Temporal knowledge graphs represent temporal facts $(s,p,o,\tau)$ relating a subject $s$ and an object $o$ via a relation label $p$ at time $\tau$, where $\tau$ could be a time point or time interval. Temporal knowledge graphs may exhibit static temporal patterns at distinct points in time and dynamic temporal patterns between different timestamps. In order to learn a rich set of static and dynamic temporal patterns and apply them for inference, several embedding approaches have been suggested in the literature. However, as most of them resort to single underlying embedding spaces, their capability to model all kinds of temporal patterns was severely limited by having to adhere to the geometric property of their one embedding space. We lift this limitation by an embedding approach that maps temporal facts into a product space of several heterogeneous geometric subspaces with distinct geometric properties, i.e.\ Complex, Dual, and Split-complex spaces. In addition, we propose a temporal-geometric attention mechanism to integrate information from different geometric subspaces conveniently according to the captured relational and temporal information. Experimental results on standard temporal benchmark datasets favorably evaluate our approach against state-of-the-art models.

翻译：摘要：时间知识图谱表示时间事实$(s,p,o,\tau)$，该事实通过关系标签$p$在时间$\tau$（可为时间点或时间区间）连接主体$s$与客体$o$。时间知识图谱可能展现不同时间点的静态时间模式与时间戳之间的动态时间模式。为学习丰富的静态与动态时间模式并将其应用于推理，已有文献提出若干嵌入方法。然而，由于大多数方法采用单一底层嵌入空间，其建模各类时间模式的能力因必须遵循单一嵌入空间的几何性质而严重受限。我们通过一种将时间事实映射到多个异质几何子空间（即复数、对偶数和分裂四元数空间）乘积空间中的嵌入方法来突破此限制。此外，我们提出一种时间-几何注意力机制，可根据捕获的关系与时间信息便捷地整合来自不同几何子空间的信息。在标准时间基准数据集上的实验结果充分证明，我们的方法优于现有最优模型。