# CompoundE: Knowledge Graph Embedding with Translation, Rotation and Scaling Compound Operations

arXiv: https://arxiv.org/abs/2207.05324 · HTML: https://mlsanity.com/paper/2207.05324/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 50 references that are in the map.
- First posted on arXiv 12 Jul 2022.

## Builds on (most cited first, 21 of 21)

- [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)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [SimplE Embedding for Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/1802.04868/) (2018)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Multilingual Knowledge Graph Embeddings for Cross-lingual Knowledge Alignment](https://mlsanity.com/paper/1611.03954/) (2016)
- [Multi-relational Poincar'e Graph Embeddings](https://mlsanity.com/paper/1905.09791/) (2019)
- [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)
- [AutoSF: Searching Scoring Functions for Knowledge Graph Embedding](https://mlsanity.com/paper/1904.11682/) (2019)
- [LargeEA: Aligning Entities for Large-scale Knowledge Graphs](https://mlsanity.com/paper/2108.05211/) (2021)
- [Geometry Interaction Knowledge Graph Embeddings](https://mlsanity.com/paper/2206.12418/) (2022)
- [LineaRE: Simple but Powerful Knowledge Graph Embedding for Link Prediction](https://mlsanity.com/paper/2004.10037/) (2020)
- [KGBoost: A Classification-based Knowledge Base Completion Method with Negative Sampling](https://mlsanity.com/paper/2112.09340/) (2021)
- [CORE: A Knowledge Graph Entity Type Prediction Method via Complex Space Regression and Embedding](https://mlsanity.com/paper/2112.10067/) (2021)

## Built on by (most cited first, 10 of 10)

- [Knowledge Graph Embedding: A Survey from the Perspective of Representation Spaces](https://mlsanity.com/paper/2211.03536/) (2022)
- [Green Learning: Introduction, Examples and Outlook](https://mlsanity.com/paper/2210.00965/) (2022)
- [An Overview on Language Models: Recent Developments and Outlook](https://mlsanity.com/paper/2303.05759/) (2023)
- [Analyzing and Evaluating Faithfulness in Dialogue Summarization](https://mlsanity.com/paper/2210.11777/) (2022)
- [Knowledge Graph Embedding: An Overview](https://mlsanity.com/paper/2309.12501/) (2023)
- [Knowledge Graph Embedding with 3D Compound Geometric Transformations](https://mlsanity.com/paper/2304.00378/) (2023)
- [Simple but Effective Compound Geometric Operations for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/2408.06603/) (2024)
- [AsyncET: Asynchronous Learning for Knowledge Graph Entity Typing with Auxiliary Relations](https://mlsanity.com/paper/2308.16055/) (2023)
- [Knowledge Graph Embeddings: A Comprehensive Survey on Capturing Relation Properties](https://mlsanity.com/paper/2410.14733/) (2024)
- [SKGE: Spherical Knowledge Graph Embedding with Geometric Regularization](https://mlsanity.com/paper/2511.02460/) (2025)

## Abstract (arXiv)

Translation, rotation, and scaling are three commonly used geometric manipulation operations in image processing. Besides, some of them are successfully used in developing effective knowledge graph embedding (KGE) models such as TransE and RotatE. Inspired by the synergy, we propose a new KGE model by leveraging all three operations in this work. Since translation, rotation, and scaling operations are cascaded to form a compound one, the new model is named CompoundE. By casting CompoundE in the framework of group theory, we show that quite a few scoring-function-based KGE models are special cases of CompoundE. CompoundE extends the simple distance-based relation to relation-dependent compound operations on head and/or tail entities. To demonstrate the effectiveness of CompoundE, we conduct experiments on three popular KG completion datasets. Experimental results show that CompoundE consistently achieves the state of-the-art performance.