Approximation by random networks with bounded number of layers

This paper discusses the function approximation properties of the Gelenbe random neural network (GNN). We use an extension of the basic model: the bipolar GNN (BGNN). We limit the networks to being feedforward and consider the case where the number of hidden layers does not exceed the number of input layers. We show that the feedforward BGNN with s hidden layers (total of s+2 layers) can uniformly approximate continuous functions of s variables.