Johannes Müller: Universal flow approximation with deep residual networks

Universität Freiburg

 

trägt über seine Masterarbeit zum Thema

 

Universal flow approximation with deep residual networks

 

im Rahmen des Oberseminar Stochastik vor

 

Abstract:

Residual networks (ResNets) are a deep learning architecture with a recursive structure which can be seen as the explicit Euler discretisation of an associated ordinary differential equation. We use this interpretation to show that by simultaneously increasing the number of skip connections as well as the expressivity of the intermediate networks arbitrary flows can be approximated uniformly by deep ReLU ResNets on compact sets. Further, we derive estimates on the number of parameters needed to do this up to a prescribed accuracy under temporal regularity assumptions. Finally, we discuss the possibility of using ResNets for diffeomorphic matching problems and propose some next steps in the theoretical foundation of this approach.