Cross-talk and transitions between multiple spatial maps in an attractor neural network model of the hippocampus: phase diagram (I)

TL;DR

This paper analyzes an attractor neural network model of hippocampal place cells, revealing phase transitions between localized and extended activity states depending on noise and environment load, with implications for spatial memory stability.

Contribution

It provides a detailed phase diagram of the network's behavior, combining statistical mechanics analysis with numerical simulations to understand spatial map encoding and cross-talk effects.

Findings

Localized activity in one environment at low noise and load

Extended activity with spatial heterogeneities at high noise and load

Analytical predictions match numerical simulations

Abstract

We study the stable phases of an attractor neural network model, with binary units, for hippocampal place cells encoding 1D or 2D spatial maps or environments. Using statistical mechanics tools we show that, below critical values for the noise in the neural response and for the number of environments, the network activity is spatially localized in one environment. We calculate the number of stored environments. For high noise and loads the network activity extends over space, either uniformly or with spatial heterogeneities due to the cross-talk between the maps, and memory of environments is lost. Analytical predictions are corroborated by numerical simulations.