SKGE：带有几何正则化的球面知识图谱嵌入
SKGE: Spherical Knowledge Graph Embedding with Geometric Regularization
AI总结：
提出球面知识图谱嵌入模型SKGE，通过可学习球化层将实体约束在超球面上并引入几何正则化，有效解决了欧氏空间建模复杂关系的局限，显著提升了表示的鲁棒性与性能。
摘要：
知识图谱嵌入（KGE）已成为多关系数据表示学习的一项基础技术。许多开创性模型（如 TransE）在无界欧几里得空间中运行，这在建模复杂关系时存在固有局限性，并可能导致训练效率低下。在本文中，我们提出了球面知识图谱嵌入（SKGE），该模型通过将实体表示约束在紧致流形（即超球面）上，挑战了这一范式。SKGE 采用一个可学习的非线性球化层将实体映射到球面上，并将关系解释为一种混合的“先平移后投影”变换。通过在三个基准数据集 FB15k-237、CoDEx-S 和 CoDEx-M 上进行的大量实验，我们证明 SKGE 持续且显著地优于其强大的欧几里得对应模型 TransE，特别是在 FB15k-237 和 CoDEx-M 等大规模基准上，这证明了球面几何先验的有效性。我们提供了深入分析以揭示这种优势的来源，表明这种几何约束作为一种强大的正则化器，在所有关系类型上均带来了全面的性能提升。更根本地，我们证明了球面几何创造了一个“固有的困难负采样”环境，自然地消除了平凡负样本，并迫使模型学习更鲁棒且语义连贯的表示。我们的发现有力地证明，流形的选择不仅仅是一个实现细节，更是一个基本的设计原则，倡导将几何先验作为设计下一代强大且稳定的 KGE 模型的基石。
英文摘要：
Knowledge graph embedding (KGE) has become a fundamental technique for representation learning on multi-relational data. Many seminal models, such as TransE, operate in an unbounded Euclidean space, which presents inherent limitations in modeling complex relations and can lead to inefficient training. In this paper, we propose Spherical Knowledge Graph Embedding (SKGE), a model that challenges this paradigm by constraining entity representations to a compact manifold: a hypersphere. SKGE employs a learnable, non-linear Spherization Layer to map entities onto the sphere and interprets relations as a hybrid translate-then-project transformation. Through extensive experiments on three benchmark datasets, FB15k-237, CoDEx-S, and CoDEx-M, we demonstrate that SKGE consistently and significantly outperforms its strong Euclidean counterpart, TransE, particularly on large-scale benchmarks such as FB15k-237 and CoDEx-M, demonstrating the efficacy of the spherical geometric prior. We provide an in-depth analysis to reveal the sources of this advantage, showing that this geometric constraint acts as a powerful regularizer, leading to comprehensive performance gains across all relation types. More fundamentally, we prove that the spherical geometry creates an "inherently hard negative sampling" environment, naturally eliminating trivial negatives and forcing the model to learn more robust and semantically coherent representations. Our findings compellingly demonstrate that the choice of manifold is not merely an implementation detail but a fundamental design principle, advocating for geometric priors as a cornerstone for designing the next generation of powerful and stable KGE models.
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