THE STATISTICAL-MECHANICS OF THE ISING PERCEPTRON

We investigate the problem of loading a single-layered perceptron of Ising (+/-1) weights, focusing on the cases of linear and binary output neurons. Previous studies of this problem have been made using the canonical ensemble, which in many cases require the breaking of replica symmetry. We consider here an alternative approach, based on the microcanonical ensemble, and show that many results that were obtained previously using replica symmetry breaking within the canonical ensemble can be easily obtained using the replica-symmetric assumption within the microcanonical ensemble. Since the nature of the replica symmetry breaking in many of the models with discrete weights is similar, we believe that our results can immediately be extended to other cases such as learning a rule from examples, and utilizing discrete weights of larger synaptic depth.