DyGHydra: A Hierarchical State-Space Model with Time Dynamics and Interactive-Relational Selectivity for Link Prediction

The task of dynamic graph link prediction is to forecast the evolution of complex systems. Empirical observations reveal that interactions within these systems exhibit an Entangled Spatio-Temporal Pattern, which manifests through three interrelated phenomena, namely Latent High-Order Bridges, Multi-Frequency Temporal Dynamics, and Spatio-Temporal Entanglement, with stronger structural ties facilitating tolerance for longer temporal gaps. However, limited by computationally prohibitive multi-hop sampling or inefficient long-sequence modeling, existing methods struggle to capture this complex pattern. Inspired by State-Space Models (SSMs) like Mamba for efficient long-range modeling yet aiming to address their native agnosticism to structural and multi-frequency dynamics, we propose a framework named DyGHydra, which couples a tailored Continuous-Time Hierarchical Mamba (CT-HMamba) backbone with a multi-hop structural encoder. The framework first employs the multi-hop structural encoder to reveal latent high-order interactions, extracting interaction-level cross-hop features. Subsequently, the CT-HMamba backbone utilizes these features to address multi-frequency dynamics through a hierarchical architecture, decomposing interaction history to simultaneously model high-frequency bursts and long-term trends. To capture the spatio-temporal entanglement, CT-HMamba further tailors its core state-space mechanism to be co-driven by physical time and structural context. Specifically, physical time governs the state transition decay to reflect temporal forgetting, while structural context modulates the input-output projections to prioritize topologically significant events. Extensive experiments on eleven real-world datasets show that DyGHydra achieves state-of-the-art performance across most settings for both transductive and inductive link prediction, validating its effectiveness in modeling complex temporal dynamics with superior efficiency.