Bump formation in a binary attractor neural network

TL;DR

This paper explores the formation of local activity bumps in binary attractor neural networks with spatially dependent connectivity, revealing conditions, stability properties, and analytical insights into their behavior.

Contribution

It introduces an analytical approximation for order parameters and maps the phase diagram, highlighting the effects of activity asymmetry on bump formation and network capacity.

Findings

Bump formations occur with activity asymmetry between retrieval and learning.

The stable region for bump formation is large but reduces storage capacity.

Analytical results closely match simulations across various network topologies.

Abstract

This paper investigates the conditions for the formation of local bumps in the activity of binary attractor neural networks with spatially dependent connectivity. We show that these formations are observed when asymmetry between the activity during the retrieval and learning is imposed. Analytical approximation for the order parameters is derived. The corresponding phase diagram shows a relatively large and stable region, where this effect is observed, although the critical storage and the information capacities drastically decrease inside that region. We demonstrate that the stability of the network, when starting from the bump formation, is larger than the stability when starting even from the whole pattern. Finally, we show a very good agreement between the analytical results and the simulations performed for different topologies of the network.