Institut de Biologie de l'ENS, Ecole Normale Supérieure, CNRS, Inserm, Université PSL, 46 rue d'Ulm, 75005 Paris, France.
Bernstein Center for Computational Neuroscience Berlin, Philippstraße 13, Haus 2, 10115 Berlin, Germany and Department of Physics, Humboldt University Berlin, Newtonstraße 15, 12489 Berlin, Germany.
Chaos. 2022 Jun;32(6):063131. doi: 10.1063/5.0096000.
Despite the incredible complexity of our brains' neural networks, theoretical descriptions of neural dynamics have led to profound insights into possible network states and dynamics. It remains challenging to develop theories that apply to spiking networks and thus allow one to characterize the dynamic properties of biologically more realistic networks. Here, we build on recent work by van Meegen and Lindner who have shown that "rotator networks," while considerably simpler than real spiking networks and, therefore, more amenable to mathematical analysis, still allow one to capture dynamical properties of networks of spiking neurons. This framework can be easily extended to the case where individual units receive uncorrelated stochastic input, which can be interpreted as intrinsic noise. However, the assumptions of the theory do not apply anymore when the input received by the single rotators is strongly correlated among units. As we show, in this case, the network fluctuations become significantly non-Gaussian, which calls for reworking of the theory. Using a cumulant expansion, we develop a self-consistent analytical theory that accounts for the observed non-Gaussian statistics. Our theory provides a starting point for further studies of more general network setups and information transmission properties of these networks.
尽管我们大脑神经网络的复杂性令人难以置信，但对神经动力学的理论描述已经使我们深入了解了可能的网络状态和动力学。开发适用于尖峰网络的理论仍然具有挑战性，因此无法描述更符合生物学的网络的动态特性。在这里，我们借鉴了 van Meegen 和 Lindner 的最新研究成果，他们表明，“旋转器网络”虽然比实际的尖峰网络简单得多，因此更便于数学分析，但仍然可以捕捉到尖峰神经元网络的动力学特性。该框架可以轻松扩展到单个单元接收不相关随机输入的情况，这可以解释为内在噪声。然而，当单个旋转器接收到的输入在单元之间存在强烈相关性时，该理论的假设不再适用。正如我们所展示的，在这种情况下，网络波动变得明显非高斯，这需要对理论进行重新研究。我们使用累积展开法开发了一种自洽的分析理论，该理论解释了观察到的非高斯统计数据。我们的理论为进一步研究更一般的网络设置和这些网络的信息传输特性提供了一个起点。
