Decomposition of Rotor Hopfield Neural Networks Using Complex Numbers

A complex-valued Hopfield neural network (CHNN) is a multistate model of a Hopfield neural network. It has the disadvantage of low noise tolerance. Meanwhile, a symmetric CHNN (SCHNN) is a modification of a CHNN that improves noise tolerance. Furthermore, a rotor Hopfield neural network (RHNN) is an extension of a CHNN. It has twice the storage capacity of CHNNs and SCHNNs, and much better noise tolerance than CHNNs, although it requires twice many connection parameters. In this brief, we investigate the relations between CHNN, SCHNN, and RHNN; an RHNN is uniquely decomposed into a CHNN and SCHNN. In addition, the Hebbian learning rule for RHNNs is decomposed into those for CHNNs and SCHNNs.