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HopfE: Knowledge Graph Representation Learning using Inverse Hopf Fibrations

Recently, several Knowledge Graph Embedding (KGE) approaches have been devised to represent entities and relations in dense vector space and employed in downstream tasks such as link prediction. A few KGE techniques address interpretability, i.e., mapping the connectivity patterns of the relations (i.e., symmetric/asymmetric, inverse, and composition) to a geometric interpretation such as rotations. Other approaches model the representations in higher dimensional space such as four-dimensional space (4D) to enhance the ability to infer the connectivity patterns (i.e., expressiveness). However, modeling relation and entity in a 4D space often comes at the cost of interpretability. This paper proposes HopfE, a novel KGE approach aiming to achieve the interpretability of inferred relations in the four-dimensional space. We first model the structural embeddings in 3D Euclidean space and view the relation operator as an SO(3) rotation. Next, we map the entity embedding vector from a 3D space to a 4D hypersphere using the inverse Hopf Fibration, in which we embed the semantic information from the KG ontology. Thus, HopfE considers the structural and semantic properties of the entities without losing expressivity and interpretability. Our empirical results on four well-known benchmarks achieve state-of-the-art performance for the KG completion task.

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