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We make an attempt to understanding convolutional neural network by exploringthe relationship between (deep) convolutional neural networks and Volterraconvolutions. We propose a novel approach to explain and study the overallcharacteristics of neural networks without being disturbed by the horriblycomplex architectures. Specifically, we attempt to convert the basic structuresof a convolutional neural network (CNN) and their combinations to the form ofVolterra convolutions. The results show that most of convolutional neuralnetworks can be approximated in the form of Volterra convolution, where theapproximated proxy kernels preserve the characteristics of the originalnetwork. Analyzing these proxy kernels may give valuable insight about theoriginal network. Base on this setup, we presented methods to approximating theorder-zero and order-one proxy kernels, and verified the correctness andeffectiveness of our results.

Toward Understanding Convolutional Neural Networks from Volterra Convolution Perspective