Function Approximation by Random Neural Networks with a Bounded Number of Layers

This paper discusses the function approximation properties of the “Gelenbe” random neural network (GNN).^5,6,9 We use two extensions of the basic model: the bipolar GNN (BGNN)⁷ and the clamped GNN (CGNN). 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. With these constraints we show that the feedforward CGNN and the BGNN with s hidden layers (total of s + 2 layers) can uniformly approximate continuous functions of s variables.