Universal Consistency of Deep Convolutional Neural Networks
Machine Learning
2021-06-24 v1 Information Theory
math.IT
Machine Learning
Abstract
Compared with avid research activities of deep convolutional neural networks (DCNNs) in practice, the study of theoretical behaviors of DCNNs lags heavily behind. In particular, the universal consistency of DCNNs remains open. In this paper, we prove that implementing empirical risk minimization on DCNNs with expansive convolution (with zero-padding) is strongly universally consistent. Motivated by the universal consistency, we conduct a series of experiments to show that without any fully connected layers, DCNNs with expansive convolution perform not worse than the widely used deep neural networks with hybrid structure containing contracting (without zero-padding) convolution layers and several fully connected layers.
Cite
@article{arxiv.2106.12498,
title = {Universal Consistency of Deep Convolutional Neural Networks},
author = {Shao-Bo Lin and Kaidong Wang and Yao Wang and Ding-Xuan Zhou},
journal= {arXiv preprint arXiv:2106.12498},
year = {2021}
}
Comments
9pages, 4 figures