We provide theoretical conditions guaranteeing that a self-organizing map efficiently develops representations of the input space. The study relies on a neural field model of spatiotemporal activity in area 3b of the primary somatosensory cortex. We rely on Lyapunov’s theory for neural fields to derive theoretical conditions for stability. We verify the theoretical conditions by numerical experiments. The analysis highlights the key role played by the balance between excitation and inhibition of lateral synaptic coupling and the strength of synaptic gains in the formation and maintenance of self-organizing maps.

中文翻译：

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神经场自组织图的稳定性分析

我们提供了理论条件，以确保自组织地图可以有效地开发输入空间的表示形式。该研究依赖于初级体感皮层区域3b中时空活动的神经场模型。我们依靠Lyapunov的神经场理论来推导稳定性的理论条件。我们通过数值实验验证了理论条件。该分析突出了在侧向突触耦合的激发与抑制之间的平衡以及在自组织图的形成和维持中突触增益的强度所起的关键作用。