Multifractal analysis of the coupling space of feedforward neural networks

被引：15

作者：

Engel, A

Weigt, M

机构：

[1] Institut für Theoretische Physik, Otto-von-Guericke-Universität Magdeburg PSF 4120, Magdeburg

来源：

PHYSICAL REVIEW E | 1996年 / 53卷 / 03期

关键词：

D O I：

10.1103/PhysRevE.53.R2064

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

Random input patterns induce a partition of the coupling space of feedforward 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. A phase transition in the multifractal spectrum corresponds to the crossover from percolating to nonpercolating cell sizes. instabilities of negative moments are related to the Vapnik-Chervonenkis (VC) dimension [Theor. Prob. Appl. 16, 264 (1971)].

引用

页码：R2064 / R2067

页数：4

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