Complete Stability of Delayed Recurrent Neural Networks With New Wave-Type Activation Functions.

Yan, Z; Sun, W; Guo, W; Li, B; Wen, S; Cao, J

Complete Stability of Delayed Recurrent Neural Networks With New Wave-Type Activation Functions.

Yan, Z Sun, W Guo, W Li, B Wen, S

Cao, J

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Publisher:: Institute of Electrical and Electronics Engineers (IEEE)
Publication Type:: Journal Article
Citation:: IEEE Trans Neural Netw Learn Syst, 2024, PP, (99), pp. 1-13
Issue Date:: 2024-05-06

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Field	Value	Language
dc.contributor.author	Yan, Z
dc.contributor.author	Sun, W
dc.contributor.author	Guo, W
dc.contributor.author	Li, B
dc.contributor.author	Wen, S https://orcid.org/0000-0001-8077-7001
dc.contributor.author	Cao, J
dc.date.accessioned	2024-08-07T05:31:24Z
dc.date.available	2024-08-07T05:31:24Z
dc.date.issued	2024-05-06
dc.identifier.citation	IEEE Trans Neural Netw Learn Syst, 2024, PP, (99), pp. 1-13
dc.identifier.issn	2162-237X
dc.identifier.issn	2162-2388
dc.identifier.uri	http://hdl.handle.net/10453/180322
dc.description.abstract	Activation functions have a significant effect on the dynamics of neural networks (NNs). This study proposes new nonmonotonic wave-type activation functions and examines the complete stability of delayed recurrent NNs (DRNNs) with these activation functions. Using the geometrical properties of the wave-type activation function and subsequent iteration scheme, sufficient conditions are provided to ensure that a DRNN with n neurons has exactly (2m + 3)n equilibria, where (m + 2)n equilibria are locally exponentially stable, the remainder (2m + 3)n - (m + 2)n equilibria are unstable, and a positive integer m is related to wave-type activation functions. Furthermore, the DRNN with the proposed activation function is completely stable. Compared with the previous literature, the total number of equilibria and the stable equilibria significantly increase, thereby enhancing the memory storage capacity of DRNN. Finally, several examples are presented to demonstrate our proposed results.
dc.format	Print-Electronic
dc.language	eng
dc.publisher	Institute of Electrical and Electronics Engineers (IEEE)
dc.relation.ispartof	IEEE Trans Neural Netw Learn Syst
dc.relation.isbasedon	10.1109/TNNLS.2024.3394854
dc.rights	info:eu-repo/semantics/restrictedAccess
dc.title	Complete Stability of Delayed Recurrent Neural Networks With New Wave-Type Activation Functions.
dc.type	Journal Article
utslib.citation.volume	PP
utslib.location.activity	United States
pubs.organisational-group	University of Technology Sydney
pubs.organisational-group	University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	University of Technology Sydney/Strength - AAII - Australian Artificial Intelligence Institute
pubs.organisational-group	University of Technology Sydney/All Manual Groups
pubs.organisational-group	University of Technology Sydney/All Manual Groups/Australian Artificial Intelligence Institute (AAII)
utslib.copyright.status	in_progress	*
dc.date.updated	2024-08-07T05:31:23Z
pubs.issue	99
pubs.publication-status	Published online
pubs.volume	PP
utslib.citation.issue	99

Abstract:

Activation functions have a significant effect on the dynamics of neural networks (NNs). This study proposes new nonmonotonic wave-type activation functions and examines the complete stability of delayed recurrent NNs (DRNNs) with these activation functions. Using the geometrical properties of the wave-type activation function and subsequent iteration scheme, sufficient conditions are provided to ensure that a DRNN with n neurons has exactly (2m + 3)n equilibria, where (m + 2)n equilibria are locally exponentially stable, the remainder (2m + 3)n - (m + 2)n equilibria are unstable, and a positive integer m is related to wave-type activation functions. Furthermore, the DRNN with the proposed activation function is completely stable. Compared with the previous literature, the total number of equilibria and the stable equilibria significantly increase, thereby enhancing the memory storage capacity of DRNN. Finally, several examples are presented to demonstrate our proposed results.

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http://hdl.handle.net/10453/180322