Multifractal Analysis of the Coupling Space of Feed-Forward Neural Networks
Condensed Matter
2009-10-28 v1 q-bio
Abstract
Random input patterns induce a partition of the coupling space of feed-forward neural networks into different cells according to the generated output sequence. For the perceptron this partition forms a random multifractal for which the spectrum can be calculated analytically using the replica trick. Phase transition in the multifractal spectrum correspond to the crossover from percolating to non-percolating cell sizes. Instabilities of negative moments are related to the VC-dimension.
Keywords
Cite
@article{arxiv.cond-mat/9512176,
title = {Multifractal Analysis of the Coupling Space of Feed-Forward Neural Networks},
author = {A. Engel and M. Weigt},
journal= {arXiv preprint arXiv:cond-mat/9512176},
year = {2009}
}
Comments
10 pages, Latex, submitted to PRL