Universal Consistency of Deep Convolutional Neural Networks

TL;DR

This paper proves that deep convolutional neural networks with expansive convolution are strongly universally consistent when trained with empirical risk minimization, and demonstrates their competitive performance without fully connected layers.

Contribution

It establishes the universal consistency of DCNNs with expansive convolution and compares their empirical performance to traditional hybrid models.

Findings

DCNNs with expansive convolution are strongly universally consistent.

Without fully connected layers, these DCNNs perform comparably to traditional models.

Empirical results support the theoretical findings.

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.