NDLI: Multistability and Instability of Neural Networks With Discontinuous Nonmonotonic Piecewise Linear Activation Functions

Content Provider	IEEE Xplore Digital Library
Author	Xiaobing Nie Wei Xing Zheng
Copyright Year	2012
Abstract	In this paper, we discuss the coexistence and dynamical behaviors of multiple equilibrium points for recurrent neural networks with a class of discontinuous nonmonotonic piecewise linear activation functions. It is proved that under some conditions, such n-neuron neural networks can have at least 5ⁿ equilibrium points, 3ⁿ of which are locally stable and the others are unstable, based on the contraction mapping theorem and the theory of strict diagonal dominance matrix. The investigation shows that the neural networks with the discontinuous activation functions introduced in this paper can have both more total equilibrium points and more locally stable equilibrium points than the ones with continuous Mexican-hat-type activation function or discontinuous two-level activation functions. An illustrative example with computer simulations is presented to verify the theoretical analysis.
Starting Page	2901
Ending Page	2913
Page Count	13
File Size	3017899
File Format	PDF
ISSN	2162237X
Volume Number	26
Issue Number	11
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Biological neural networks Mathematical model Learning systems Pattern recognition Eigenvalues and eigenfunctions Computer simulation neural networks. Discontinuous nonmonotonic piecewise linear activation functions instability multistability neural networks
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Computer Networks and Communications Computer Science Applications Software

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