Understanding Convolutional Neural Networks from Volterra Convolution Perspective

We make an attempt to understanding convolutional neural network by exploring the relationship between (deep) convolutional neural networks and Volterra convolutions. We propose a novel approach to explain and study the overall characteristics of neural networks without being disturbed by the horribly complex architectures. Specifically, we convert the basic structures and their combinations to the form of Volterra convolutions. The results show that most of convolutional neural networks can be converted to the form of Volterra convolution, where the converted proxy kernels preserve the characteristics of the original network. Analyzing these proxy kernels may give valuable insight about the original network. Base on this setup, we presented methods to approximating the order-zero and order-one proxy kernels, and verified the correctness and effectiveness of our results.