Laboratoire de Neurosciences Cognitives et Computationnelles, INSERM U960, Ecole Normale Superieure-PSL Research University, Paris, France.
PLoS Comput Biol. 2023 Jan 23;19(1):e1010855. doi: 10.1371/journal.pcbi.1010855. eCollection 2023 Jan.
How the connectivity of cortical networks determines the neural dynamics and the resulting computations is one of the key questions in neuroscience. Previous works have pursued two complementary approaches to quantify the structure in connectivity. One approach starts from the perspective of biological experiments where only the local statistics of connectivity motifs between small groups of neurons are accessible. Another approach is based instead on the perspective of artificial neural networks where the global connectivity matrix is known, and in particular its low-rank structure can be used to determine the resulting low-dimensional dynamics. A direct relationship between these two approaches is however currently missing. Specifically, it remains to be clarified how local connectivity statistics and the global low-rank connectivity structure are inter-related and shape the low-dimensional activity. To bridge this gap, here we develop a method for mapping local connectivity statistics onto an approximate global low-rank structure. Our method rests on approximating the global connectivity matrix using dominant eigenvectors, which we compute using perturbation theory for random matrices. We demonstrate that multi-population networks defined from local connectivity statistics for which the central limit theorem holds can be approximated by low-rank connectivity with Gaussian-mixture statistics. We specifically apply this method to excitatory-inhibitory networks with reciprocal motifs, and show that it yields reliable predictions for both the low-dimensional dynamics, and statistics of population activity. Importantly, it analytically accounts for the activity heterogeneity of individual neurons in specific realizations of local connectivity. Altogether, our approach allows us to disentangle the effects of mean connectivity and reciprocal motifs on the global recurrent feedback, and provides an intuitive picture of how local connectivity shapes global network dynamics.
皮质网络的连接性如何决定神经动力学和由此产生的计算是神经科学的关键问题之一。以前的工作已经采用了两种互补的方法来量化连接中的结构。一种方法从生物实验的角度出发，其中只有小群神经元之间的连接模式的局部统计数据是可访问的。另一种方法则基于人工神经网络的角度，其中全局连接矩阵是已知的，特别是它的低秩结构可以用于确定由此产生的低维动力学。然而，这两种方法之间目前还没有直接的关系。具体来说，仍然需要澄清局部连接统计数据和全局低秩连接结构是如何相互关联并塑造低维活动的。为了弥合这一差距，我们在这里开发了一种将局部连接统计数据映射到近似全局低秩结构的方法。我们的方法基于使用特征向量来近似全局连接矩阵，我们使用随机矩阵的微扰理论来计算这些特征向量。我们证明，对于满足中心极限定理的局部连接统计数据定义的多群体网络，可以通过具有高斯混合统计数据的低秩连接来近似。我们特别将这种方法应用于具有互惠模式的兴奋性抑制网络，并表明它可以对低维动力学和群体活动的统计数据进行可靠的预测。重要的是，它在局部连接的特定实现中分析性地解释了单个神经元的活动异质性。总之，我们的方法允许我们分离平均连接和互惠模式对全局递归反馈的影响，并提供了一个直观的图景，说明局部连接如何塑造全局网络动力学。
