# Knowledge Graph Embedding with 3D Compound Geometric Transformations

arXiv: https://arxiv.org/abs/2304.00378 · HTML: https://mlsanity.com/paper/2304.00378/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 83 references that are in the map.
- First posted on arXiv 1 Apr 2023.

## Builds on (most cited first, 30 of 43)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [ConceptNet 5.5: An Open Multilingual Graph of General Knowledge](https://mlsanity.com/paper/1612.03975/) (2016)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [KG-BERT: BERT for Knowledge Graph Completion](https://mlsanity.com/paper/1909.03193/) (2019)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Holographic Embeddings of Knowledge Graphs](https://mlsanity.com/paper/1510.04935/) (2015)
- [RippleNet: Propagating User Preferences on the Knowledge Graph for Recommender Systems](https://mlsanity.com/paper/1803.03467/) (2018)
- [Learning Hierarchy-Aware Knowledge Graph Embeddings for Link Prediction](https://mlsanity.com/paper/1911.09419/) (2019)
- [Improving Conversational Recommender Systems via Knowledge Graph based Semantic Fusion](https://mlsanity.com/paper/2007.04032/) (2020)
- [SimKGC: Simple Contrastive Knowledge Graph Completion with Pre-trained Language Models](https://mlsanity.com/paper/2203.02167/) (2022)
- [Analogical Inference for Multi-Relational Embeddings](https://mlsanity.com/paper/1705.02426/) (2017)
- [PairRE: Knowledge Graph Embeddings via Paired Relation Vectors](https://mlsanity.com/paper/2011.03798/) (2020)
- [Learning Symmetric Collaborative Dialogue Agents with Dynamic Knowledge Graph Embeddings](https://mlsanity.com/paper/1704.07130/) (2017)
- [InteractE: Improving Convolution-based Knowledge Graph Embeddings by Increasing Feature Interactions](https://mlsanity.com/paper/1911.00219/) (2019)
- [Knowledge Graph Embedding with Iterative Guidance from Soft Rules](https://mlsanity.com/paper/1711.11231/) (2017)
- [Relation Prediction as an Auxiliary Training Objective for Improving Multi-Relational Graph Representations](https://mlsanity.com/paper/2110.02834/) (2021)
- [Improving Knowledge Graph Embedding Using Simple Constraints](https://mlsanity.com/paper/1805.02408/) (2018)
- [AutoSF: Searching Scoring Functions for Knowledge Graph Embedding](https://mlsanity.com/paper/1904.11682/) (2019)
- [Green Learning: Introduction, Examples and Outlook](https://mlsanity.com/paper/2210.00965/) (2022)
- [Relation Embedding with Dihedral Group in Knowledge Graph](https://mlsanity.com/paper/1906.00687/) (2019)
- [Multilingual Knowledge Graph Completion via Ensemble Knowledge Transfer](https://mlsanity.com/paper/2010.03158/) (2020)
- [On Supervised Feature Selection from High Dimensional Feature Spaces](https://mlsanity.com/paper/2203.11924/) (2022)
- [BiQUE: Biquaternionic Embeddings of Knowledge Graphs](https://mlsanity.com/paper/2109.14401/) (2021)

## Built on by (most cited first, 3 of 3)

- [Time Sensitive Knowledge Editing through Efficient Finetuning](https://mlsanity.com/paper/2406.04496/) (2024)
- [Knowledge Graph Embedding: An Overview](https://mlsanity.com/paper/2309.12501/) (2023)
- [Two-dimensional Taxonomy for N-ary Knowledge Representation Learning Methods](https://mlsanity.com/paper/2506.05626/) (2025)

## Abstract (arXiv)

The cascade of 2D geometric transformations were exploited to model relations between entities in a knowledge graph (KG), leading to an effective KG embedding (KGE) model, CompoundE. Furthermore, the rotation in the 3D space was proposed as a new KGE model, Rotate3D, by leveraging its non-commutative property. Inspired by CompoundE and Rotate3D, we leverage 3D compound geometric transformations, including translation, rotation, scaling, reflection, and shear and propose a family of KGE models, named CompoundE3D, in this work. CompoundE3D allows multiple design variants to match rich underlying characteristics of a KG. Since each variant has its own advantages on a subset of relations, an ensemble of multiple variants can yield superior performance. The effectiveness and flexibility of CompoundE3D are experimentally verified on four popular link prediction datasets.