Firing Rate Models as Associative Memory: Excitatory-Inhibitory Balance for Robust Retrieval

TL;DR

This paper develops a mathematical framework for firing rate models to serve as biologically plausible associative memory systems, analyzing stability conditions for robust memory retrieval.

Contribution

It introduces a general framework ensuring stable memory patterns in firing rate models, bridging the gap between biological realism and associative memory design.

Findings

Re-scaled memory patterns can be stable equilibria in firing rate models.

Conditions for local and global stability of memories are derived.

Framework enhances robustness and biological plausibility of associative memory models.

Abstract

Firing rate models are dynamical systems widely used in applied and theoretical neuroscience to describe local cortical dynamics in neuronal populations. By providing a macroscopic perspective of neuronal activity, these models are essential for investigating oscillatory phenomena, chaotic behavior, and associative memory processes. Despite their widespread use, the application of firing rate models to associative memory networks has received limited mathematical exploration, and most existing studies are focused on specific models. Conversely, well-established associative memory designs, such as Hopfield networks, lack key biologically-relevant features intrinsic to firing rate models, including positivity and interpretable synaptic matrices that reflect excitatory and inhibitory interactions. To address this gap, we propose a general framework that ensures the emergence of re-scaled memory patterns as stable equilibria in the firing rate dynamics. Furthermore, we analyze the conditions under which the memories are locally and globally asymptotically stable, providing insights into constructing biologically-plausible and robust systems for associative memory retrieval.