Neural networks with high-order connections
Jeferson J. Arenzon, Rita M. C. de Almeida · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1993
We present results for two different kinds of high-order connections between neurons acting as corrections to the Hopfield model. Equilibrium properties are analyzed using the replica mean-field theory and compared with numerical simulations. An optimal learning algorithm for fourth-order connections is given that improves the storage capacity without increasing the weight of the higher-order term. While the behavior of one of the models qualitatively resembles the original Hopfield one, the other presents a new and very rich behavior: depending on the strength of the fourth-order connections and the temperature, the system presents two distinct retrieval regions separated by a gap, as well as several phase transitions. Also, the spin-glass states seems to disppear above a certain value of the load parameter \ensuremath{\alpha}, ${\mathrm{\ensuremath{\alpha}}}_{\mathit{g}}$.