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：时序知识图谱通过三元组 $(s,p,o,\tau)$ 表示时序事实，其中主体 $s$ 与客体 $o$ 通过关系标签 $p$ 在时间点或时间区间 $\tau$ 下关联。时序知识图谱可能表现出不同时间点上的静态时序模式以及不同时间戳之间的动态时序模式。为学习丰富的静态与动态时序模式并将其应用于推理，现有文献提出了多种嵌入方法。然而，由于大多方法依赖单一底层嵌入空间，其建模各类时序模式的能力因受限于单一嵌入空间的几何性质而严重受限。本文通过提出一种将时序事实映射至多个异构几何子空间（即复空间、对偶空间与分裂复空间）乘积空间的嵌入方法，突破了这一限制。此外，我们提出一种时序-几何注意力机制，根据捕获的关系与时序信息灵活整合不同几何子空间的信息。在标准时序基准数据集上的实验结果表明，我们的方法优于现有最先进模型。