On the Number of Linear Regions of Convolutional Neural Networks
Document Type
Article
Source of Publication
arXiv: Learning
Publication Date
6-1-2020
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.
Disciplines
Computer Sciences | Education
Recommended Citation
Xiong, Huan; Huang, Lei; Yu, Mengyang; Liu, Li; Zhu, Fan; and Shao, Ling, "On the Number of Linear Regions of Convolutional Neural Networks" (2020). All Works. 2568.
https://zuscholars.zu.ac.ae/works/2568
Indexed in Scopus
no
Open Access
no