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Titel: Designing rotationally invariant neural networks from PDEs and variational methods
VerfasserIn: Alt, Tobias
Schrader, Karl
Weickert, Joachim
Peter, Pascal
Augustin, Matthias
Sprache: Englisch
Titel: Research in the Mathematical Sciences
Bandnummer: 9
Heft: 3
Verlag/Plattform: Springer Nature
Erscheinungsjahr: 2022
Freie Schlagwörter: Partial differential equations
Variational methods
Neural networks
Rotation invariance
Coupling
DDC-Sachgruppe: 004 Informatik
Dokumenttyp: Journalartikel / Zeitschriftenartikel
Abstract: Partial differential equation models and their associated variational energy formulations are often rotationally invariant by design. This ensures that a rotation of the input results in a corresponding rotation of the output, which is desirable in applications such as image analysis. Convolutional neural networks (CNNs) do not share this property, and existing remedies are often complex. The goal of our paper is to investigate how diffusion and variational models achieve rotation invariance and transfer these ideas to neural networks. As a core novelty, we propose activation functions which couple network channels by combining information from several oriented filters. This guarantees rotation invariance within the basic building blocks of the networks while still allowing for directional filtering. The resulting neural architectures are inherently rotationally invariant. With only a few small filters, they can achieve the same invariance as existing techniques which require a fine-grained sampling of orientations. Our findings help to translate diffusion and variational models into mathematically well-founded network architectures and provide novel concepts for model-based CNN design.
DOI der Erstveröffentlichung: 10.1007/s40687-022-00339-x
URL der Erstveröffentlichung: https://link.springer.com/article/10.1007/s40687-022-00339-x
Link zu diesem Datensatz: urn:nbn:de:bsz:291--ds-387831
hdl:20.500.11880/34955
http://dx.doi.org/10.22028/D291-38783
ISSN: 2522-0144
2197-9847
Datum des Eintrags: 20-Jan-2023
Fakultät: MI - Fakultät für Mathematik und Informatik
Fachrichtung: MI - Informatik
Professur: MI - Prof. Dr. Joachim Weickert
Sammlung:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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