Two approximations to learning from examples

We investigate the learning of a rule from examples of the case of boolean perceptron. Previous studies of this problem have been made using the full quenched theory. We consider here two alternative approaches that can be ap plied easily. The two-replicas interactions approach considerably improves upon the well-known first-order approach. The mean field approach proved so me results that have been obtained previously using the complex full quench ed theory. Both approximations have been applied to both continuous weights and discrete weights perceptron.