An emerging paradigm proposes that neural computations can be understood at the level of dynamical 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 hyper-parameters. 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.
Shaping manifolds in equivariant recurrent neural networks
Laboratoire de Neurosciences Cognitives et Computationnelles, INSERM U960, École Normale Supérieure - PSL Research University（认知与计算神经科学实验室，INSERM U960，巴黎高等师范学院-PSL研究大学）；SISSA - Theoretical and Scientific Data Science（的里雅斯特国际高等研究院-理论与科学数据科学）
Efficiency and robustness partition the solution space for memory in recurrent networks
Harvard University（哈佛大学）；Kempner Institute for the Study of Natural and Artificial Intelligence（肯普纳自然与人工智能研究所）；John A. Paulson School of Engineering and Applied Sciences（约翰·A·保尔森工程与应用科学学院）；Center for Brain Science（脑科学中心）
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）
Divisive Normalization Shapes Low-Rank Slow Manifolds for Continuous Working Memory
School of System Science, Beijing Normal University（北京师范大学系统科学学院）；State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University（北京师范大学认知神经科学与学习国家重点实验室）；Qiyuan Laboratory（启元实验室）
A ghost mechanism: An analytical model of abrupt learning in recurrent networks
Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA；Geometric Intelligence Lab, University of California, Santa Barbara, CA 93106, USA；CNC Program, Stanford University, Stanford, CA 94305, USA；Physics of Artificial Intelligence Group, NTT Research Inc., Sunnyvale, CA 94085, USA；KUIS AI, Department of Computer Engineering, Koc University, Istanbul, Turkey；Computer Science, Stanford University, Stanford, CA 94305, USA；James H. Clark Center for Biomedical Engineering \& Sciences, Stanford University, Stanford；Howard Hughes Medical Institute, Stanford University, Stanford, CA 94305, USA；CBS-NTT Program in Physics of Intelligence, Harvard University, Cambridge, MA 94305, USA
