# Relation Embedding with Dihedral Group in Knowledge Graph

arXiv: https://arxiv.org/abs/1906.00687 · HTML: https://mlsanity.com/paper/1906.00687/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2019.

## Built on by (most cited first, 25 of 25)

- [Knowledge Graph Embedding: A Survey from the Perspective of Representation Spaces](https://mlsanity.com/paper/2211.03536/) (2022)
- [Is Neuro-Symbolic AI Meeting its Promise in Natural Language Processing? A Structured Review](https://mlsanity.com/paper/2202.12205/) (2022)
- [Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networks](https://mlsanity.com/paper/2107.10234/) (2021)
- [Rot-Pro: Modeling Transitivity by Projection in Knowledge Graph Embedding](https://mlsanity.com/paper/2110.14450/) (2021)
- [Hyperbolic Geometry is Not Necessary: Lightweight Euclidean-Based Models for Low-Dimensional Knowledge Graph Embeddings](https://mlsanity.com/paper/2103.14930/) (2021)
- [Sem@K: Is my knowledge graph embedding model semantic-aware?](https://mlsanity.com/paper/2301.05601/) (2023)
- [Knowledge Graph Embedding: An Overview](https://mlsanity.com/paper/2309.12501/) (2023)
- [STaR: Knowledge Graph Embedding by Scaling, Translation and Rotation](https://mlsanity.com/paper/2202.07130/) (2022)
- [Unlocking the Potential of Generative AI through Neuro-Symbolic Architectures: Benefits and Limitations](https://mlsanity.com/paper/2502.11269/) (2025)
- [High-Dimensional Learning Dynamics of Quantized Models with Straight-Through Estimator](https://mlsanity.com/paper/2510.10693/) (2025)
- [Knowledge Graph Embedding with 3D Compound Geometric Transformations](https://mlsanity.com/paper/2304.00378/) (2023)
- [HaSa: Hardness and Structure-Aware Contrastive Knowledge Graph Embedding](https://mlsanity.com/paper/2305.10563/) (2023)
- [MQuinE: a cure for "Z-paradox" in knowledge graph embedding models](https://mlsanity.com/paper/2402.03583/) (2024)
- [Hyperbolic Hierarchical Knowledge Graph Embeddings for Link Prediction in Low Dimensions](https://mlsanity.com/paper/2204.13704/) (2022)
- [Integrating Knowledge Graph embedding and pretrained Language Models in Hypercomplex Spaces](https://mlsanity.com/paper/2208.02743/) (2022)
- [Knowledge Graph Embeddings: A Comprehensive Survey on Capturing Relation Properties](https://mlsanity.com/paper/2410.14733/) (2024)
- [Beyond Discreteness: Sample Complexity Analysis of Straight-Through Estimator for 1-bit Quantization](https://mlsanity.com/paper/2505.18113/) (2025)
- [FFHR: Fully and Flexible Hyperbolic Representation for Knowledge Graph Completion](https://mlsanity.com/paper/2302.04088/) (2023)
- [On Addressing the Limitations of Graph Neural Networks](https://mlsanity.com/paper/2306.12640/) (2023)
- [Knowledge Graph Embedding by Normalizing Flows](https://mlsanity.com/paper/2409.19977/) (2024)
- [Two-dimensional Taxonomy for N-ary Knowledge Representation Learning Methods](https://mlsanity.com/paper/2506.05626/) (2025)
- [Knowledgebra: An Algebraic Learning Framework for Knowledge Graph](https://mlsanity.com/paper/2204.07328/) (2022)
- [Learning Attention-based Representations from Multiple Patterns for Relation Prediction in Knowledge Graphs](https://mlsanity.com/paper/2206.04801/) (2022)
- [Prior Bilinear Based Models for Knowledge Graph Completion](https://mlsanity.com/paper/2309.13834/) (2023)
- [Croppable Knowledge Graph Embedding](https://mlsanity.com/paper/2407.02779/) (2024)

## Abstract (arXiv)

Link prediction is critical for the application of incomplete knowledge graph (KG) in the downstream tasks. As a family of effective approaches for link predictions, embedding methods try to learn low-rank representations for both entities and relations such that the bilinear form defined therein is a well-behaved scoring function. Despite of their successful performances, existing bilinear forms overlook the modeling of relation compositions, resulting in lacks of interpretability for reasoning on KG. To fulfill this gap, we propose a new model called DihEdral, named after dihedral symmetry group. This new model learns knowledge graph embeddings that can capture relation compositions by nature. Furthermore, our approach models the relation embeddings parametrized by discrete values, thereby decrease the solution space drastically. Our experiments show that DihEdral is able to capture all desired properties such as (skew-) symmetry, inversion and (non-) Abelian composition, and outperforms existing bilinear form based approach and is comparable to or better than deep learning models such as ConvE.