提出可稳定存储记忆的神经放电率模型框架，兼顾生物合理性与记忆鲁棒性。
Firing Rate Models as Associative Memory: Excitatory-Inhibitory Balance for Robust Retrieval
- 构建通用框架，使重缩放后的记忆模式成为稳定的平衡点。
- 证明记忆在局部和全局渐近稳定，条件明确可调控。
- 适合研究生物合理神经网络的记忆机制，如皮层动力学建模。
放电率模型是应用与理论神经科学中广泛使用的动力系统，用于描述神经元群体的局部皮层动态。这类模型从宏观层面刻画神经活动，对研究振荡现象、混沌行为及关联记忆过程至关重要。尽管应用广泛，放电率模型在关联记忆网络中的数学分析仍有限，且多集中于特定模型。相比之下，成熟的关联记忆设计如霍普菲尔德网络，缺乏放电率模型的关键生物特征，例如正性以及可解释的兴奋-抑制突触矩阵。为填补这一空白，本文提出一种通用框架，确保重缩放后的记忆模式在放电率动力学中成为稳定平衡点。此外，我们分析了记忆实现局部与全局渐近稳定性的条件，为构建生物合理且鲁棒的关联记忆系统提供了理论依据。
原文摘要 · Abstract (English)
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.
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