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_pr that carries more information than the others. Regardless of the network order p, the elements in T_pr are shown to be those interconnections T that fall within the range of √m, ⩽|T|⩽2√m, where m_s equals the number of stored code words. Memories that use only T_pr can maintain original generalization performance, using less than 50 percent of the total number of interconnections