Title: Capturing Long-Range Spatio-Temporal Patterns in Continuous-Time Dynamic Graphs via State Space Models

Abstract: Continuous-time dynamic graphs (CTDGs) offer a more granular framework for modeling temporal patterns within evolving relational datasets. A primary obstacle in learning representations for these graphs is the propagation of long-range information, which necessitates the ability to preserve and update data across extensive temporal spans. Current methods are often limited to one-hop or local temporal neighborhoods, thereby failing to identify multi-hop or global structural configurations. To address this limitation, we propose CTDG-SSM, a parameter-efficient state-space modeling framework for CTDGs derived from first principles. Central to this approach is the introduction of CTT-HiPPO, a new memory-based reformulation of HiPPO that simultaneously encodes graph structure and temporal dynamics. This method projects the classical HiPPO solution via a polynomial of the Laplacian matrix, resulting in topology-aware memory updates that can be equivalently formulated as a state-space model for CTDGs. For practical implementation, we employ a zero-order hold technique to derive a computationally efficient discrete formulation. Our evaluations on dynamic link prediction, dynamic node classification, and sequence classification benchmarks demonstrate that CTDG-SSM delivers state-of-the-art results. Significantly, the model exhibits substantial performance improvements on datasets demanding long-range temporal (LRT) and spatial reasoning.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC