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

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 w...

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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems 2024-05, Vol.PP, p.1-13
Main Authors: Yan, Zepeng, Sun, Wen, Guo, Wanli, Li, Biwen, Wen, Shiping, Cao, Jinde
Format: Article
Language:English
Subjects:
Artificial neural networks
Complete stability
delayed recurrent neural network (DRNN)
Delays
Neurons
Numerical stability
Stability criteria
Sun
Thermal stability
time-varying delay
wave-type activation function
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Summary: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.
ISSN:2162-237X
2162-2388
DOI:10.1109/TNNLS.2024.3394854