Harmonic analysis of deep convolutional neural networks

A central task in machine learning, computer vision, and signal processing is to extract characteristic features of signals. Feature extractors based on deep convolutional neural networks have been applied with significant success in a wide range of practical machine learning tasks such as classification of images in the ImageNet data set, image captioning, or control-policy-learning to play Atari games or the board game Go. Since deep convolutional neural networks lead to remarkable results across a broad range of applications, it is essential to understand their underlying mechanisms. In this thesis, we develop a mathematical theory of deep convolutional neural networks for feature extraction using concepts from applied harmonic analysis. We investigate the impact of network topology and building blocks - convolution filters, non-linearities, and pooling operators - on the network‘s feature extraction capabilities.