A07 Signal processing on graphs and complexes

The goal of this project is to advance our understanding of graph neural networks and related signal processing methods for data defined on non-Euclidean domains. We will explore two selected facets within this broad area: a) how the structure of the domain on which the neural network is defined constrains its expressibility, and b) how the structure of the neural network influences its training via gradient descent and related algorithms. In both cases we concentrate on the roles of symmetries and (approximate) low rank structures within those networks, i.e., low-dimensional (sparse) substructures within these networks.