A multifractal phase-space analysis of perceptrons with biased patterns

Abstract

We calculate the multifractal spectrum of the partition of the coupling space of a perceptron induced by random input-output pairs with non-zero mean. From the results we infer the influence of the input and output bias respectively on both the storage and generalization properties of the network. It turns out that the value of the input bias is irrelevant as long as it is different from zero. The generalization problem with output bias is new and shows an interesting two-level scenario. To compare our analytical results with simulations we introduce a simple and efficient algorithm to implement Gibbs learning.

7 pages, Latex, 2 eps-files, submitted to J. Phys. A, new title, enlarged description of the simulation algorithm, typos corrected

References in corpus (4)

• Weight Space Structure and Internal Representations: a Direct Approach to Learning and Generalization in Multilayer Neural Network
• Analytical and Numerical Study of Internal Representations in Multilayer Neural Networks with Binary Weights
• Multifractal Analysis of the Coupling Space of Feed-Forward Neural Networks
• Multifractality and percolation in the coupling space of perceptrons