On the power of Boolean computations in generalized RBF neural networks

Abstract

Generalized radial basis function (RBF) neurons are extensions of the RBF neuron model where the Euclidean norm is replaced by a weighted norm. We study binary-valued variants of generalized RBF neurons and compare their computational power in the Boolean domain with linear threshold neurons. As one of the main results, we show that generalized binary RBF neurons with any weighted norm can compute every Boolean function that is computed by a linear threshold neuron. While this inclusion turns into an equality if the RBF neuron uses the Euclidean norm, we exhibit a weighted norm where the inclusion is proper. Applications of the results yield bounds on the Vapnik–Chervonenkis (VC) dimension of RBF neural networks with binary inputs.