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

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 $\texttt{(CTDG-SSM)}$ from first principles. We first introduce continuous-time Topology-Aware higher order polynomial projection operator ($\texttt{CTT-HiPPO}$), a novel memory-based reformulation of $\texttt{HiPPO}$ to jointly encode temporal dynamics and graph structure. The solution from $\texttt{CTT-HiPPO}$ 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 ($\texttt{CTDG-SSM}$). 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, $\texttt{CTDG-SSM}$ achieves state-of-the-art performance. Notably, it achieves large performance gains on datasets that require long range temporal (LRT) and spatial reasoning.

Many real-world networks, such as financial transactions, communication networks, and social media platforms, change continuously over time. To analyze these systems accurately, AI models need to remember a vast history of interactions and understand how a change in one corner of a network impacts distant areas. Existing AI methods struggle because they either have short-term memory or can only look at immediate, local connections, missing the global picture. We address this limitation by creating a new mathematical framework called CTDG-SSM. This framework acts as an advanced memory system that compresses an endless history of network changes into a compact set of equations. Crucially, it blends time and network structure together, allowing information to travel deep across the network without losing track of past context. Our model is exceptionally lightweight and efficient. When tested on real-world datasets, it matched or outperformed the best existing AI models while requiring significantly fewer adjustable settings. This makes it a powerful, cost-effective tool for tracking complex, fast-moving networks over long periods.