Multifractal analysis of perceptron learning with errors

Abstract

Random input patterns induce a partition of the coupling space of a perceptron into cells labeled by their output sequences. Learning some data with a maximal error rate leads to clusters of neighboring cells. By analyzing the internal structure of these clusters with the formalism of multifractals, we can handle different storage and generalization tasks for lazy students and absent-minded teachers within one unified approach. The results also allow some conclusions on the spatial distribution of cells.