# Quaternion Knowledge Graph Embeddings

arXiv: https://arxiv.org/abs/1904.10281 · HTML: https://mlsanity.com/paper/1904.10281/

## Key facts

- Cited by 175 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Apr 2019.

## Built on by (most cited first, 30 of 175)

- [A Survey of Knowledge Graph Reasoning on Graph Types: Static, Dynamic, and Multimodal](https://mlsanity.com/paper/2212.05767/) (2022)
- [Knowledge Graph Reasoning with Relational Digraph](https://mlsanity.com/paper/2108.06040/) (2021)
- [Knowledge Graphs: Opportunities and Challenges](https://mlsanity.com/paper/2303.13948/) (2023)
- [Knowledge Graph Contrastive Learning Based on Relation-Symmetrical Structure](https://mlsanity.com/paper/2211.10738/) (2022)
- [Knowledge Graph Embedding: A Survey from the Perspective of Representation Spaces](https://mlsanity.com/paper/2211.03536/) (2022)
- [ChronoR: Rotation Based Temporal Knowledge Graph Embedding](https://mlsanity.com/paper/2103.10379/) (2021)
- [Role-Aware Modeling for N-ary Relational Knowledge Bases](https://mlsanity.com/paper/2104.09780/) (2021)
- [HousE: Knowledge Graph Embedding with Householder Parameterization](https://mlsanity.com/paper/2202.07919/) (2022)
- [AdaProp: Learning Adaptive Propagation for Graph Neural Network based Knowledge Graph Reasoning](https://mlsanity.com/paper/2205.15319/) (2022)
- [Logical Message Passing Networks with One-hop Inference on Atomic Formulas](https://mlsanity.com/paper/2301.08859/) (2023)
- [IMF: Interactive Multimodal Fusion Model for Link Prediction](https://mlsanity.com/paper/2303.10816/) (2023)
- [Inductive Logical Query Answering in Knowledge Graphs](https://mlsanity.com/paper/2210.08008/) (2022)
- [Relational Memory Augmented Language Models](https://mlsanity.com/paper/2201.09680/) (2022)
- [High-Order Pooling for Graph Neural Networks with Tensor Decomposition](https://mlsanity.com/paper/2205.11691/) (2022)
- [Vector-valued Distance and Gyrocalculus on the Space of Symmetric Positive Definite Matrices](https://mlsanity.com/paper/2110.13475/) (2021)
- [BiQUE: Biquaternionic Embeddings of Knowledge Graphs](https://mlsanity.com/paper/2109.14401/) (2021)
- [Efficient Federated Learning on Knowledge Graphs via Privacy-preserving Relation Embedding Aggregation](https://mlsanity.com/paper/2203.09553/) (2022)
- [Geometry Interaction Knowledge Graph Embeddings](https://mlsanity.com/paper/2206.12418/) (2022)
- [Convolutional Hypercomplex Embeddings for Link Prediction](https://mlsanity.com/paper/2106.15230/) (2021)
- [Multi-task Pre-training Language Model for Semantic Network Completion](https://mlsanity.com/paper/2201.04843/) (2022)
- [Link Prediction with Attention Applied on Multiple Knowledge Graph Embedding Models](https://mlsanity.com/paper/2302.06229/) (2023)
- [Knowledge Graph informed Fake News Classification via Heterogeneous Representation Ensembles](https://mlsanity.com/paper/2110.10457/) (2021)
- [Searching to Sparsify Tensor Decomposition for N-ary Relational Data](https://mlsanity.com/paper/2104.10625/) (2021)
- [CAKE: A Scalable Commonsense-Aware Framework For Multi-View Knowledge Graph Completion](https://mlsanity.com/paper/2202.13785/) (2022)
- [ExpressivE: A Spatio-Functional Embedding For Knowledge Graph Completion](https://mlsanity.com/paper/2206.04192/) (2022)
- [zrLLM: Zero-Shot Relational Learning on Temporal Knowledge Graphs with Large Language Models](https://mlsanity.com/paper/2311.10112/) (2023)
- [Node Co-occurrence based Graph Neural Networks for Knowledge Graph Link Prediction](https://mlsanity.com/paper/2104.07396/) (2021)
- [Reasoning Through Memorization: Nearest Neighbor Knowledge Graph Embeddings](https://mlsanity.com/paper/2201.05575/) (2022)
- [SMiLE: Schema-augmented Multi-level Contrastive Learning for Knowledge Graph Link Prediction](https://mlsanity.com/paper/2210.04870/) (2022)
- [Knowledge Sheaves: A Sheaf-Theoretic Framework for Knowledge Graph Embedding](https://mlsanity.com/paper/2110.03789/) (2021)

## Abstract (arXiv)

In this work, we move beyond the traditional complex-valued representations, introducing more expressive hypercomplex representations to model entities and relations for knowledge graph embeddings. More specifically, quaternion embeddings, hypercomplex-valued embeddings with three imaginary components, are utilized to represent entities. Relations are modelled as rotations in the quaternion space. The advantages of the proposed approach are: (1) Latent inter-dependencies (between all components) are aptly captured with Hamilton product, encouraging a more compact interaction between entities and relations; (2) Quaternions enable expressive rotation in four-dimensional space and have more degree of freedom than rotation in complex plane; (3) The proposed framework is a generalization of ComplEx on hypercomplex space while offering better geometrical interpretations, concurrently satisfying the key desiderata of relational representation learning (i.e., modeling symmetry, anti-symmetry and inversion). Experimental results demonstrate that our method achieves state-of-the-art performance on four well-established knowledge graph completion benchmarks.