On the Local-Field Distribution in Attractor Neural Networks

In this paper a simple two-layer neural network's model, similar to that, studied by D.Amit and N.Brunel [11] , is investigated in the frames of the mean-field approximation. The distributions of the local fields are analytically derived and compared to those obtained in ref.[11]. The dynamic properties are discussed and the basin of attraction in some parametric space is found. A procedure for driving the system into a basin of attraction by using a regulation imposed on the network is proposed. The effect of outer stimulus is shown to have a destructive influence on the attractor, forcing the later to disappear if the distribution of the stimulus has high enough variance or if the stimulus has a spatial structure with sufficient contrast. The techniques, used in this paper, for obtaining the analytical results can be applied to more complex topologies of linked recurrent neural networks. Keywords: attractor neural networks, basins of attractors, local-fields, learnability, stability...