A backpropagation and initialization routine for hyperbolic sigma-pi neural networks
Neural, Parallel & Scientific Computations
Uniform Approximation Capabilities of Sum-of-Product and Sigma-Pi-Sigma Neural Networks
ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Advances in Neural Networks
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A feedforward Sigma-Pi neural network with a single hidden layer of m neurons is given by mΣj=1cjg(nΠk=1xk-θkj/λkj) where cj, θkj, λk∈R. We investigate the approximation of arbitrary functions f: Rn→R by a Sigma-Pi neural network in the Lp norm. An Lp locally integrable function g(t) can approximate any given function, if and only if g(t) can not be written in the form Σj=1nΣk=0mαjk(ln|t|)j-1tk.