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.
Abstract (translated)
发放率模型是广泛应用于应用神经科学和理论神经科学的动力系统，用于描述皮层局部的神经元群体动力学。通过提供宏观视角来观察神经活动，这些模型对于研究振荡现象、混沌行为及联想记忆过程至关重要。尽管这些模型被广泛应用，但将发放率模型应用于联想记忆网络的数学探索却相对有限，大部分现有研究集中在特定模型上。相反，一些已建立的联想记忆设计，如霍普菲尔德网络，缺乏与发放率模型固有的生物学相关特征，比如正性以及能够解释兴奋性和抑制性相互作用的可解读突触矩阵。为解决这一差距，我们提出了一种通用框架，确保重新缩放的记忆模式在发放率动态中作为稳定的平衡点出现。此外，我们分析了记忆局部和全局渐近稳定的条件，从而提供构建生物学上合理且稳健的联想记忆检索系统的见解。
URL
https://arxiv.org/abs/2411.07388
