Simplification of the learning phase in the alpha-beta associative memories

An associative memory is a system that relates input patterns and output patterns, furthermore is able to recover the output vector associated although the input pattern was contaminated by some kind of noise. Alpha Beta associative memories are robust to subtractive and additive noise and are one of the fastest associative memories besides other qualities. In this paper we show a way to reduce the number of operations in the learning phase. The operation alpha used in the learning phase allow us to propose 8 theorems; with those theorems is possible to construct an alternative learning method. By this method, the number of alpha operations needed to learning each pattern is reduced and replaced by assignations, furthermore we also eliminate the min and max operations. This reduces the learning time drastically with either big dimension patterns or a big number of patterns.