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Series in Communication Theory 

Edited by Helmut Bölcskei

Vol. 15:







Thomas Wiatowski


Harmonic Analysis of

Deep Convolutional

Neural Networks


1st Edition 2018. 214 pages. € 64,00.

ISBN 978-3-86628-610-8













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.


About the author:

Thomas Wiatowski was born in Strzelce Opolskie, Poland, on December 20, 1987, and received the BSc in Mathematics and the MSc in Mathematics from Technical University of Munich, Germany, in 2010 and 2012, respectively. In 2012 he was a researcher at the Institute of Computational Biology at Helmholtz Zentrum in Munich, Germany. He joined ETH Zurich in 2013, where he graduated with the Dr. sc. degree in 2017. His research interests are in deep machine learning, mathematical signal processing, and applied harmonic analysis.



Keywords: Frame theory; Machine learning, Convolutional neural networks, Feature extraction, Deep learning


Series in Communication Theory

Hartung-Gorre Verlag Konstanz

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