Information Bottleneck Theory on Convolutional Neural Networks

TL;DR

This paper applies Information Bottleneck theory to CNNs, revealing that the compression phase is not always observed, indicating more complex behaviors than previously understood in feedforward neural networks.

Contribution

It investigates the applicability of IB theory to CNNs and analyzes how architectural features influence CNN dynamics, challenging previous assumptions about the compression phase.

Findings

The compression phase is not observed in CNNs on MNIST and Fashion-MNIST.

CNNs exhibit more complex behaviors than feedforward neural networks.

Architectural features impact CNN performance and dynamics.

Abstract

Recent years, 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 (IB) theory 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 such as convolutional layer width, kernel size, network depth, pooling layers and multi-fully connected layer 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 shows us the CNNs have a rather complicated behavior than feedforward neural networks.