Abstract
This paper presents a new theory that enables one to obtain a set of Boolean functions from one learnt Boolean function. We do this by transposition of the weight matrices of the unit or network once they have learnt a single Boolean function. The methodology we utilise has its root in mathematics and in particular the field of matrix geometric transformations. Here, a transformation of a surface, a plane or a function is a manipulation of the function in such a manner that each point of the transposed function (or 'image') corresponds uniquely to a point in the original function. We develop the theory that enables us to learn Boolean functions without training.
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