Cellular Neural Networks: A Unified Analysis of the Stability Issue

A cellular neural network (CNN) is a recurrent neural network model. Like other models of this kind, the complete stability issue remains an open question. Leaving aside the unstable cyclic output case, the existence of stable outputs itself, known as the partial stability problem, ends up being a quite reliable guarantee for complete stability. Yet, no necessary and sufficient condition for partial stability has been established either. As a workaround, the past ten years provided several sufficient conditions. Some were ported from other neural network models, whereas others came out of various mathematical properties of CNNs. Consequently, the available criteria are disparate and hence, do not help finding any broader criterion. Based on a new viewpoint of the neighborhood consistency condition [1], this paper introduces a design principle of partial stability criteria for CNNs. Every of the currently established partial stability criteria, are then shown to be quite simple derivations of this principle, so opening a new way towards the complete stability problem.