Power series and neural-net computing

Kalveram, KTh., Power series and neurat-net computing, Neurocomputing 5 (1993) 165-174. A power series expansion is represented by a threeJayer feedforward network, the number of nodes in the hidden layer conesponding to the number of terms retained in the series, and the synaptic weights in the hidden layer representing the exponents used. The activation functions addrcssed to input, hidden and output nodes are log, anti-log and linear. The training rules applied to determine the weights of the output layer, that means the optimal power series coefficients, are the ordinary delta rule and a least squares based simultaneous leaming rule called lSQ-ruIe. The performance of this network is compared to a three-layer network with the same number of nodes but sigmoidal activation functions, tmined by backpropagation. With respect to the selected four functions to be approximated, the delta rule yields an output error considerably less than the enor of the sigmoid network. Best results, however, are obtained combining the power network with the tSQ-ruIe. In this case, 'performance related to number of training trials' is-on avgrage-about 30,(X)0 times better, compared to backprcpagation.