  Redundancy in deep neural network (DNN) models has always been one of their
most intriguing and important properties. DNNs have been shown to
overparameterize, or extract a lot of redundant features. In this work, we
explore the impact of size (both width and depth), activation function, and
weight initialization on the susceptibility of deep neural network models to
extract redundant features. To estimate the number of redundant features in
each layer, all the features of a given layer are hierarchically clustered
according to their relative cosine distances in feature space and a set
threshold. It is shown that both network size and activation function are the
two most important components that foster the tendency of DNNs to extract
redundant features. The concept is illustrated using deep multilayer perceptron
and convolutional neural networks on MNIST digits recognition and CIFAR-10
dataset, respectively.
