Conditions for the emergence of spatial asymmetric retrieval states in attractor neural network

In this paper we show that during the retrieval process in a binary symmetric Hebb neural network, spatial localized states can be observed when the connectivity of the network is distance-dependent and when a constraint on the activity of the network is imposed, which forces different levels of activity in the retrieval and learning states. This asymmetry in the activity during the retrieval and learning is found to be sufficient condition in order to observe spatial localized retrieval states. The result is confirmed analytically and by simulation. Corresponding author; [email protected]; Inst. for Computer Systems, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria G.Nadjakov Institute of Solid State Physics, Bulgarian Academy of Sciences, 1784, Sofia, Bulgaria