Title

On the Number of Linear Regions of Convolutional Neural Networks

Document Type

Conference Proceeding

Publication Title

37th International Conference on Machine Learning, ICML 2020

Abstract

One fundamental problem in deep learning is understanding the outstanding performance of deep Neural Networks (NNs) in practice. One explanation for the superiority of NNs is that they can realize a large class of complicated functions, i.e., they have powerful expressivity. The expressivity of a ReLU NN can be quantified by the maximal number of linear regions it can separate its input space into. In this paper, we provide several mathematical results needed for studying the linear regions of CNNs, and use them to derive the maximal and average numbers of linear regions for one-layer ReLU CNNs. Furthermore, we obtain upper and lower bounds for the number of linear regions of multi-layer ReLU CNNs. Our results suggest that deeper CNNs have more powerful expressivity than their shallow counterparts, while CNNs have more expressivity than fully-connected NNs per parameter.

First Page

10445

Last Page

10454

Publication Date

1-1-2020

Comments

IR deposit conditions: none described

Proceedings for ICML available on PMLR (OA)

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