RAM-based Sigma-pi nets for high accuracy function mapping

We investigate the use of digital “Higher Order” Sigma-pi nodes and study continuous input RAM-based Sigma-pi units trained with the backpropagation training regime to learn functions to a high accuracy, using these hardware realisable units which may be implemented in microelectronic technology. One of our goals was to achieve accuracies of better than one percent for target output functions in the range Y∈[0,1]. This is equivalent to an average mean square error (MSE) over all training vectors of 0.0001 or an error modulus of 0.01. We present a development of a Sigma-pi node which enables us to provide high accuracy outputs utilising the cubic node´s methodology of storing quantised weights (site-values) in locations that are stored in RAM-based units. The networks we present are trained with the backpropagation training regime that may be implemented on-line in hardware. One of the novelties of this article is that we show how one may utilise the bounded quantised site-values (weights) of Sigma-pi nodes to enable training of these neurocomputing systems to be relatively simple. We do this by using pre-calculated constrained look-up tables to train these nets