Spectral-temporal graph neural network is a promising abstraction underlying most time series forecasting models that are based on graph neural networks (GNNs). However, more is needed to know about the underpinnings of this branch of methods. In this paper, we establish a theoretical framework that unravels the expressive power of spectral-temporal GNNs. Our results show that linear spectral-temporal GNNs are universal under mild assumptions, and their expressive power is bounded by our extended first-order Weisfeiler-Leman algorithm on discrete-time dynamic graphs. To make our findings useful in practice on valid instantiations, we discuss related constraints in detail and outline a theoretical blueprint for designing spatial and temporal modules in spectral domains. Building on these insights and to demonstrate how powerful spectral-temporal GNNs are based on our framework, we propose a simple instantiation named Temporal Graph GegenConv (TGC), which significantly outperforms most existing models with only linear components and shows better model efficiency.

翻译：谱-时图神经网络是基于图神经网络的时间序列预测模型所依赖的一种有前景的抽象框架。然而，对该类方法的基本原理仍需更深入的理解。本文建立了一个理论框架，系统揭示了谱-时图神经网络的表达能力。研究结果表明：在温和假设条件下，线性谱-时图神经网络具有普适性，且其表达能力受限于我们扩展的一阶Weisfeiler-Lehman算法在离散时间动态图上的表现。为使研究成果在有效实例化中具备实践价值，我们详细讨论了相关约束条件，并勾勒出谱域中时空模块设计的理论蓝图。基于上述见解，为验证谱-时图神经网络在此框架下的强大能力，我们提出了一种简洁的实例化模型——时态图GegenConv（TGC）。该模型仅采用线性组件即显著优于现有大多数方法，并展现出更优的模型效率。