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    This study introduces multicurvature adaptive embedding (MADE) for temporal knowledge graph completion (TKGC). MADE effectively models complex temporal knowledge graphs by utilizing multiple curvature spaces, outperforming existing methods.

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    Area of Science:

    • Artificial Intelligence
    • Data Science
    • Knowledge Representation

    Background:

    • Temporal knowledge graphs (TKGs) are crucial for understanding evolving information.
    • Traditional embedding methods struggle with TKGs' complex geometric structures and time-dependent nature.
    • Existing temporal knowledge graph completion (TKGC) models face challenges with high-dimensional, nonlinear data.

    Purpose of the Study:

    • To propose a novel TKGC model, multicurvature adaptive embedding (MADE), capable of handling complex geometric structures in TKGs.
    • To address the limitations of embedding TKGs solely in Euclidean space.
    • To improve the accuracy and robustness of TKGC.

    Main Methods:

    • Developed MADE, a model that embeds TKGs in multicurvature spaces (Euclidean, hyperbolic, hyperspherical).
    • Employs data-driven weighting to adaptively leverage different curvature spaces.
    • Introduced a quadruplet distributor (QD) for enhanced information interaction within geometric spaces.
    • Implemented innovative temporal regularization to ensure timestamp embedding smoothness.

    Main Results:

    • MADE demonstrated superior performance compared to state-of-the-art TKGC models in experiments.
    • The multicurvature approach effectively captures diverse geometric structures within TKGs.
    • Adaptive weighting and temporal regularization significantly improved embedding quality.

    Conclusions:

    • MADE offers a powerful new approach for temporal knowledge graph completion.
    • Modeling TKGs in multicurvature spaces is more effective for complex, evolving knowledge.
    • The proposed methods enhance the representation and completion of temporal knowledge graphs.