When are two multi-layer cellular neural networks the same?. (July 2016)

• Record Type: Journal Article
• Authors: Ban, Jung-Chao; Chang, Chih-Hung
• Is Part Of: Neural networks. Volume 79(2016)
• Page Start: 12
• Page End: 19
• Publication Date: 2016-07
• Subjects: primary 34A33 37B10 -- secondary 11K55 47A35; Multi-layer cellular neural networks -- Hidden layers -- Sofic shifts -- Topological conjugacy -- Total amalgamation -- Williams classification theorem; Neural computers -- Periodicals; Neural networks (Computer science) -- Periodicals; Neural networks (Neurobiology) -- Periodicals; Nervous System -- Periodicals; Ordinateurs neuronaux -- Périodiques; Réseaux neuronaux (Informatique) -- Périodiques; Réseaux neuronaux (Neurobiologie) -- Périodiques; Neural computers; Neural networks (Computer science); Neural networks (Neurobiology); Periodicals; 006.32
• DOI: 10.1016/j.neunet.2016.03.005
• Languages: English
• ISSNs: 0893-6080

Abstract

Abstract: This paper aims to characterize whether a multi-layer cellular neural network is of deep architecture; namely, when can an n -layer cellular neural network be replaced by an m -layer cellular neural network for m < n yet still preserve the same output phenomena? From a mathematical point of view, such characterization involves investigating whether the topological structure of two (or multiple) layers is conjugate. A decision procedure that addresses the necessary and sufficient condition for the topological conjugacy between two layers in a network is revealed.