CORE: Cyclic Orthotope Relation Embedding for Knowledge Graph Completion

Knowledge graphs (KGs) organize real-world knowledge as triplets and underpin many downstream applications. Due to their inherent incompleteness, knowledge graph completion (KGC) is widely studied and is typically formulated as triplet prediction, with link prediction as the dominant paradigm. However, this formulation focuses on the incompleteness of triplet-wise information and overlooks the incompleteness of entity-relation compatibility information. To address this limitation, we introduce a relation set completion task (RSC), which complements the link prediction task and aims to reason about missing relations that are semantically compatible with a given entity. We further propose a Relation Set Embedding model (RelSetE), which models latent patterns among the observed relations of entities to infer missing ones. To evaluate RelSetE, we derive three benchmark datasets from standard KG benchmarks. Extensive experiments demonstrate that RelSetE effectively captures entity-relation compatibility patterns and performs favorably in inferring missing relations of entities. Code and data are publicly available.

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. First, our model introduces modulus transformation to model hierarchies, driving abstract concepts toward smaller moduli and concrete instances toward larger ones. Second, it introduces a tail-centric relation ball to model one-to-one, one-to-many, many-to-one, and many-to-many relations. RelBall offers the following advantages: (1) coverage of all relational patterns, including the ones mentioned above; (2) an interpretable hierarchical representation where the modulus directly reflect semantic levels; (3) support for one-to-one, one-to-many, many-to-one, and many-to-many relations. Experiments on multiple datasets demonstrate RelBall's competitive link prediction performance against various baselines.

Link prediction in knowledge graphs fundamentally depends on the quality of learned embeddings for entities and relations. However, most existing methods derive these embeddings by aggregating only the local neighborhood of each entity, neglecting the global structure of the knowledge graph. This limited view prevents models from capturing higher-level structural patterns that are essential for accurate and generalizable link prediction. To address these limitations, we introduce Model Graph Inductive Learning (\textbf{MGIL}), a framework that constructs a model graph by clustering entities based on the similarity of their incoming and outgoing relational structures or their entity types. A GNN is then applied to this model graph to produce embeddings that capture the global view of the knowledge graph. These embeddings subsequently serve as high-quality initial features %embeddings for the original knowledge graph, replacing random initialization and leading to more stable and expressive representations. Extensive experiments on standard and recently proposed inductive benchmarks demonstrate that MGIL achieves state-of-the-art or highly competitive performance in inductive link prediction, highlighting its effectiveness across diverse graph settings.