Function Approximation with Spiked Random Networks

This paper examines the function approximation properties of the “random neural-network model” (RNN) whose output is computed from the firing probabilities of selected neurons. We consider a feedforward Bipolar Random Neural Network (BGNN) model which has both “positive and negative neurons” in the output layer, and prove that it is a universal function approximator for bounded and continuous functions. Specifically, for any continuous and bounded function f, we constructively prove that there exists a feedforward BGNN which approximates f uniformly with error less than a given fixed epsilon. We also show that after some appropriate clamping operation on its output, the feedforward RNN, without the artifice of negative neurone,  is also a universal function approximator.