arXiv:2510.06372v1 Announce Type: new
Abstract: We provide an upper bound on the number of neurons required in a shallow
neural network to approximate a continuous function on a compact set with a
given accuracy. This method, inspired by a specific proof of the
Stone-Weierstrass theorem, is constructive and more general than previous
bounds of this character, as it applies to any continuous function on any
compact set.