Neural circuits are composed of multiple regions, each with rich dynamics and engaging in communication with other regions. The combination of local, within-region dynamics and global, network-level dynamics is thought to provide computational flexibility. However, the nature of such multiregion dynamics and the underlying synaptic connectivity patterns remain poorly understood. Here, we study the dynamics of recurrent neural networks with multiple interconnected regions. Within each region, neurons have a combination of random and structured recurrent connections. Motivated by experimental evidence of communication subspaces between cortical areas, these networks have low-rank connectivity between regions, enabling selective routing of activity. These networks exhibit two interacting forms of dynamics: high-dimensional fluctuations within regions and low-dimensional signal transmission between regions. To characterize this interaction, we develop a dynamical mean-field theory to analyze such networks in the limit where each region contains infinitely many neurons, with cross-region currents as key order parameters. Regions can act as both generators and transmitters of activity, roles that we show are in conflict. Specifically, taming the complexity of activity within a region is necessary for it to route signals to and from other regions. Unlike previous models of routing in neural circuits, which suppressed the activities of neuronal groups to control signal flow, routing in our model is achieved by exciting different high-dimensional activity patterns through a combination of connectivity structure and nonlinear recurrent dynamics. This theory provides insight into the interpretation of both multiregion neural data and trained neural networks.

翻译：神经回路由多个区域组成，每个区域具有丰富的动力学特性，并与其他区域进行通信。局部区域内部动力学与全局网络层面动力学的结合被认为提供了计算灵活性。然而，这种多区域动力学的本质及其背后的突触连接模式仍知之甚少。本文研究了具有多个互连区域的递归神经网络的动力学特性。在每个区域内，神经元具有随机和结构化递归连接的组合。受皮层间通信子空间实验证据的启发，这些网络在区域间采用低秩连接，从而实现对活动的选择性路由。这些网络表现出两种相互作用的动力学形式：区域内部的高维波动与区域间的低维信号传输。为刻画这种相互作用，我们发展了一种动力学平均场理论，在假设每个区域包含无限多神经元的极限下分析此类网络，并将跨区域电流作为关键序参量。区域既可充当活动的生成器，也可作为活动的传输器，我们证明这两种角色存在冲突。具体而言，抑制区域内部活动的复杂性是实现区域间信号路由的必要条件。与以往通过抑制神经元群体活动来控制信号流的神经回路路由模型不同，本研究中的路由通过连接结构与非线性递归动力学的组合，激发不同的高维活动模式来实现。该理论为多区域神经数据及训练后的神经网络解释提供了深刻见解。