底层图扰动下的神经网络谱鲁棒性
Neural network spectral robustness under perturbations of the underlying graph
摘要：
最近的研究一直在使用图论方法来模拟复杂网络（如社会，基础设施或生物网络），以及它们的硬连线电路如何与它们随时间的动态演化相关。理解配置如何反映动态节点系统中的耦合行为可能非常重要，例如在大脑连接体如何影响大脑功能的背景下。然而，大脑网络中出现的连接模式，以及它们对网络动态的个体影响，还远未被完全理解。我们研究了边缘配置和动态之间的连接，在一个简单的定向网络组成的两个相互连接的集团（代表大脑反馈调节电路）。在本文中，我们的主要目标是研究图邻接矩阵和拉普拉斯矩阵的谱，特别关注三个方面：（1）响应于改变模块内和模块间边缘密度的谱的灵敏度/鲁棒性，（2）在保持密度固定的情况下扰动边缘配置对谱的影响，以及（3）增加网络大小的影响。我们研究了一些听话的方面解析，然后模拟更一般的结果数值。本文的目的是澄清，从分析和建模的角度来看，我们的相关工作的基础，这进一步解决了图形属性如何影响网络的时间动态和相变。我们认为，这种类型的结果可能有助于研究小网络，如宏观脑回路。我们建议潜在的应用程序，以了解学习网络中的突触重组，以及网络配置的情绪调节神经回路的功能的影响。
英文摘要：
Recent studies have been using graph theoretical approaches to model complex networks (such as social, infrastructural or biological networks), and how their hardwired circuitry relates to their dynamic evolution in time. Understanding how configuration reflects on the coupled behavior in a system of dynamic nodes can be of great importance, for example in the context of how the brain connectome is affecting brain function. However, the connectivity patterns that appear in brain networks, and their individual effects on network dynamics, are far from being fully understood. We study the connections between edge configuration and dynamics in a simple oriented network composed of two interconnected cliques (representative of brain feedback regulatory circuitry). In this paper, our main goal is to study the spectra of the graph adjacency and Laplacian matrices, with a focus on three aspects in particular: (1) the sensitivity/robustness the spectrum in response to varying the intra and inter-modular edge density, (2) the effects on the spectrum of perturbing the edge configuration, while keeping the densities fixed and (3) the effects of increasing the network size. We study some tractable aspects analytically, then simulate more general results numerically. This paper aims to clarify, from analytical and modeling perspectives, the underpinnings of our related work, which further addresses how graph properties affect the network's temporal dynamics and phase transitions. We propose that this type of results may be helpful when studying small networks such as macroscopic brain circuits. We suggest potential applications to understanding synaptic restructuring in learning networks, and the effects of network configuration to function of emotion-regulatory neural circuits.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
