CTDG-SSM: Continuous-time Dynamic Graph State Space Models for Long Range Propagation

Ayushman Raghuvanshi, Thummaluru Siddartha Reddy, Sundeep Prabhakar Chepuri, Mahesh Chandran

Keywords: Continuous time dynamic graphs, State space models, Long range propogation, Higher-order polynomial projection operator

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 in learning representations for CTDGs, 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 limitations of the current approaches, we derive the state-space modelling 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, where solution for memory representations from $\texttt{CTT-HiPPO}$ are 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 ($\texttt{CTDG-SSM}$). This is then discretized (e.g., using the zero-order hold method) for practical implementation. We further provide theoretical guarantees demonstrating the robustness of memory representations under graph structure perturbations. 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 dynamic link prediction and sequence classification tasks, specifically on datasets that require long range temporal (LRT) and spatial reasoning.

Primary Area: learning on graphs and other geometries & topologies

Submission Number: 24420