Basic dynamical properties of cross-coupled Hopfield nets

The authors clarify basic dynamical properties of cross-coupled Hopfield nets (CCHNs) using the simple CCHN in which two Hopfield nets (HNs) are connected to each other via two-layered feedforward neural networks. In the case that each HN composed of two units has two point attractors and each equilibrium state of one HN has a one-to-one mapping relation to that of the other, the authors investigate which of the equilibrium points the state parameters converge onto. They study the nature of the energy plane in one HN for the variation of two state-parameters in the other HN. The comparison with the original HN shows that energy planes in both HNs are dynamically varied by interactions of the network states. After sufficient learning, the CCHN´s output converges onto a desired stable state so as to be satisfied with a given relation between two HNs. In the simple CCHN employed, the connection weights of internetworks can be regarded as those of the original HN itself. Therefore, the simple CCHN gives a method for determining connection weights in HNs efficiently