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

TL;DR

This paper demonstrates that spatial localized states can emerge in a binary symmetric Hebb neural network when connectivity is distance-dependent and activity constraints are imposed, with analytical and simulation confirmation.

Contribution

It identifies specific conditions involving connectivity and activity constraints that lead to spatial asymmetric states during retrieval in neural networks.

Findings

Spatial localized states occur with distance-dependent connectivity.

Activity constraints induce asymmetry between retrieval and learning.

Analytical and simulation results confirm the emergence of localized states.

Abstract

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 states. The result is confirmed analytically and by simulation.