Title: Spectral Sheaf Filtering: A Topological Approach to Spatio-Temporal Modeling
Primary area: learning on graphs and other geometries & topologies
Keywords: Spatio-temporal data, Graph neural networks, Time-series forecasting, Spectral graph filtering

Abstract: Spatio-temporal data pose significant challenges for graph-based learning due to their complex, non-stationary dependencies and the limitations of conventional message passing in capturing high-order, asymmetric interactions. We introduce Spectral Sheaf Filtering (SSF), a novel and theoretically grounded framework that redefines information propagation on graphs using the algebraic topology of cellular sheaves. By assigning vector spaces and restriction maps to nodes and edges, SSF encodes context-dependent, localized dynamics that extend far beyond traditional adjacency structures. To further enhance expressivity and efficiency, we introduce spectral filtering over the sheaf Laplacian, enabling frequency-aware decomposition via the graph Fourier transform while emphasizing latent spectral features. This spectral view allows SSF to adaptively modulate information flow across frequency components, effectively mitigating oversmoothing in deep graph neural networks. Extensive experiments on diverse spatio-temporal traffic forecasting benchmarks show that SSF consistently outperforms state-of-the-art methods, especially in long-horizon forecasting tasks. Our results highlight the value of topological structures in advancing graph learning for spatio-temporal systems. The code is available at: https://github.com/anonymous-submisssion/SSF.

TL;DR: Spectral Sheaf Filtering (SSF) uses sheaf topology and spectral filtering to better capture complex spatio-temporal dependencies, achieving state-of-the-art results in long-term traffic forecasting.