随机图神经网络
Stochastic Graph Neural Networks
摘要：
图神经网络（GNN）对图数据中的非线性表示进行建模，并应用于分布式代理协调，控制和规划等。当前的GNN架构假设理想场景，忽略了由于环境、人为因素或外部攻击而发生的链路波动。在这些情况下，如果不相应地考虑拓扑随机性，GNN就无法解决其分布式任务。为了克服这个问题，我们提出了随机图神经网络（SGNN）模型：一个GNN，其中分布式图卷积模块负责随机网络变化。由于随机性带来了一种新的学习范式，我们对SGNN输出方差进行统计分析，以确定学习的滤波器应该满足的条件，以实现对扰动场景的鲁棒转移，最终揭示随机链路损耗的明确影响。我们进一步开发了一个基于随机梯度下降（SGD）的SGNN学习过程，并推导出该学习过程收敛到一个稳定点的学习速率的条件。数值结果证实了我们的理论研究结果，并比较SGNN鲁棒迁移的好处与传统的GNN，在学习过程中忽略图形扰动。
英文摘要：
Graph neural networks (GNNs) model nonlinear representations in graph data with applications in distributed agent coordination, control, and planning among others. Current GNN architectures assume ideal scenarios and ignore link fluctuations that occur due to environment, human factors, or external attacks. In these situations, the GNN fails to address its distributed task if the topological randomness is not considered accordingly. To overcome this issue, we put forth the stochastic graph neural network (SGNN) model: a GNN where the distributed graph convolution module accounts for the random network changes. Since stochasticity brings in a new learning paradigm, we conduct a statistical analysis on the SGNN output variance to identify conditions the learned filters should satisfy for achieving robust transference to perturbed scenarios, ultimately revealing the explicit impact of random link losses. We further develop a stochastic gradient descent (SGD) based learning process for the SGNN and derive conditions on the learning rate under which this learning process converges to a stationary point. Numerical results corroborate our theoretical findings and compare the benefits of SGNN robust transference with a conventional GNN that ignores graph perturbations during learning.
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