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| Autori principali: | , , , |
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| Natura: | Preprint |
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2024
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| Accesso online: | https://arxiv.org/abs/2411.07388 |
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| _version_ | 1866909764417486848 |
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| author | Betteti, Simone Baggio, Giacomo Bullo, Francesco Zampieri, Sandro |
| author_facet | Betteti, Simone Baggio, Giacomo Bullo, Francesco Zampieri, Sandro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07388 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Firing Rate Models as Associative Memory: Excitatory-Inhibitory Balance for Robust Retrieval Betteti, Simone Baggio, Giacomo Bullo, Francesco Zampieri, Sandro Neurons and Cognition Disordered Systems and Neural Networks Statistical Mechanics Artificial Intelligence Dynamical Systems 37N25 (Primary) 34D45, 34D23 (Secondary) I.2.11; I.5.1 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. |
| title | Firing Rate Models as Associative Memory: Excitatory-Inhibitory Balance for Robust Retrieval |
| topic | Neurons and Cognition Disordered Systems and Neural Networks Statistical Mechanics Artificial Intelligence Dynamical Systems 37N25 (Primary) 34D45, 34D23 (Secondary) I.2.11; I.5.1 |
| url | https://arxiv.org/abs/2411.07388 |