An equivalence between multi-layer perceptrons with step function type nonlinearity and a class of cellular neural networks

It is shown that, to any multilayer perceptron with step function type nonlinearity, an equivalent cellular neural network (CNN) can be constructed. Equivalence means that, for the same input and after finite time, the CNN will produce the same output as the perceptron with a probability which can be designed to be arbitrarily close to one. This result shows that CNNs, of which only a specialized subclass is exploited here, are much more general and powerful architecture than perceptrons, and it allows some theorems on and applications of perceptrons to be carried over to CNNs