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where ''N'' is the number of neurons in the hidden layer, <math>\mathbf c_i</math> is the center vector for neuron ''i'', and <math>a_i</math> are the weights of the linear output neuron. In the basic form all inputs are connected to each hidden neuron. The norm is typically taken to be the [[Euclidean distance]] and the basis function is taken to be [[Normal distribution|Gaussian]]
:<math> \rho \big ( \left \Vert \mathbf{x} - \mathbf{c}_i \right \Vert \big ) = \exp \left[ -\beta \left \Vert \mathbf{x} - \mathbf{c}_i \right \Vert ^2 \right] </math>.
The Gaussian basis functions are local in the sense that
:<math>\lim_{||x|| \to \infty}\rho(\left \Vert \mathbf{x} - \mathbf{c}_i \right \Vert) = 0</math>
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