Distinguished from traditional knowledge graphs (KGs), temporal knowledge
graphs (TKGs) must explore and reason over temporally evolving facts
adequately. However, existing TKG approaches still face two main challenges,
i.e., the limited capability to model arbitrary timestamps continuously and the
lack of rich inference patterns under temporal constraints. In this paper, we
propose an innovative TKGE method (PTBox) via polynomial decomposition-based
temporal representation and box embedding-based entity representation to tackle
the above-mentioned problems. Specifically, we decompose time information by
polynomials and then enhance the model's capability to represent arbitrary
timestamps flexibly by incorporating the learnable temporal basis tensor. In
addition, we model every entity as a hyperrectangle box and define each
relation as a transformation on the head and tail entity boxes. The entity
boxes can capture complex geometric structures and learn robust
representations, improving the model's inductive capability for rich inference
patterns. Theoretically, our PTBox can encode arbitrary time information or
even unseen timestamps while capturing rich inference patterns and higher-arity
relations of the knowledge base. Extensive experiments on real-world datasets
demonstrate the effectiveness of our method.

通过多项式分解的时间表示和基于盒子嵌入的实体表示，我们提出了一种创新的 TKGE 方法（PTBox），以解决传统知识图谱中的时态知识表示困难和富含时间约束的推理模式缺失的问题。