Learning Long Range Spatio-Temporal Representations over Continuous Time Dynamic Graphs with State Space Models

• URL: http://arxiv.org/abs/2606.04672v2
• Date: Thu, 04 Jun 2026 09:25:02 GMT
• Title: Learning Long Range Spatio-Temporal Representations over Continuous Time Dynamic Graphs with State Space Models
• Abstract summary: Continuous-time dynamic graphs (CTDGs) provide a richer framework to capture fine-grained temporal patterns in evolving data.<n>We derive a parameter-efficient state-space modeling framework for continuous-time dynamic graphs.<n>CTDG-SSM achieves large performance gains on datasets that require long range temporal (LRT) and spatial reasoning.
• Score: 22.610672356493378
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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