Stronger generalization bounds for deep nets via a compression approach

TL;DR

This paper introduces a compression-based framework that provides significantly tighter generalization bounds for deep neural networks, supported by new theoretical insights and empirical validation of noise stability properties.

Contribution

It presents a novel, explicit compression approach that yields superior generalization bounds and extends analysis to convolutional networks, explaining their empirical success.

Findings

Compression-based bounds outperform naive parameter counting

Deep nets exhibit noise stability properties

Bounds extend to convolutional neural networks

Abstract

Deep nets generalize well despite having more parameters than the number of training samples. Recent works try to give an explanation using PAC-Bayes and Margin-based analyses, but do not as yet result in sample complexity bounds better than naive parameter counting. The current paper shows generalization bounds that're orders of magnitude better in practice. These rely upon new succinct reparametrizations of the trained net --- a compression that is explicit and efficient. These yield generalization bounds via a simple compression-based framework introduced here. Our results also provide some theoretical justification for widespread empirical success in compressing deep nets. Analysis of correctness of our compression relies upon some newly identified \textquotedblleft noise stability\textquotedblright properties of trained deep nets, which are also experimentally verified. The study of these properties and resulting generalization bounds are also extended to convolutional nets, which had eluded earlier attempts on proving generalization.