A given neural network in the brain is involved in many different tasks. This implies that, when considering a specific task, the network's connectivity contains a component which is related to the task and another component which can be considered random. Understanding the interplay between the structured and random components, and their effect on network dynamics and functionality is an important open question. Recent studies addressed the co-existence of random and structured connectivity, but considered the two parts to be uncorrelated. This constraint limits the dynamics and leaves the random connectivity non-functional. Algorithms that train networks to perform specific tasks typically generate correlations between structure and random connectivity. Here we study nonlinear networks with correlated structured and random components, assuming the structure to have a low rank. We develop an analytic framework to establish the precise effect of the correlations on the eigenvalue spectrum of the joint connectivity. We find that the spectrum consists of a bulk and multiple outliers, whose location is predicted by our theory. Using mean-field theory, we show that these outliers directly determine both the fixed points of the system and their stability. Taken together, our analysis elucidates how correlations allow structured and random connectivity to synergistically extend the range of computations available to networks.
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）
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）
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）
Center for Quantitative Biology, Academy for Advanced Interdisciplinary Studies, Peking University（北京大学前沿交叉学科研究院定量生物学中心）；School of Physics, Peking University（北京大学物理学院）；Center for Bioinformatics, National Laboratory of Protein Engineering and Plant Genetic Engineering, School of Life Sciences and Center for Quantitative Biology, Academy for Advanced Interdisciplinary Studies,Peking University（北京大学生命科学学院、前沿交叉学科研究院定量生物学中心及蛋白质工程与植物基因工程国家重点实验室生物信息中心）；CNRS, LJAD and Institute NeuroMod, Université Côte d’Azur（法国蔚蓝海岸大学神经调节研究所、LJAD及法国国家科学研究中心）
