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Knowledge Graph Completion (KGC) aims to predict missing links using known triples, thereby enhancing graph coverage. A key challenge is modeling diverse relational patterns such as symmetry, antisymmetry, inversion, composition and semantic hierarchy. Existing models such as RotatE can capture symmetric, antisymmetric, inverse, and commutative composition patterns, yet struggle with non-commutative composition. Rotate3D addresses this by introducing non-commutativity via three-dimensional rotations, but still fails to capture the semantic hierarchies prevalent in knowledge graphs. Moreover, both models cannot effectively model one-to-many relations. To overcome these limitations, we propose RelBall, which extends Rotate3D with two innovations. First, our model introduces modulus transformation to model hierarchies, driving abstract concepts toward smaller moduli","title":"RelBall: Relation Ball with Quaternion Rotation for Knowledge Graph Completion","url":"https://arxiv.org/abs/2606.27967","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.27967v1 Announce Type: new \nAbstract: Real-world knowledge graphs are often incomplete, lacking many valid facts. Knowledge Graph Completion (KGC) aims to predict missing links using known triples, thereby enhancing graph coverage. A key challenge is modeling diverse relational patterns such as symmetry, antisymmetry, inversion, composition and semantic hierarchy. Existing models such as RotatE can capture symmetric, antisymmetric, inverse, and commutative composition patterns, yet struggle with non-commutative composition. Rotate3D addresses this by introducing non-commutativity via three-dimensional rotations, but still fails to capture the semantic hierarchies prevalent in knowledge graphs. Moreover, both models cannot effectively model one-to-many relations. To overcome these limitations, we propose RelBall, which extends Rotate3D with two innovations. 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