Stochastic analysis of the Abe formulation of Hopfield networks.

Marie Kratz; Miguel Atencia; Gonzalo Joya

hal-00179439, version 1

Stochastic analysis of the Abe formulation of Hopfield networks.

Marie Kratz () ^1, 2, 3, Miguel Atencia () ⁴, Gonzalo Joya () ⁵

European Symposium on Artificial Neural Networks (2005) x

Abstract: This work studies the influence of random noise in the application of Hopfield networks to combinatorial optimization. It has been suggested that the Abe formulation, rather than the original Hopfield formulation, is better suited to optimization, but the eventual presence of noise in the connection weights of this model has not been considered up to now. This consideration leads to a model that is formulated as a stochastic differential equation. In the stochastic setting, the analysis reveals that the model is stable, and the states converge towards an attractive set, assuming the noise intensity is bounded. The relation of the attractor with that of the deterministic model requires further study.

1: Mathématiques appliquées Paris 5 (MAP5)
CNRS : UMR8145 – Université Paris V - Paris Descartes
2: Statistique Appliquée et MOdélisation Stochastique (SAMOS)
Université Paris I - Panthéon-Sorbonne
3: Modélisation Appliquée, Trajectoires Institutionnelles et Stratégies Socio-Économiques (MATISSE)
CNRS : UMR8595 – Université Paris I - Panthéon-Sorbonne
4: Departamento de Matemática Aplicada
Universidad de Málaga
5: Departamento de Tecnología Electrónica
Universidad de Málaga

hal-00179439, version 1
http://hal.archives-ouvertes.fr/hal-00179439
oai:hal.archives-ouvertes.fr:hal-00179439
From: Marie Kratz <>
Submitted on: Monday, 15 October 2007 15:02:25
Updated on: Tuesday, 16 October 2007 15:25:51

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