Higher-order neural networks and the arithmetic transform

Neural networks are currently enjoying a resurgence of interest which is manifesting itself by the large number of papers, books and conferences. In all of this research only a small proportion seems to deal with the mathematical theory behind the networks-the majority being concerned with applications or implementations. The wealth of theoretical research that was done in the 1960´s in fields such as cybernetics and threshold logic seems to have been neglected. The paper brings together ideas from cybernetic modelling, threshold logic design and multi-layer perceptrons to try to establish a coherent view on the subject