Stable Patterns Realized by a Class of One-Dimensional Two-Layer CNNs

Abstract

Stable patterns that can be realized by a class of 1-D two-layer cellular neural networks (CNNs) are studied in this paper. We first introduce the notions of potentially stable pattern, potentially stable local pattern, and local pattern set. We then show that all of 256 possible sets can be realized as the local pattern set of the two-layer CNN, while only 59 sets can be realized as the local pattern set of the single-layer CNN. We also propose a simple way to optimize the template values of the CNN, which is formulated as a set of linear programming problems, and present the obtained values for all of 256 sets.

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“…4 (Palm, 2012; Aghdam and Heravi, 2017). Several studies and engineering applications have indicated that a NN of two hidden layers with few neurons can replace a network with numerous neurons in a hidden layer (Willis et al, 1991;Hush et al, 1993;Ji andPsaltis, 1998: Huang, 2003;Takahashi et al, 2008;Wang et al, 2019;Chu, et al, 2020: Fei and. In the study, the framework of CNN with two hidden layers is performed as in Fig.…”

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“…The publications during the past decades clearly show that the research on the twodimensional CNNs has attracted the overwhelming attentions of the researchers. As a result, obviously inadequate research efforts have been made on either studying some other CNN models such as the one-dimensional CNN [27], the three-dimensional CNN and the CNN even in higher dimensions or continuously exploring the potential applications of these models.…”

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