A SIMPLE GEOMETRICAL BOUND FOR REPLICA SYMMETRY STABILITY IN NEURAL NETWORKS MODELS

Abstract

In the statistical mechanics framework of formal neural networks learning theory, we discuss a very simple geometrical interpretation of the stability line (the AT-line) for the replica symmetric phase. The geometrical bound on the maximal fraction of patterns storable on hyperplanes — which depends only on the local fields distribution — is shown to coincide with the AT-line both for single layer models and for a simple toy model of multilayer net.