Scalability of asynchronous networks is limited by one-to-one mapping between effective connectivity and correlations

Network models are routinely downscaled compared to nature in terms of numbers of nodes or edges because of a lack of computational resources, often without explicit mention of the limitations this entails. While reliable methods have long existed to adjust parameters such that the first-order statistics of network dynamics are conserved, here we show that limitations already arise if also second-order statistics are to be maintained. The temporal structure of pairwise averaged correlations in the activity of recurrent networks is determined by the effective population-level connectivity. We first show that in general the converse is also true and explicitly mention degenerate cases when this one-to-one relationship does not hold. The one-to-one correspondence between effective connectivity and the temporal structure of pairwise averaged correlations implies that network scalings should preserve the effective connectivity if pairwise averaged correlations are to be held constant. Change...

受计算资源所限，网络模型在节点数与边数维度上通常会相较于真实自然网络进行规模缩减，且相关研究往往未明确阐明该操作带来的局限性。尽管长期以来已有可靠方法可调整模型参数，以保证网络动力学的一阶统计量（first-order statistics）保持恒定，但本研究表明，若同时要求维持二阶统计量（second-order statistics），则会产生新的局限性。循环神经网络（recurrent network）活动中两两平均相关性的时域结构，由有效群体级连接（effective population-level connectivity）决定。我们首先证明，一般情况下该命题的逆命题同样成立，并明确指出了当这一一对应关系不成立时的退化（degenerate）情形。有效连接与两两平均相关性时域结构之间的一一对应关系表明：若要维持两两平均相关性恒定，则网络规模缩放操作应当保留有效连接特性。更改……