AI Insight
This paper introduces CTDG-SSM, a novel state-space modeling framework for learning representations from continuous-time dynamic graphs that evolve over time. The approach addresses the challenge of capturing long-range temporal and spatial patterns by developing a topology-aware memory mechanism (CTT-HiPPO) that jointly encodes temporal dynamics and graph structure through polynomial projections of the Laplacian matrix. The method achieves state-of-the-art performance across multiple benchmarks including dynamic link prediction, node classification, and sequence classification, with particularly strong improvements on tasks requiring long-range reasoning.
Why it matters
This work has important applications for analyzing evolving networks in domains such as social networks, traffic systems, financial transactions, and biological networks where understanding both short-term and long-term dependencies is crucial. The parameter-efficient approach makes it computationally feasible to model complex temporal patterns in large-scale dynamic graph data.
arXiv:2606.04672v2 Announce Type: replace-cross
Abstract: Continuous-time dynamic graphs (CTDGs) provide a richer framework to capture fine-grained temporal patterns in evolving relational data. Long-range information propagation is a key challenge while learning representations, wherein it is important to retain and update information over long temporal horizons. Existing approaches restrict models to capture one-hop or local temporal neighborhoods and fail to capture multi-hop or global structural patterns. To mitigate this, we derive a parameter-efficient state-space modeling framework for continuous-time dynamic graphs (CTDG-SSM) from first principles. We first introduce continuous-time Topology-Aware higher order polynomial projection operator (CTT-HiPPO), a novel memory-based reformulation of HiPPO to jointly encode temporal dynamics and graph structure. The solution from CTT-HiPPO is obtained by projecting the classical HiPPO solution through a polynomial of the Laplacian matrix, yielding topology-aware memory updates that admit an equivalent state-space formulation for CTDGs (CTDG-SSM). Then a computationally efficient discrete formulation is obtained using the zero-order hold approach for model implementation.
Across benchmarks on dynamic link prediction, dynamic node classification, and sequence classification, CTDG-SSM achieves state-of-the-art performance. Notably, it achieves large performance gains on datasets that require long range temporal (LRT) and spatial reasoning.