Multifractal analysis of perceptron learning with errors

Details Multifractal analysis of perceptron learning with errors Multifractal analysis of perceptron learning with errors

1997-07-17

arxiv.org/abs/cond-mat/9707178v2

Phys. Rev E57, 955 (1998)

Physics

Condensed Matter

Disordered Systems and Neural Networks

11 pages, RevTex, 3 eps figures, version to be published in Phys. Rev. E 01Jan98

Scientific paper

10.1103/PhysRevE.57.955

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.

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