Permitted and forbidden sets in discrete-time linear threshold recurrent neural networks

Authors:
Zhang Yi;Lei Zhang;Jiali Yu;Kok Kiong Tan
Affiliations:
College of Computer Science, Sichuan University, Chengdu, China;Department of Computer Science and Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong;School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China;Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore
Venue:
IEEE Transactions on Neural Networks
Year:
2009

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Abstract

The concepts of permitted and forbidden sets enable a new perspective of the memory in neural networks. Such concepts exhibit interesting dynamics in recurrent neural networks. This paper studies the basic theories of permitted and forbidden sets of the linear threshold discrete-time recurrent neural networks. The linear threshold transfer function has been regarded as an adequate transfer function for recurrent neural networks. Networks with this transfer function form a class of hybrid analog and digital networks which are especially useful for perceptual computations. Networks in discrete time can directly provide algorithms for efficient implementation in digital hardware. The main contribution of this paper is to establish foundations of permitted and forbidden sets. Necessary and sufficient conditions for the linear threshold discrete-time recurrent neural networks are obtained for complete convergence, existence of permitted and forbidden sets, as well as conditionally multiattractivity, respectively. Simulation studies explore some possible interesting practical applications.