NEURAL NETWORKS WITH HIGH-ORDER CONNECTIONS

We present results for two different kinds of high-order connections b etween neurons acting as corrections to the Hopfield model. Equilibriu m properties are analyzed using the replica mean-field theory and comp ared with numerical simulations. An optimal learning algorithm for fou rth-order connections is given that improves the storage capacity with out increasing the weight of the higher-order term. While the behavior of one of the models qualitatively resembles the original Hopfield on e, the other presents a new and very rich behavior: depending on the s trength of the fourth-order connections and the temperature, the syste m presents two distinct retrieval regions separated by a gap, as well as several phase transitions. Also, the spin-glass states seems to dis appear above a certain value of the load parameter alpha, alpha(g).