Let q ≥ 1 be an integer, Sq be the unit sphere embedded in the Euclidean space Rq+1. A Zonal Function (ZF) network with an activation function φ : [−1, 1] → R and n neurons is a function on Sq of the form x 7→ nk=1 akφ(x · ξk), where ak’s are real numbers, ξk’s are points on Sq. We consider the activation functions φ for which the coefficients {φ̂(`)} in… (More)