Optimization of Binary-Output CNNs: First Step of an Analytical Design Process

A binary-output cellular neural network implements a threshold-logic function. It maps every input-vector to one vertice of a hypercube and uses a hyperplane to determine its class. The task achieved by a given cellular neural network is considered non-optimal if the hyperplane is poorly positioned in the hypercube, being unnecessarily close to one of its vertices. This property is crucial since cellular neural networks deal with analog signals, meaning that even binary values (namely, the inputs and the initial internal states) will slightly vary about their mean value. This paper presents an algorithm which partially solves this optimization problem. It is based on an original Boolean representation of the threshold-logic function achieved by a cellular neural network. By analyzing its functional symmetries, this algorithm tweaks the original hyperplane to make it fit them. It results in an improved implementation of the threshold-logic function. This algorithm turns out to be the first step of an analytical design method, capable of computing the best hyperplane position, out of a non-optimal one.