How random connectivity shapes the fluctuating dynamics of finite-size neural populations
Institute of Mathematics, Technical University Berlin（柏林工业大学数学研究所）；Bernstein Center for Computational Neuroscience Berlin（柏林伯恩斯坦计算神经科学中心）；Institut de Biologie de l'ENS, Ecole normale supérieure, PSL University, CNRS（巴黎高等师范学院生物学研究所，法兰西公学院，PSL大学，法国国家科学研究中心）
Mesoscopic models of finite-size neuronal populations are crucial to understand the dynamics of neural networks in the brain, especially their fluctuations and response to stimuli. However, current theories to derive such models are based on homogeneous all-to-all (full) connectivity. This assumption neglects the variance in the connectivity of biologically realistic networks with connection probabilities $p<1$ (non-full connectivity). To gain insight into the different fluctuation mechanisms underlying neural variability at the population level, we derive and analyze a stochastic mean-field model for finite-size networks of Poisson neurons with random connectivity (including non-full connectivity), external noise and disordered mean inputs. We treat the quenched disorder of the connectivity by an annealed approximation enabling a doubly stochastic description of synaptic inputs for finite network size. A further reduction leads to a low-dimensional closed system of coupled Langevin equations for the mean and variance of the membrane potentials as well as a variable capturing finite-size fluctuations. Compared to microscopic simulations, the mesoscopic model describes the fluctuations and nonlinearities well and outperforms previous theories that neglected the variance in the connectivity. The joint effect of connectivity disorder and finite network size can be analytically understood by a softening of the effective nonlinearity and the multiplicative character of spiking noise. The mesoscopic theory shows that quenched disorder can stabilize the asynchronous state, and it correctly predicts large quantitative and non-trivial qualitative effects of connection probability on the variance of the population firing rate and its dependence on stimulus strength. In conclusion, our theory elucidates how disordered connectivity shapes nonlinear dynamics and fluctuations of neural populations.
How connectivity structure shapes rich and lazy learning in neural circuits
University of Washington（华盛顿大学）；Allen Institute for Brain Science（艾伦脑科学研究所）；Mila - Quebec AI Institute（米拉-魁北克人工智能研究所）；Samsung - SAIT AI Lab（三星-SAIT人工智能实验室）；McGill University（麦吉尔大学）；Université de Montréal（蒙特利尔大学）
Connectivity structure and dynamics of nonlinear recurrent neural networks
Zuckerman Institute, Columbia University（哥伦比亚大学祖克曼研究所）；Kavli Institute for Brain Science, Columbia University（哥伦比亚大学卡弗里脑科学研究所）；Center for Brain Science, Harvard University（哈佛大学脑科学中心）
Complexity and dynamics of partially symmetric random neural networks
University of Houston（休斯顿大学）；Lehigh University（利哈伊大学）；Brandeis University（布兰迪斯大学）；Carnegie Mellon University（卡内基梅隆大学）；Baylor College of Medicine（贝勒医学院）；Rice University（莱斯大学）
