Hidden representations in deep neural networks: Part 1. Classification problems

Deep neural networks have evolved into a powerful tool applicable for a wide range of problems. However, a clear understanding of their internal mechanism has not been developed satisfactorily yet. Factors such as the architecture, number of hidden layers and neurons, and activation function are largely determined in a guess-and-test manner that is reminiscent of alchemy more than of chemistry. In this paper, we attempt to address these concerns systematically using carefully chosen model systems to gain insights for classification problems. We show how wider networks result in several simple patterns identified on the input space, while deeper networks result in more complex patterns. We show also the transformation of input space by each layer and identify the origin of techniques such as transfer learning, weight normalization and early stopping. This paper is an initial step towards a systematic approach to uncover key hidden properties that can be exploited to improve the performance and understanding of deep neural networks. (C) 2019 Elsevier Ltd. All rights reserved.