用状态空间模型捕捉动态图的长程时空依赖,提升时序与结构推理能力。
Learning Long Range Spatio-Temporal Representations over Continuous Time Dynamic Graphs with State Space Models

- 基于连续时间拓扑感知多项式投影,融合图结构与时间动态建模
- 在长时序和长距离任务上显著优于现有方法,尤其在需全局推理的数据集上
- 参数高效且可离散化实现,适合大规模动态图学习
连续时间动态图(CTDGs)能更精细地捕捉演化关系数据中的时序模式。学习表示时的关键挑战是长程信息传播,需在长时间跨度上保持并更新信息。现有方法通常仅限于一跳或局部时序邻域,难以捕捉多跳或全局结构模式。为此,我们从原理出发,提出一种参数高效的连续时间动态图状态空间模型(CTDG-SSM)。首先引入连续时间拓扑感知高阶多项式投影算子(CTT-HiPPO),将经典HiPPO重构为同时编码时间动态与图结构的记忆机制。通过拉普拉斯矩阵的多项式投影获得拓扑感知记忆更新,并导出适用于CTDGs的状态空间形式。进一步采用零阶保持法实现计算高效的离散化版本。在动态链接预测、动态节点分类与序列分类等基准测试中,CTDG-SSM达到当前最优性能,尤其在需要长程时序(LRT)与空间推理的数据集上表现突出。
原文摘要 · Abstract (English)
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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