Learning and generalization in a linear perceptron stochastically trained with noisy data

A linear perceptron is stochastically trained on a corrupted training data set; this enables the effect of noise on the data to be studied. The average properties of the network are calculated using the Gardner method following Seung et al. A weight decay term is added to the training energy and the effect on generalization studied and compared with previously known results. A prescription for setting the optimal weight decay parameter at finite temperature is presented. The results also suggest an initial temperature for an annealing schedule.