Title :
Permitted and Forbidden Sets in Discrete-Time Linear Threshold Recurrent Neural Networks
Author :
Yi, Zhang ; Zhang, Lei ; Yu, Jiali ; Tan, Kok Kiong
Author_Institution :
Coll. of Comput. Sci., Sichuan Univ., Chengdu
fDate :
6/1/2009 12:00:00 AM
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.
Keywords :
discrete time systems; linear systems; recurrent neural nets; set theory; digital hardware; discrete time linear threshold recurrent neural networks; forbidden sets; linear threshold transfer function; multiattractivity; permitted sets; Complete convergence; discrete-time recurrent neural networks; forbidden set; linear threshold; multiattractivity; permitted set; Algorithms; Computer Simulation; Feedback; Linear Models; Neural Networks (Computer); Pattern Recognition, Automated;
Journal_Title :
Neural Networks, IEEE Transactions on
DOI :
10.1109/TNN.2009.2014373