DNNs as Layers of Cooperating Classifiers

January 20, 2020 A BSTRACT A robust theoretical framework that can describe and predict the generalization ability of deep neural networks (DNNs) in general circumstances remains elusive. Classical attempts have produced complexity metrics that rely heavily on global measures of compactness and capacity with little investigation into the effects of sub-component collaboration. We demonstrate intriguing regularities in the activation patterns of the hidden nodes within fully-connected feedforward networks. By tracing the origin of these patterns, we show how such networks can be viewed as the combination of two information processing systems: one continuous and one discrete. We describe how these two systems arise naturally from the gradient-based optimization process, and demonstrate the classification ability of the two systems, individually and in collaboration. This perspective on DNN classification offers a novel way to think about generalization, in which different subsets of the training data are used to train distinct classifiers; those classifiers are then combined to perform the classification task, and their consistency is crucial for accurate classification. 1 Introduction One of the central tenets of computational learning theory (CL T) is that the ability of a machine-learning system to generalize to unseen data results from its compactness. That is, if the system employs a number of parameters that is small relative to the number of training samples that it processes appropriately, we can be confident that the system will generalize well to unseen samples drawn from the same distribution as the training data.