摘要：In both neuroscience and machine learning, understanding how network connectivity shapes dynamics and computation is crucial. Past studies have approached connectivity analysis either through biological experiments, focusing on local connectivity motifs in small neuron groups, or via artificial neural networks, examining network-wide low-rank connectivity patterns influencing low-dimensional dynamics. While both approaches suggest network connectivity's influence on activity patterns and dynamics, there's a gap in understanding how local connectivity statistics relate to global connectivity and impact network dynamics. To address this, we introduce an analytical method mapping locally-defined biological connectivity statistics to an approximate global low-rank structure (Shao & Ostojic, 2023). Leveraging perturbation theory for random matrices, we approximate the global connectivity matrix using dominant eigenvectors. This method demonstrates that networks with local connectivity statistics, under the central limit theorem, can be approximated by low-rank connectivity with Gaussian-mixture statistics. Applied to excitatory-inhibitory networks, our method accurately predicts low-dimensional dynamics, the balance between excitation and inhibition, and population activity statistics. All in all, our approach allows us to disentangle the effects of mean connectivity and multiple types of second-order motifs on global recurrent feedback and feedforward propagation, providing an intuitive picture of how local connectivity shapes global network dynamics.
报告人简介：邵宇秀于 2023 年 11 月加入北京师范大学系统科学学院，现任助理研究员。她的研究关注于生物神经元和人工神经网络的交叉方向，重点是揭示生物/人工神经网络系统背后的统一框架。在巴黎高等师范学院做博士后期间，她师从理论神经科学家Srdjan Ostojic，采用数学方法研究网络连接性与动力学之间的复杂关系。在此之前，她在北京老员工命科学学院攻读计算神经科学方向博士学位，师从Louis Tao教授。
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