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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.
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