TRIPODS Winter School & Workshop-Gitta Kutyniok
Abstract– Deep neural networks have recently seen an impressive comeback with spectacular applications ranging from autonomous driving over game intelligence to the health care sector. However, most of the related research is empirically driven and a comprehensive mathematical foundation is still missing. Regarding deep learning as a statistical learning problem yields three main theoretical problem complexes, the first of which is expressivity. This research direction studies the expressive power of certain network architectures and aims to estimate the error resulting from approximating the unknown distribution/function by the hypothesis class of neural networks (of a certain type). One vision is to provide precise guidelines on how to set up an optimal architecture for specific applications. In this tutorial, we will provide an introduction into this exciting research field.