Reducing Smoothness with Expressive Memory Enhanced Hierarchical Graph Neural Networks

Abstract: Graphical forecasting models learn the structure of time series data via projecting onto a graph, with recent techniques capturing spatial-temporal associations between variables via edge weights. Hierarchical variants offer a distinct advantage by analysing the time series across multiple resolutions, making them particularly effective in tasks like global weather forecasting, where low-resolution variable interactions are significant. A critical challenge in hierarchical models is information loss during forward or backward passes through the hierarchy. We propose the Hierarchical Graph Flow (HiGFlow) network, which introduces a memory buffer variable of dynamic size to store previously seen information across variable resolutions. We theoretically show two key results: HiGFlow reduces smoothness when mapping onto new feature spaces in the hierarchy and non-strictly enhances the utility of message-passing by improving Weisfeiler-Lehman (WL) expressivity. Empirical results demonstrate that HiGFlow outperforms state-of-the-art baselines, including transformer models, by at least an average of 6.1% in MAE and 6.2% in RMSE. Code is available at https://github.com/TB862/ HiGFlow.git.