Approximation with spiked random networks

We examine the function approximation properties of the “random neural network model” or GNN. We consider a feedforward bipolar GNN (BGNN) model which has both “positive (excitatory) and negative (inhibitory) neurons” in the output layer, and prove that the BGNN is a universal function approximator. Specifically, for any f∈C([0, 1]^s) and any ε>0, we show that there exists a feedforward BGNN which approximates f uniformly with error less than ε. We also show that after a clamping operation on its output, the feedforward GNN is a universal continuous function approximator