Deformation Stability of Deep Convolutional Neural Networks on Sobolev Spaces

Michael Koller, Johannes Grobmann, Ullrich Monich, Holger Boche

Publikation: Beitrag in Buch/Bericht/KonferenzbandKonferenzbeitragBegutachtung

3 Zitate (Scopus)

Abstract

Our work is based on a recently introduced mathematical theory of deep convolutional neural networks (DCNNs). It was shown that DCNN s are stable with respect to deformations of bandlimited input functions. In the present paper, we generalize this result: We prove deformation stability on Sobolev spaces. Further, we show a weak form of deformation stability for the whole input space L2(Rd). The basic components of DCNNs are semi-discrete frames. For practical applications, a concrete choice is necessary. Therefore, we conclude our work by suggesting a construction method for semi-discrete frames based on bounded uniform partitions of unity (BUPUs) and give a specific example that uses B-splines.

OriginalspracheEnglisch
Titel2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Proceedings
Herausgeber (Verlag)Institute of Electrical and Electronics Engineers Inc.
Seiten6872-6876
Seitenumfang5
ISBN (Print)9781538646588
DOIs
PublikationsstatusVeröffentlicht - 10 Sept. 2018
Extern publiziertJa
Veranstaltung2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Calgary, Kanada
Dauer: 15 Apr. 201820 Apr. 2018

Publikationsreihe

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Band2018-April
ISSN (Print)1520-6149

Konferenz

Konferenz2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018
Land/GebietKanada
OrtCalgary
Zeitraum15/04/1820/04/18

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