SKGE: Spherical Knowledge Graph Embedding with Geometric Regularization

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.