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 fine-grained 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 real-world dynamic graph datasets highlight the superiority of our approach in capturing complex structural evolution, surpassing existing methods across multiple metrics.

Many real-world networks, such as social interactions, communication patterns, or biological systems, change over time and current embedding methods in Euclidean or hyperbolic space cannot simultaneously capture their evolving structures and hierarchical relationships.We propose a unified framework that aligns each graph substructure with the most suitable geometry—Euclidean for flat regions and hyperbolic for hierarchical regions—while using a temporal state aggregator and an evolution-driven objective to learn how nodes and links develop.By adapting the embedding space as the graph evolves, our approach more accurately tracks complex structural changes and greatly improves temporal link prediction performance, enabling better modeling for applications like recommendation systems, epidemic monitoring, and evolving knowledge graphs.