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dc.contributor.author
Vlačić, Verner
dc.contributor.author
Bölcskei, Helmut
dc.date.accessioned
2022-02-08T13:35:29Z
dc.date.available
2021-05-31T14:23:49Z
dc.date.available
2021-05-31T14:26:22Z
dc.date.available
2022-02-08T13:35:29Z
dc.date.issued
2022
dc.identifier.issn
0176-4276
dc.identifier.issn
1432-0940
dc.identifier.other
10.1007/s00365-021-09544-3
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/487741
dc.identifier.doi
10.3929/ethz-b-000487741
dc.description.abstract
This paper addresses the following question of neural network identifiability: Does the input–output map realized by a feed-forward neural network with respect to a given nonlinearity uniquely specify the network architecture, weights, and biases? The existing literature on the subject (Sussman in Neural Netw 5(4):589–593, 1992; Albertini et al. in Artificial neural networks for speech and vision, 1993; Fefferman in Rev Mat Iberoam 10(3):507–555, 1994) suggests that the answer should be yes, up to certain symmetries induced by the nonlinearity, and provided that the networks under consideration satisfy certain “genericity conditions.” The results in Sussman (1992) and Albertini et al. (1993) apply to networks with a single hidden layer and in Fefferman (1994) the networks need to be fully connected. In an effort to answer the identifiability question in greater generality, we derive necessary genericity conditions for the identifiability of neural networks of arbitrary depth and connectivity with an arbitrary nonlinearity. Moreover, we construct a family of nonlinearities for which these genericity conditions are minimal, i.e., both necessary and sufficient. This family is large enough to approximate many commonly encountered nonlinearities to within arbitrary precision in the uniform norm.
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dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Springer
en_US
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
dc.subject
Deep neural networks
en_US
dc.subject
Identifiability
en_US
dc.subject
Sigmoidal nonlinearities
en_US
dc.title
Neural Network Identifiability for a Family of Sigmoidal Nonlinearities
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution 4.0 International
dc.date.published
2021-05-07
ethz.journal.title
Constructive Approximation
ethz.journal.volume
55
en_US
ethz.journal.issue
1
en_US
ethz.journal.abbreviated
Constr Approx
ethz.pages.start
173
en_US
ethz.pages.end
224
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
New York, NY
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02140 - Dep. Inf.technologie und Elektrotechnik / Dep. of Inform.Technol. Electrical Eng.::03610 - Boelcskei, Helmut / Boelcskei, Helmut
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02140 - Dep. Inf.technologie und Elektrotechnik / Dep. of Inform.Technol. Electrical Eng.::03610 - Boelcskei, Helmut / Boelcskei, Helmut
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02140 - Dep. Inf.technologie und Elektrotechnik / Dep. of Inform.Technol. Electrical Eng.::03610 - Boelcskei, Helmut / Boelcskei, Helmut
ethz.date.deposited
2021-05-31T14:23:56Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2022-02-08T13:35:36Z
ethz.rosetta.lastUpdated
2022-03-29T18:43:10Z
ethz.rosetta.versionExported
true
ethz.COinS
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