Data from: 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. Changes in effective connectivity can even push a network from a linearly stable to an unstable, oscillatory regime and vice versa. On this basis, we derive conditions for the preservation of both mean population-averaged activities and pairwise averaged correlations under a change in numbers of neurons or synapses in the asynchronous regime typical of cortical networks. We find that mean activities and correlation structure can be maintained by an appropriate scaling of the synaptic weights, but only over a range of numbers of synapses that is limited by the variance of external inputs to the network. Our results therefore show that the reducibility of asynchronous networks is fundamentally limited.

受限于计算资源，网络模型在节点与边的数量上通常需相较于自然系统进行降尺度处理，且往往未明确提及这一操作所带来的局限性。尽管长期以来已有可靠方法可通过调整参数使网络动力学的一阶统计量得以保留，但本文证明，若需同时维持二阶统计量，局限性实则早已存在。循环神经网络（recurrent networks）活动中两两平均相关性的时间结构由有效群体水平连接性（effective population-level connectivity）决定。我们首先证明，一般而言其逆命题同样成立，并明确指出了当这一一对应关系不成立时的简并情况。有效连接性与两两平均相关性的时间结构之间的一一对应关系意味着，若要保持两两平均相关性恒定，网络降尺度操作应当保留有效连接性。有效连接性的变化甚至可将网络从线性稳定状态推至不稳定的振荡状态，反之亦然。基于此，我们推导得出：在皮层网络典型的异步态下，当神经元或突触的数量发生变化时，同时保留群体平均活动均值与两两平均相关性的条件。我们发现，通过适当调整突触权重，可维持平均活动与相关性结构，但仅在受网络外部输入方差限制的突触数量范围内可行。因此，我们的研究结果表明，异步网络的可降尺度性从根本上受到限制。