Universal flow approximation with deep residual networks

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

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch
• Notes: Universität Freiburg, Masterarbeit, 2019

Classification and Topics

• Keyword: Neuronales Netz ; Approximation ; Gewöhnliche Differentialgleichung

Contributors, Places and Time

• Event: Veröffentlichung
• (where): Freiburg
• (who): Universität
• (when): 2020
• Creator: Müller, Johannes
• Contributor: Harms, Philipp

Further information

• DOI: 10.6094/UNIFR/151788
• URN: urn:nbn:de:bsz:25-freidok-1517881
• Rights: Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 14.08.2025, 11:01 AM CEST