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.

翻译：与传统知识图谱不同，时序知识图谱需充分探索和推理随时间演化的时序事实。然而，现有时序知识图谱方法仍面临两大挑战：一是对连续任意时间戳的建模能力有限，二是缺乏时序约束下丰富的推理模式。本文提出一种创新的时序知识图谱嵌入方法（PTBox），通过基于多项式分解的时序表示与基于盒子嵌入的实体表示来解决上述问题。具体而言，我们将时间信息进行多项式分解，并引入可学习的时序基础张量增强模型灵活表征任意时间戳的能力。此外，我们将每个实体建模为超矩形盒子，并将每个关系定义为头实体盒子与尾实体盒子上的变换。实体盒子能够捕捉复杂几何结构并学习鲁棒表示，提升了模型对丰富推理模式的归纳能力。理论上，我们的PTBox可编码任意时间信息甚至未见时间戳，同时捕捉知识库中的丰富推理模式和高元关系。在真实数据集上的大量实验证明了我们方法的有效性。