Temporal Knowledge Graphs (TKGs) incorporate a temporal dimension, allowing for a precise capture of the evolution of knowledge and reflecting the dynamic nature of the real world. Typically, TKGs contain complex geometric structures, with various geometric structures interwoven. However, existing Temporal Knowledge Graph Completion (TKGC) methods either model TKGs in a single space or neglect the heterogeneity of different curvature spaces, thus constraining their capacity to capture these intricate geometric structures. In this paper, we propose a novel Integrating Multi-curvature shared and specific Embedding (IME) model for TKGC tasks. Concretely, IME models TKGs into multi-curvature spaces, including hyperspherical, hyperbolic, and Euclidean spaces. Subsequently, IME incorporates two key properties, namely space-shared property and space-specific property. The space-shared property facilitates the learning of commonalities across different curvature spaces and alleviates the spatial gap caused by the heterogeneous nature of multi-curvature spaces, while the space-specific property captures characteristic features. Meanwhile, IME proposes an Adjustable Multi-curvature Pooling (AMP) approach to effectively retain important information. Furthermore, IME innovatively designs similarity, difference, and structure loss functions to attain the stated objective. Experimental results clearly demonstrate the superior performance of IME over existing state-of-the-art TKGC models.

翻译：摘要：时序知识图谱通过引入时间维度，能够精确捕捉知识的演化过程，反映现实世界的动态特性。通常，时序知识图谱包含复杂的几何结构，且不同几何结构相互交织。然而，现有时序知识图谱补全方法要么在单一空间建模时序知识图谱，要么忽略不同曲率空间的异质性，从而限制了其捕获这些复杂几何结构的能力。本文提出了一种新颖的面向时序知识图谱补全任务的多曲率共享与特定嵌入融合（IME）模型。具体而言，IME将时序知识图谱建模到包括超球面空间、双曲空间和欧氏空间在内的多曲率空间中。随后，IME引入了两个关键特性，即空间共享特性和空间特定特性：空间共享特性有助于学习不同曲率空间之间的共性，并缓解多曲率空间异构性导致的空间差异；而空间特定特性则用于捕获各曲率空间的特征信息。同时，IME提出了一种可调节多曲率池化（AMP）方法以有效保留重要信息。此外，IME创新性地设计了相似度损失、差异损失和结构损失函数以实现既定目标。实验结果表明，IME的性能显著优于现有最先进的时序知识图谱补全模型。