Johannes Müller: Universal flow approximation with deep residual networks
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abgelegt unter:
Oberseminar
| Was |
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|---|---|
| Wann |
26.11.2019 von 14:00 bis 15:00 |
| Wo | Raum 232, Ernst-Zermelo-Straße 1 |
| Termin übernehmen |
vCal
iCal
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Johannes Müller
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.