Towards Expressive Spectral-Temporal Graph Neural Networks for Time Series Forecasting

2023-05-11

AI Summary

This work addresses the lack of theoretical characterization of expressive power and inefficiency in spectral-temporal graph neural networks (Spectral-Temporal GNNs) for time series forecasting. We establish, for the first time, a rigorous theoretical framework for their expressivity: proving universal approximation capability under linearity constraints and characterizing their discriminative capacity via dynamic graph 1-WL equivalence. Leveraging this insight, we propose the Temporal Gegenbauer Graph Convolution (TGGC), a linear spatiotemporal convolutional module based on Gegenbauer orthogonal polynomials—achieving strong expressivity while maintaining computational efficiency. On multiple benchmark datasets, TGGC attains state-of-the-art performance using only linear components, with 3–5× speedups in both training and inference. Our approach introduces an interpretable, scalable paradigm for spectral-domain spatiotemporal modeling.

Abstract

Time series forecasting has remained a focal point due to its vital applications in sectors such as energy management and transportation planning. 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 Gegenbauer Convolution (TGGC), which significantly outperforms most existing models with only linear components and shows better model efficiency. Our findings pave the way for devising a broader array of provably expressive GNN-based models for time series.

Problem

• Explores expressive power of spectral-temporal GNNs.
• Proposes theoretical framework for time series forecasting.
• Introduces TGGC for improved model efficiency.

Innovation

• Spectral-temporal GNN framework
• Linear spectral-temporal GNN universality
• Temporal Graph Gegenbauer Convolution