Toward Understanding Convolutional Neural Networks from Volterra Convolution Perspective
This provides a theoretical framework for analyzing complex CNNs, which is incremental as it builds on existing convolution theory.
The authors tackled the problem of understanding convolutional neural networks (CNNs) by exploring their relationship with Volterra convolutions, showing that most CNNs can be approximated in this form, with proxy kernels preserving original network characteristics.
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 attempt to convert the basic structures of a convolutional neural network (CNN) and their combinations to the form of Volterra convolutions. The results show that most of convolutional neural networks can be approximated in the form of Volterra convolution, where the approximated 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.