Abstract

We show that a multiple input, single output, single hidden layer feedforward network with (known) hardwired connections from input to hidden layer, monotone squashing at the hidden layer and no squashing at the output embeds as a special case a "Fourier network" which yields a Fourier series approximation to a given function as its output. Thus, such networks possess all the approximation properties of Fourier series representations. In particular, approximation to any desired accuracy of any square integrable function can be achieved by such a network, using sufficiently many hidden units. In this sense, such networks do not make avoidable mistakes.

Citations