Associative recall using a contraction operator

An associative memory can be defined as a transformation between two sets. Under mild conditions, the associative recall problem can be formulated as that of solving an equation of the form y=f (x), where y is known and the corresponding value x is not. Here, the associative recall problem is formulated in this way, and conditions on f are developed such that a contraction operator can be developed which solves the given equation. A specific piecewise-linear function is then chosen, and its associative recall properties are discussed. This associative memory is shown to converge rapidly and to have noise rejection properties and some learning capability