Firing Rate Models as Associative Memory: Synaptic Design for Robust Retrieval

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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 reflecting the action of long-term potentiation and long-term depression. To address this gap, we propose a general framework that ensures the emergence of rescaled 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.

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