Neural-network model composed of multidimensional spin neurons
Yasuyuki Nakamura, K. Torii, Toyonori Munakata · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1995
As an extension of the Hopfield model, we propose a neural network composed of D-dimensional spin neurons (D\ensuremath{\ge}1). Our model is equivalent to the Hopfield model in the case of D=1 and is related to the clock neural network in the case of D=2. We derive the free energy of our model using the replica symmetric theory. When a finite number of patterns are embedded they are found to be retrievable if the tempeature T is lower than 1/D. The phase diagram and the storage capacity of the network are also obtained with the storage capacity ${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$=0.0743 (D=2) and ${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$=0.0432 (D=3) for T=0.