Universal Consistency of Deep Convolutional Neural Networks
This addresses a theoretical gap for researchers in machine learning, though it is incremental as it builds on existing consistency concepts.
The paper tackles the lack of theoretical understanding of deep convolutional neural networks (DCNNs) by proving that DCNNs with expansive convolution are strongly universally consistent, and experiments show they perform comparably to hybrid networks without fully connected layers.
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.