Universal flow approximation with deep residual networks
Year: 2019
Type: preprint
Abstract: Residual networks (ResNets) are a deep learning architecture with a recursive structure given through residual blocks and the copying of the input is called a skip connection. This structure 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 connection as well as the expressivity of the networks Rk the flow of an arbitrary right hand side 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.
Source: arXiv (Cornell University)
DOI: 10.6094/unifr/151788
Author: Müller, Johannes
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2981531693