Reduction of interconnection weights in higher order associative memory networks

The existence of principal connection weights Tpr useful in solving the problem of proliferation of weights in higher-order Hebbian-type associative memories is introduced. Among all connection weights T based on the outer-product rule, it is shown that those weights near √M, where M=number of stored patterns, contain, more information than the others. The recall capability of Hopfield associative memories which use only principal weights Tpr, where Tpr∈T and √M⩽||Tpr||⩽M, is investigated by a statistical method and computer simulations. It is shown how such memories can maintain original recall capability using less than 50% of the original number of connection weights