L-p approximation of Sigma-Pi neural networks

A feedforward Sigma-Pi neural networks with a single hidden layer of m nenr al is given by Sigma (m)(j=1) c(j)g (Pi (n)(k=1) x(k) - theta (j)(k)/lambda (j)(k)) where c(j), theta (j)(k), lambda (k) epsilon R. In this paper, we investiga te the approximation of arbitrary functions f: R-n --> R by a Sigma-Pi neur al networks in the L-p norm. For an L-p locally integrable function g(t) ca n approximation any given function, if and only if g(t) can not be written in the form Sigma (n)(j=1) Sigma (m)(k=0) a(jk)(ln \t\)(j-1) t(k).