Domain Dynamics in Hopfield Model

We propose a domain model of a neural network, in which individual spin-neurons are joined into larger-scale aggregates, the so-called domains. The updating rule in the domain model is defined by analogy with the usual spin dynamics: if the state of a domain in an inhomogeneous local field is unstable, then it flips, in the opposite case its state undergoes no changes. The number of stable states of the domain network grows linearly with the domain's size k, where k is the number of spins in the domain. We show that the proposed model is effective for optimization problems, since the use of domain dynamics lowers the number of calculations in k
²
times and allows one to find deeper minima than the standard Hopfield model does.