An Algorithm for Approximating Continuous Functions on Compact Subsets with a Neural Network with one Hidden Layer
This addresses a computational gap in universal approximation theory for researchers in neural networks, though it is incremental as it builds on Cybenko's foundational result.
The paper tackles the problem of constructing a neural network with one hidden layer to approximate continuous functions, providing an algorithm to find the network parameters, which was not addressed in prior work.
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.