Dynamic Sheaf Diffusion Networks with Adaptive Local Structure for Heterogeneous Spatio-Temporal Graph Learning

TL;DR

This paper introduces a novel spatio-temporal sheaf diffusion graph neural network that dynamically adapts to local patterns, improving modeling of heterogeneous responses and achieving state-of-the-art results in forecasting tasks.

Contribution

It proposes a sheaf-based GNN with learned dynamic restriction maps that adapt over time, enhancing expressiveness and mitigating oversmoothing in spatio-temporal graph learning.

Findings

The model guarantees and empirically demonstrates reduced oversmoothing.

It achieves state-of-the-art performance on multiple real-world benchmarks.

Sheaf topological representations provide a principled foundation for the task.

Abstract

Spatio-temporal processes often exhibit highly heterogeneous and non-intuitive responses to localized disruptions, limiting the effectiveness of conventional message passing approaches in modeling local heterogeneity. We reformulate spatio-temporal forecasting as the problem of learning information flow over locally structured spaces, rather than propagating globally aligned node representations. To this end, we introduce a spatio-temporal sheaf diffusion graph neural network (ST-Sheaf GNN) that embeds graph topology into sheaf-based vector spaces connected by learned linear restriction maps. Unlike prior approaches relying on static or globally shared transformations, our model learns dynamic restriction maps that evolve over time and adapt to local spatio-temporal patterns, enabling more expressive interactions. The proposed framework both theoretically guarantees and empirically demonstrates evidence that the proposed diffusion mechanism mitigates oversmoothing, preserving discriminative node representations even with increasing diffusion layer depth. Experiments on diverse real-world spatio-temporal forecasting benchmarks across multiple domains demonstrate state-of-the-art performance, highlighting the effectiveness of sheaf topological representations as a principled foundation for spatio-temporal graph learning. The code is available at: https://anonymous.4open.science/r/ST-SheafGNN-6523/.