Complex-valued Hopfield associative memories with hybrid connections

Abstract

A complex-valued Hopfield associative memory (CVHAM) has been studied as a multistate model of neural associative memory. The weak noise tolerance is a disadvantage of CVHAM. A symmetric complex-valued Hopfield associative memory (SCVHAM), a modification of CVHAM, provides much better noise tolerance than CVHAM, though the projection rule is not applicable. In this work, a hybrid complex-valued Hopfield associative memory (HCVHAM) is proposed. An HCVHAM is a combination of a CVHAM and an SCVHAM, and takes both advantages of CVHAMs and SCVHAMs. The quaternion projection rule, which was first introduced to rotor Hopfield associative memories, is applied to an HCVHAM. Computer simulations show that the HCVHAMs provide excellent noise tolerance.