Analytical Construction on Geometric Architectures: Transitioning from Static to Temporal Link Prediction

Static systems exhibit diverse structural properties, such as hierarchical, scale-free, and isotropic patterns, where different geometric spaces offer unique advantages. Methods combining multiple geometries have proven effective in capturing these characteristics. However, real-world systems often evolve dynamically, introducing significant challenges in modeling their temporal changes. To overcome this limitation, we propose a unified cross-geometric learning framework for dynamic systems, which synergistically integrates Euclidean and hyperbolic spaces, aligning embedding spaces with structural properties through finegrained substructure modeling. Our framework further incorporates a temporal state aggregation mechanism and an evolution-driven optimization objective, enabling comprehensive and adaptive modeling of both nodal and relational dynamics over time. Extensive experiments on diverse realworld dynamic graph datasets highlight the superiority of our approach in capturing complex structural evolution, surpassing existing methods across multiple metrics.