Multifractal Analysis of the Coupling Space of Feed-Forward Neural Networks

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 $f(\alpha )$ 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.

arXiv comment10 pages, Latex, submitted to PRL

References in corpus (2)

• Weight Space Structure and Internal Representations: a Direct Approach to Learning and Generalization in Multilayer Neural Network
• Block diagonalizing ultrametric matrices

Cited by in corpus (7)

• Techniques of replica symmetry breaking and the storage problem of the McCulloch-Pitts neuron
• Weight space structure and analysis using a finite replica number in the Ising perceptron
• On the VC-dimension of neural networks with binary weights
• Multifractality and percolation in the coupling space of perceptrons
• On the Vapnik-Chervonenkis dimension of the Ising-perceptron
• A multifractal phase-space analysis of perceptrons with biased patterns
• Multifractal analysis of perceptron learning with errors