CDRGN-SDE: Cross-Dimensional Recurrent Graph Network with neural Stochastic Differential Equation for temporal knowledge graph embedding

The temporal knowledge graph builds upon the static knowledge graph by introducing the time dimension and finds extensive applications in real artificial intelligence scenarios. However, the temporal knowledge graph’s incompleteness restricts the applicability of numerous temporal knowledge graph tasks. Temporal knowledge graph embedding (TKGE) is a representation learning technique that effectively addresses the temporal knowledge graph’s incompleteness. These methods aim to map entities and relations in the knowledge graph to a low-dimensional vector space while capturing features over time. However, the current TKGE methods encounter three main challenges: (1) how to resolve the continuity problem of dynamic features in the continuous time domain; (2) how to simultaneously model the dependence of structural knowledge representation on time and dimension; (3) how to address the heterogeneity of time representation in a temporal knowledge graph. We propose the CDRGN-SDE, a Cross-Dimensional Recurrent Graph Network with a neural Stochastic Differential Equation framework, to tackle these challenges. The CDRGN-SDE model effectively addresses the above challenges and establishes a unified framework: (1) we employ a neural ordinary differential equation with stochastic noise to simulate the continuity of dynamic systems in the continuous time domain; (2) we propose a Dimension-Segment-Wise (DSW) embedding method for TKGE, which effectively integrates time and dimensional information; (3) we introduce a simple and effective time representation method that integrates complex time features into the model. Experimental evaluations on benchmark datasets demonstrate that the CDRGN-SDE model outperforms the state-of-the-art temporal knowledge graph reasoning models.