Over-squashing in Spatiotemporal Graph Neural Networks

Ivan Marisca, Jacob Bamberger, Cesare Alippi, Michael M. Bronstein

Keywords: Graph Neural Networks, Spatiotemporal Graph Neural Networks, Over-squashing, Time Series Processing, Time Series Forecasting

TL;DR: We formalize the over-squashing phenomenon in spatiotemporal graph neural networks and analyze how it affects information propagation across the spatial and temporal dimensions.

Abstract: Graph Neural Networks (GNNs) have achieved remarkable success across various domains. However, recent theoretical advances have identified fundamental limitations in their information propagation capabilities, such as over-squashing, where distant nodes fail to effectively exchange information. While extensively studied in static contexts, this issue remains unexplored in Spatiotemporal GNNs (STGNNs), which process sequences associated with graph nodes. Nonetheless, the temporal dimension amplifies this challenge by increasing the information that must be propagated. In this work, we formalize the spatiotemporal over-squashing problem and demonstrate its distinct characteristics compared to the static case. Our analysis reveals that, counterintuitively, convolutional STGNNs favor information propagation from points temporally distant rather than close in time. Moreover, we prove that architectures that follow either time-and-space or time-then-space processing paradigms are equally affected by this phenomenon, providing theoretical justification for computationally efficient implementations. We validate our findings on synthetic and real-world datasets, providing deeper insights into their operational dynamics and principled guidance for more effective designs.

Primary Area: Deep learning (e.g., architectures, generative models, optimization for deep networks, foundation models, LLMs)

Submission Number: 24363