Challenge: Existing knowledge graph embedding models lack links between entities and relationships, which is a problem for knowledge graphs.
Approach: They propose a translation-based knowledge geraph embedding method via efficient relation rotation that rotates the head and tail entities with their corresponding unit quaternions.
Outcome: The proposed method can be used to embed knowledge graphs on 10 benchmark datasets with fewer parameters than the previous translation-based models.

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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.
Approach: They propose a 3D Rotation and Translation in Hyperbolic space model that captures relation patterns simultaneously.
Outcome: The proposed model outperforms state-of-the-art models in terms of accuracy, hierarchy property, and other relation patterns in low-dimensional space, while performing similarly in high-dimensional spaces.
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.
Outcome: The proposed method outperforms state-of-the-art methods on link prediction and path query answering.
TranSHER: Translating Knowledge Graph Embedding with Hyper-Ellipsoidal Restriction (2022.emnlp-main)

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Challenge: Existing knowledge graph embedding methods restrict entities on hyper-ellipsoid surfaces, resulting in suboptimal knowledge graph completion.
Approach: They propose a score function that leverages relation-specific translations between head and tail entities to relax constraints on hyper-ellipsoid surfaces.
Outcome: The proposed method achieves state-of-the-art performance on link prediction and generalizes well to datasets in different domains and scales.
Learning Hierarchy-Aware Quaternion Knowledge Graph Embeddings with Representing Relations as 3D Rotations (2022.coling-1)

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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.
TranS: Transition-based Knowledge Graph Embedding with Synthetic Relation Representation (2022.findings-emnlp)

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Challenge: Knowledge graph embedding (KGE) is a computational approach to learn continuous vector representations of relations and entities in knowledge graphs.
Approach: They propose a transition-based method to learn continuous vector representations of relations and entities in knowledge graph (KG) it replaces a single relation vector in the relation part with a synthetic relation representation with entity-relation interactions to solve these problems.
Outcome: The proposed method achieves state-of-the-art on a large knowledge graph dataset.
Pretrained Knowledge Base Embeddings for improved Sentential Relation Extraction (2022.acl-srw)

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Challenge: Existing models that perform explicit on-task training of graph embeddings are inadequate.
Approach: They propose to combine pretrained knowledge base graph embeddings with transformer based language models to improve performance on sentential Relation Extraction task.
Outcome: The proposed model outperforms state-of-the-art models on the sentential Relation Extraction task.
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.
Approach: They propose to combine semantic matching with entity’s geometric distance to better measure the plausibility of triplets.
Outcome: The proposed model outperforms existing models on well-known knowledge graph completion benchmark datasets.
Orthogonal Relation Transforms with Graph Context Modeling for Knowledge Graph Embedding (2020.acl-main)

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Challenge: Existing knowledge graph embeddings have improved the knowledge graph link prediction task, but complex relations such as N-to-1, 1-to-N and N- to-N remain challenging to predict.
Approach: They propose to extend RotatE from 2D complex domain to high dimensional space with orthogonal transforms to model relations.
Outcome: The proposed method improves on N-to-1, 1-to-N and N- to-N cases while maintaining the capability for modeling symmetric/anti-symmetric, inverse and compositional relations.
RatE: Relation-Adaptive Translating Embedding for Knowledge Graph Completion (2020.coling-main)

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Challenge: Existing approaches for knowledge graph embedding have limitations in complex vector space . embeddability of one-to-many relations is not explicitly alleviated .
Approach: They propose a relation-adaptive translating embedding function that can be extended to complex vector space.
Outcome: The proposed translation function improves expressive power and alleviates embedding ambiguity problem.
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.
Approach: They propose a KGE model employing matrices for entities and block-diagonal orthogonal matrics with Riemannian optimization for relations that captures several relation patterns that rotation-based methods can identify.
Outcome: The proposed model outperforms state-of-the-art models while reducing the number of relation parameters.

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