Learning Continuous Temporal Dynamics on Symplectic Manifolds for Temporal Knowledge Graph Embedding

摘要

Temporal knowledge graph embedding (TKGE) aims to model the temporal evolution of relational facts. However, existing approaches predominantly rely on discrete timestamp lookup tables and high-dimensional embedding spaces, which lack explicit structural constraints for continuous-time dynamics. As a result, temporal patterns are often captured through capacity scaling rather than principled dynamic modeling, leading to limited parameter efficiency and scalability.To address these limitations, we propose , a physics-inspired framework that embeds temporal dynamics into a symplectic phase space. Our model introduces a structure-preserving Hamiltonian evolution mechanism based on a pairwise-decoupled Hamiltonian generator and its Cayley transform, ensuring that temporal transformations adhere to the symplectic group \mathrm{Sp}(2d) and preserve phase-space volume with linear computational complexity. In addition, we design a Time-Aware Parameter Modulation mechanism that integrates continuous Rotary Time Embeddings via Feature-wise Linear Modulation, enabling smooth temporal evolution while capturing event-driven variations. Theoretical analysis establishes the geometric validity of the proposed framework. Extensive experiments on standard TKGE benchmarks demonstrate that achieves competitive performance with substantially lower embedding dimensions. Furthermore, empirical results show that the proposed continuous Hamiltonian evolution facilitates generalization to unseen timestamps by learning transferable temporal dynamics from the underlying geometric structure.