained with the outputs of another classifier as soft labels, instead of from ground truth data. So far, however, there is no satisfactory theoretical explanation of this phenomenon. In this work, we provide the first insights into the working mechanisms of distillation by studying the special case of linear and deep linear classifiers. Specifically, we prove a generalization bound that establishes fast convergence of the expected risk of a distillation-trained linear classifier. From the bound and its proof we extract three key factors that determine the success of distillation: * data geometry -- geometric properties of the data distribution, in particular class separation, has a direct influence on the convergence speed of the risk; * optimization bias -- gradient descent optimization finds a very favorable minimum of the distillation objective; and * strong monotonicity -- the expected risk of the student classifier always decreases when the size of the training set grows.