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Media type:
E-Article
Title:
Continuous limits of residual neural networks in case of large input data
Contributor:
Herty, Michael;
Thünen, Anna;
Trimborn, Torsten;
Visconti, Giuseppe
imprint:
Walter de Gruyter GmbH, 2022
Published in:Communications in Applied and Industrial Mathematics
Language:
English
DOI:
10.2478/caim-2022-0008
ISSN:
2038-0909
Origination:
Footnote:
Description:
<jats:title>Abstract</jats:title>
<jats:p>Residual deep neural networks (ResNets) are mathematically described as interacting particle systems. In the case of infinitely many layers the ResNet leads to a system of coupled system of ordinary differential equations known as neural differential equations. For large scale input data we derive a mean–field limit and show well–posedness of the resulting description. Further, we analyze the existence of solutions to the training process by using both a controllability and an optimal control point of view. Numerical investigations based on the solution of a formal optimality system illustrate the theoretical findings.</jats:p>