Approximation error of single hidden layer neural networks with fixed weights

Neural networks with finitely many fixed weights have the universal approximation property under certain conditions on compact subsets of the d-dimensional Euclidean space, where approximation process is considered. Such conditions were delineated in our paper [26]. But for many compact sets it is impossible to approximate multivariate functions with arbitrary precision and the question on estimation or efficient computation of approximation error arises. This paper provides an explicit formula for the approximation error of single hidden layer neural networks with two fixed weights. •An explicit formula for computing the approximation error of single hidden layer neural networks is obtained.•A recipe for the efficient computation of approximation error is provided.•Practical and helpful examples for single hidden layer neural network approximation with fixed weights are given.