Challenge: Existing knowledge graph embedding models fail to model semantic hierarchies . Existing methods fail to understand the semantic hierarchies of knowledge graphs .
Approach: They propose a model which embeds entities as pure quaternions and constrains the modulus of entities to make them have hierarchical distributions.
Outcome: The proposed model can encode symmetry/antisymmetry, inversion, composition, multiple relation patterns and learn semantic hierarchies simultaneously.

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Distance-Adaptive Quaternion Knowledge Graph Embedding with Bidirectional Rotation (2025.coling-main)

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Challenge: Existing knowledge graph embedding models measure the plausibility of triplets either through semantic matching or distance scoring functions.
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RotateCT: Knowledge Graph Embedding by Rotation and Coordinate Transformation in Complex Space (2022.coling-1)

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Challenge: Existing knowledge graph embedding methods fail to model non-commutative composition patterns . Existing methods are limited to complex space, resulting in a large number of parameters.
Approach: They propose a knowledge graph embedding method that transforms the coordinates of each entity and then represents each relation as a rotation from head entity to tail entity in complex space.
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3D Rotation and Translation for Hyperbolic Knowledge Graph Embedding (2024.eacl-long)

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Challenge: Existing knowledge graph embeddings do not capture relation patterns, but they capture symmetry, antisymmetry, inversion, commutative composition, non-commutable composition, hierarchy, and multiplicity.
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Knowledge Graph Embedding with Hierarchical Relation Structure (D18-1)

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Challenge: Existing knowledge graph embedding models embed entities and relations into latent vectors without leveraging rich information from relation structure.
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Low-Dimensional Hyperbolic Knowledge Graph Embeddings (2020.acl-main)

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Challenge: Existing methods for predicting missing facts do not account for hierarchical and logical patterns in KGs.
Approach: They propose a class of hyperbolic KG embedding models that capture hierarchical and logical patterns.
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Block-Diagonal Orthogonal Relation and Matrix Entity for Knowledge Graph Embedding (2024.findings-emnlp)

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Challenge: Existing knowledge graph embeddings (KGs) are limited in their flexibility and difficulties in generalizing them for higher-dimensional rotations.
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RotateQVS: Representing Temporal Information as Rotations in Quaternion Vector Space for Temporal Knowledge Graph Completion (2022.acl-long)

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Challenge: Existing methods for temporal knowledge graphs can hardly model temporal relation patterns, lacking of interpretability.
Approach: They propose a temporal modeling method which represents temporal entities as Rotations in Quaternion Vector Space and relations as complex vectors in Hamilton’s quaterniont space.
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Dual Complex Number Knowledge Graph Embeddings (2024.lrec-main)

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Challenge: Existing knowledge graph embedding methods fail to model non-commutative composition patterns . extending to such sophisticated spaces increases the amount of parameters, which greatly reduces the parameter efficiency.
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TransERR: Translation-based Knowledge Graph Embedding via Efficient Relation Rotation (2024.lrec-main)

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Challenge: Existing knowledge graph embedding models lack links between entities and relationships, which is a problem for knowledge graphs.
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Knowledge GeoGebra: Leveraging Geometry of Relation Embeddings in Knowledge Graph Completion (2024.lrec-main)

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Challenge: Knowledge graph embedding models are limited to the algebra and geometry of the entity embeddable space, the algebra of the relation embeddible space, and the interaction between relation and entity embeds.
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