Learning from noisy data: An exactly solvable model

Abstract
Exact results are derived for the learning of a linearly separable rule with a single-layer perceptron. We consider two sources of noise in the training data: the random inversion of the example outputs and weight noise in the teacher network. In both scenarios, we investigate on-line learning schemes that utilize only the latest in a sequence of uncorrelated random examples for an update of the student weights. We study Hebbian learning as well as on-line algorithms that achieve an optimal decrease of the generalization error. The latter realize an asymptotic decay of the generalization error that coincides, apart from prefactors, with the one found for off-line schemes.