  George Cybenko's landmark 1989 paper showed that there exists a feedforward
neural network, with exactly one hidden layer (and a finite number of neurons),
that can arbitrarily approximate a given continuous function $f$ on the unit
hypercube. The paper did not address how to find the weight/parameters of such
a network, or if finding them would be computationally feasible. This paper
outlines an algorithm for a neural network with exactly one hidden layer to
reconstruct any continuous scalar or vector valued continuous function.
