Structure-preserving deep learning

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dc.citation.issue5
dc.citation.volume32
dc.contributor.authorCelledoni E
dc.contributor.authorEhrhardt MJ
dc.contributor.authorEtmann C
dc.contributor.authorMcLachlan RI
dc.contributor.authorOwren B
dc.contributor.authorSchonlieb CB
dc.contributor.authorSherry F
dc.date.accessioned2023-11-20T22:24:22Z
dc.date.accessioned2024-07-25T06:39:18Z
dc.date.available2021-05-27
dc.date.available2023-11-20T22:24:22Z
dc.date.available2024-07-25T06:39:18Z
dc.date.issued2021-10
dc.description.abstractOver the past few years, deep learning has risen to the foreground as a topic of massive interest, mainly as a result of successes obtained in solving large-scale image processing tasks. There are multiple challenging mathematical problems involved in applying deep learning: most deep learning methods require the solution of hard optimisation problems, and a good understanding of the trade-off between computational effort, amount of data and model complexity is required to successfully design a deep learning approach for a given problem.. A large amount of progress made in deep learning has been based on heuristic explorations, but there is a growing effort to mathematically understand the structure in existing deep learning methods and to systematically design new deep learning methods to preserve certain types of structure in deep learning. In this article, we review a number of these directions: some deep neural networks can be understood as discretisations of dynamical systems, neural networks can be designed to have desirable properties such as invertibility or group equivariance and new algorithmic frameworks based on conformal Hamiltonian systems and Riemannian manifolds to solve the optimisation problems have been proposed. We conclude our review of each of these topics by discussing some open problems that we consider to be interesting directions for future research.
dc.description.confidentialfalse
dc.edition.editionOctober 2021
dc.format.pagination888-936
dc.identifier.author-urlhttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000693800500009&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=c5bb3b2499afac691c2e3c1a83ef6fef
dc.identifier.citationCelledoni E, Ehrhardt MJ, Etmann C, Mclachlan RI, Owren B, Schonlieb CB, Sherry F. (2021). Structure-preserving deep learning. European Journal of Applied Mathematics. 32. 5. (pp. 888-936).
dc.identifier.doi10.1017/S0956792521000139
dc.identifier.eissn1469-4425
dc.identifier.elements-typejournal-article
dc.identifier.issn0956-7925
dc.identifier.numberPII S0956792521000139
dc.identifier.urihttps://mro.massey.ac.nz/handle/10179/70624
dc.languageEnglish
dc.publisherCambridge University Press
dc.publisher.urihttps://www.cambridge.org/core/journals/european-journal-of-applied-mathematics/article/structurepreserving-deep-learning/15384A9F2776B2D1C1F1D3CDA390D779
dc.relation.isPartOfEuropean Journal of Applied Mathematics
dc.rightsCC BY 4.0
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectDeep learning
dc.subjectordinary differential equations
dc.subjectoptimal control
dc.subjectstructure-preserving methods
dc.titleStructure-preserving deep learning
dc.typeJournal article
pubs.elements-id446044
pubs.organisational-groupOther
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