Spatio-temporal sheaf network improves forecasting on graphs
ChronoSheaf: Joint Spatio-Temporal Spectral Filtering on Cellular Sheaves
Machine Learning
Summary
Predicting how things change over time and space, like traffic or weather, is tricky because connected points influence each other in complex ways that evolve. The paper presents ChronoSheaf, a method that models both space and time together using advanced math tools called sheaves, which relate data at connected points and moments. This approach helps capture how signals spread through networks over time without making the model overly complicated. Tests show that ChronoSheaf predicts future states better than existing methods on several forecasting tasks.
What this means in practice
- •For traffic control teams: Improve predictions of traffic patterns on road networks using spatio-temporal models that account for directional time influences between intersections.
- •For energy grid operators: Forecast energy demand and supply changes over time and location by modeling sensor data with joint space-time network filters.
Authors
Abeer Mostafa, Zahra Ahmadi
Abstract
Sheaf neural networks generalize graph neural networks by assigning each edge a learned linear restriction map that specifies how the local representations of adjacent nodes relate to one another, thereby mitigating oversmoothing. Existing sheaf architectures, however, define the sheaf Laplacian as an instantaneous spatial operator and therefore cannot explicitly model how signals evolve over time on a graph. We first introduce a spectral sheaf Laplacian, defined jointly over space and time, such that a single operator regulates signal propagation across both the spatial graph and the temporal domain. Directly extending this operator's receptive field in space or time would require increasingly complex sheaf structures. Instead, we propose a spectral filter that expands the effective receptive field along both dimensions without enlarging the underlying sheaf. Building on this operator, we introduce ChronoSheaf, a spatio-temporal sheaf network with two key components. First, Transitional Restriction Maps (TRM) decompose each node's restriction map into a spatial term and two temporal frames that independently control its relation to neighboring nodes at the preceding and following timestep, enabling asymmetric temporal influence. Second, the Dual Spectral Filter (DSF) applies a single bounded-degree polynomial filter with an adaptively estimated spectral radius to the joint spatio-temporal sheaf operator. We validate ChronoSheaf on a diverse set of spatio-temporal forecasting benchmarks, where it outperforms state-of-the-art baselines. The code is available at: https://anonymous.4open.science/r/ChronoSheaf-1D7D/.