Institute of Science and Technology for Brain-Inspired Intelligence, <a href="https://ror.org/013q1eq08">Fudan University</a>, Shanghai 200433, China; Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence (<a href="https://ror.org/013q1eq08">Fudan University</a>), Ministry of Education, Shanghai 200433, China; and MOE Frontiers Center for Brain Science, <a href="https://ror.org/013q1eq08">Fudan University</a>, Shanghai 200433, China.
Phys Rev E. 2024 Aug;110(2-1):024310. doi: 10.1103/PhysRevE.110.024310.
Continuous rate-based neural networks have been widely applied to modeling the dynamics of cortical circuits. However, cortical neurons in the brain exhibit irregular spiking activity with complex correlation structures that cannot be captured by mean firing rate alone. To close this gap, we consider a framework for modeling irregular spiking activity, called the moment neural network, which naturally generalizes rate models to second-order moments and can accurately capture the firing statistics of spiking neural networks. We propose an efficient numerical method that allows for rapid evaluation of moment mappings for neuronal activations without solving the underlying Fokker-Planck equation. This allows simulation of coupled interactions of mean firing rate and firing variability of large-scale neural circuits while retaining the advantage of analytical tractability of continuous rate models. We demonstrate how the moment neural network can explain a range of phenomena including diverse Fano factor in networks with quenched disorder and the emergence of irregular oscillatory dynamics in excitation-inhibition networks with delay.
基于速率的连续神经网络已被广泛应用于皮质电路动力学建模。然而，大脑中的皮质神经元表现出不规则的尖峰活动，具有复杂的相关结构，仅凭平均发放率无法捕捉到这些结构。为了弥补这一差距，我们考虑了一种用于建模不规则尖峰活动的框架，称为矩神经网络，它自然地将率模型推广到二阶矩，并能准确地捕获尖峰神经网络的发放统计。我们提出了一种有效的数值方法，允许在不求解底层福克-普朗克方程的情况下快速评估神经元激活的矩映射。这允许模拟大规模神经回路的平均发放率和发放变异性的耦合相互作用，同时保留连续率模型的分析可处理性优势。我们展示了矩神经网络如何解释一系列现象，包括淬火噪声网络中的不同福克因子以及具有延迟的兴奋-抑制网络中不规则振荡动力学的出现。
