发表机构
Scripps Research（斯克里普斯研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文分析研究不同程度局部连接平衡的随机循环网络，发现该平衡以依赖单单元非线性的方式重塑动力学，是现实无序网络集体动力学的新控制参数。
AI 中文摘要
由大量相互作用单元构成的无序动力学系统，从生态群落到神经回路，无处不在，而理解连接性如何塑造其集体行为是核心理论挑战。神经回路一个长期公认的特征是局部连接平衡，即汇聚到每个单元的兴奋性和抑制性权重近似抵消。尽管局部连接平衡被认为具有门控输入信号等功能，但其对网络集体动力学的影响仍不清楚。本文分析研究了具有不同程度局部连接平衡的随机连接循环网络，发现这种平衡使连接谱保持不变，但以关键依赖于单单元非线性的方式显著重塑动力学：当激活函数呈线性或更快速缩放时，局部平衡抑制网络状态的无界增长并稳定网络动力学；而当激活函数为亚线性或饱和时，它会驱动网络进入混沌状态。重要的是，这些效应对奇数激活函数（此前研究中常用的假设）会消失。进一步发现，对于饱和非线性，动力学的有效维度随平衡程度呈非单调变化。所有这些现象都源于一个统一机制：局部连接平衡抑制了自生成反馈输入。研究结果确定局部连接平衡是现实无序网络集体动力学的一个此前被忽视的控制参数。
英文摘要
Disordered dynamical systems comprising many interacting units, from ecological communities to neural circuits, are ubiquitous, and understanding how connectivity shapes their collective behavior is a central theoretical challenge. One long-recognized feature of neural circuits is local connectivity balance, in which the excitatory and inhibitory weights converging onto each unit approximately cancel. Although local connectivity balance has been proposed to serve functions such as gating incoming signals, its effect on collective network dynamics remains unclear. Here we analytically study randomly connected recurrent networks with varying degrees of local connectivity balance. We show that this balance leaves the connectivity spectrum unchanged yet drastically reshapes the dynamics in a manner that depends critically on the single-unit nonlinearity. Local balance suppresses unbounded growth of the network state and stabilizes network dynamics when the activation function scales linearly or faster, whereas it drives the network into chaos when the activation function is sub-linear or saturating. Importantly, these effects vanish for odd activation functions, which are commonly assumed in previous work. We further find that, for saturating nonlinearities, the effective dimension of the dynamics varies nonmonotonically with the degree of balance. We show that all these phenomena arise from a unifying mechanism: the suppression of a self-generated feedback input by local connectivity balance. Our results identify local connectivity balance as a previously overlooked control parameter for collective dynamics in realistic disordered networks.
