Principal interconnections in higher order Hebbian-type associative memories

The existence of principal interconnections useful in solving the proliferation problem in higher order Hebbian-type associative memories is introduced. Among all legal interconnections, the author proves there exists a subset T/sub pr/ that carries more information than the others. Regardless of the network order p, the elements in T/sub pr/ are shown to be those interconnections T that fall within the range of /spl radic/m, /spl les/|T|/spl les/2/spl radic/m, where m/sub s/ equals the number of stored code words. Memories that use only T/sub pr/ can maintain original generalization performance, using less than 50 percent of the total number of interconnections.