  In this paper we consider a new class of RBF (Radial Basis Function) neural
networks, in which smoothing factors are replaced with shifts. We prove under
certain conditions on the activation function that these networks are capable
of approximating any continuous multivariate function on any compact subset of
the $d$-dimensional Euclidean space. For RBF networks with finitely many fixed
centroids we describe conditions guaranteeing approximation with arbitrary
precision.
