title: When are two multi-layer cellular neural networks the same?
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.
authors.affiliation: Department of Applied Mathematics, National Dong Hwa University, Hualien 970003, Taiwan, ROC.
authors.forename: Jung-Chao
authors.initials: JC
authors.lastname: Ban
authors.affiliation: Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 81148, Taiwan, ROC. Electronic address: chchang@nuk.edu.tw.
authors.forename: Chih-Hung
authors.initials: CH
authors.lastname: Chang
mesh_terms: D000465:Algorithms; D008959:Models, Neurological; D016571:Neural Networks, Computer
keywords: Hidden layers; Multi-layer cellular neural networks; Sofic shifts; Topological conjugacy; Total amalgamation; Williams classification theorem