The course focuses on the mathematical aspects of modern network-based representation methods, specifically the well-known (deep) Neural Networks (NN) and the lesser-known hierarchical Tensor Networks (TN), which have been popular in quantum physics for a long time. Thematically, it is situated in the field of Numerical Analysis but also incorporates concepts from Functional Analysis and Statistics in some investigations. The emphasis lies on the approximation properties of the two network representations, with particular attention to their expressiveness in approximating high-dimensional functions with suitable structure. In the second half of the course, we will (likely) turn to compositional structures that can play an important role in both NN and TN. For this, a particularly interesting aspect is the study of high-dimensional transport processes.
- Trainer/in: Martin Eigel