An emerging paradigm proposes that neural computations can be understood at the level of dynamic systems that govern low-dimensional trajectories of collective neural activity. How the connectivity structure of a network determines the emergent dynamical system, however, remains to be clarified. Here we consider a novel class of models, gaussian-mixture, low-rank recurrent networks in which the rank of the connectivity matrix and the number of statistically defined populations are independent hyperparameters. We show that the resulting collective dynamics form a dynamical system, where the rank sets the dimensionality and the population structure shapes the dynamics. In particular, the collective dynamics can be described in terms of a simplified effective circuit of interacting latent variables. While having a single global population strongly restricts the possible dynamics, we demonstrate that if the number of populations is large enough, a rank R network can approximate any R-dimensional dynamical system.

中文翻译：

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在低秩循环网络中塑造具有多个群体的动态。

一个新兴的范式提出，可以在控制集体神经活动的低维轨迹的动态系统的水平上理解神经计算。然而，网络的连接结构如何决定涌现的动力系统仍有待澄清。在这里，我们考虑一类新的模型，高斯混合，低秩循环网络，其中连接矩阵的秩和统计定义的种群数量是独立的超参数。我们表明，由此产生的集体动态形成了一个动态系统，其中等级设置了维度，人口结构塑造了动态。特别是，集体动力学可以用相互作用的潜在变量的简化有效电路来描述。