SOME NEW RESULTS ON NEURAL-NETWORK APPROXIMATION

We show that standard feedforward networks with as few as a single hidden layer can uniformly approximate continuous functions on compacta provided that the activation function psi is locally Riemann integrable and nonpolynomial, and have universal L(p)(mu) approximation capabilities for finite and compactly supported input environment measures mu provided that psi is locally bounded and nonpolynomial. In both cases, the input-to-hidden weights and hidden layer biases can be constrained to arbitrarily small sets; if in addition psi is locally analytic a single universal bias will do.