  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.
