Essential rate for approximation by spherical neural networks
We consider the optimal rate of approximation by single hidden feed-forward neural networks on the unit sphere. It is proved that there exists a neural network with n n neurons, and an analytic, strictly increasing, sigmoidal activation function such that the deviation of a Sobolev class W 2 r 2 ( S d ) from the class of neural networks ? n ? , behaves asymptotically as n ? 2 r d ? 1 . Namely, we prove that the essential rate of approximation by spherical neural networks is n ? 2 r d ? 1 .
essential rate approximation neural networks spherical polynomials