Stochastic analysis of the Abe formulation of Hopfield networks.

International audienceThis 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

Stochastic analysis of the Abe formulation of Hopfield networks

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.