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.
['Jung-Chao Ban', 'Chih-Hung Chang']
When are two multi-layer cellular neural networks the same?