Firing Rate Models as Associative Memory: Excitatory-Inhibitory Balance for Robust Retrieval
This work addresses the gap between theoretical neuroscience and associative memory design by integrating biologically-relevant features like excitatory-inhibitory balance, though it appears incremental in extending existing models.
The authors tackled the limited mathematical exploration of firing rate models for associative memory by proposing a general framework that ensures memory patterns emerge as stable equilibria, analyzing conditions for local and global asymptotic stability to enable robust retrieval.
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.