Magnetic order and categorization in attractor neural networks

Abstract The thermodynamic behavior of an extended Hopfield model for an attractor neural network with units in three Ising-states Si and symmetrically random diluted synaptic connections Jijd, between units i and j, is discussed here in the thermodynamic limit within replica-symmetric mean-field theory. A macroscopic set of random patterns in a two-level hierarchical structure of ancestors and descendents is used to construct the synaptic connections and to determine the magnetic order associated with the recognition of ancestors.