Information Bottleneck Methods on Convolutional Neural Networks

Recent year, many researches attempt to open the black box of deep neural networks and propose a various of theories to understand it. Among them, information bottleneck theory (IB) claims that there are two distinct phases consisting of fitting phase and compression phase in the course of training. This statement attracts many attentions since its success in explaining the inner behavior of feedforward neural networks. In this paper, we employ IB theory to understand the dynamic behavior of convolutional neural networks (CNNs) and investigate how the fundamental features have impact on the performance of CNNs. In particular, through a series of experimental analysis on benchmark of MNIST and Fashion-MNIST, we demonstrate that the compression phase is not observed in all these cases. This show us the CNNs have a rather complicated behavior than feedforward neural networks.