🤖 AI Summary
Existing continuous-time dynamic graph methods struggle to capture long-range spatiotemporal dependencies due to their reliance on local neighborhoods. This work proposes CTDG-SSM, which introduces the first topology-aware memory mechanism by extending HiPPO through a Continuous-Time Topology-aware High-order Polynomial Projection Operator (CTT-HiPPO). This operator jointly models graph structure and temporal dynamics, yielding an efficient state-space representation. By integrating graph Laplacian polynomial projections with zero-order hold discretization, the framework achieves parameter-efficient modeling of long-range spatiotemporal interactions. Empirical results demonstrate state-of-the-art performance across dynamic link prediction, node classification, and sequence classification tasks, with particularly pronounced gains in scenarios requiring long-range reasoning.
📝 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.