# STaR: Knowledge Graph Embedding by Scaling, Translation and Rotation

arXiv: https://arxiv.org/abs/2202.07130 · HTML: https://mlsanity.com/paper/2202.07130/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 36 references that are in the map.
- First posted on arXiv 15 Feb 2022.

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

- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [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)
- [A Survey on Knowledge Graphs: Representation, Acquisition and Applications](https://mlsanity.com/paper/2002.00388/) (2020)
- [KG-BERT: BERT for Knowledge Graph Completion](https://mlsanity.com/paper/1909.03193/) (2019)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (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)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [Canonical Tensor Decomposition for Knowledge Base Completion](https://mlsanity.com/paper/1806.07297/) (2018)
- [A Novel Embedding Model for Knowledge Base Completion Based on Convolutional Neural Network](https://mlsanity.com/paper/1712.02121/) (2017)
- [Learning Hierarchy-Aware Knowledge Graph Embeddings for Link Prediction](https://mlsanity.com/paper/1911.09419/) (2019)
- [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)
- [Duality-Induced Regularizer for Tensor Factorization Based Knowledge Graph Completion](https://mlsanity.com/paper/2011.05816/) (2020)
- [Relation Embedding with Dihedral Group in Knowledge Graph](https://mlsanity.com/paper/1906.00687/) (2019)
- [Strong Baselines for Simple Question Answering over Knowledge Graphs with and without Neural Networks](https://mlsanity.com/paper/1712.01969/) (2017)

## Built on by (most cited first, 6 of 6)

- [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)
- [Progressive Knowledge Graph Completion](https://mlsanity.com/paper/2404.09897/) (2024)
- [Bridge: A Unified Framework to Knowledge Graph Completion via Language Models and Knowledge Representation](https://mlsanity.com/paper/2411.06660/) (2024)
- [RSCF: Relation-Semantics Consistent Filter for Entity Embedding of Knowledge Graph](https://mlsanity.com/paper/2505.20813/) (2025)
- [VisKnow: Constructing Visual Knowledge Base for Object Understanding](https://mlsanity.com/paper/2512.08221/) (2025)

## Abstract (arXiv)

The bilinear method is mainstream in Knowledge Graph Embedding (KGE), aiming to learn low-dimensional representations for entities and relations in Knowledge Graph (KG) and complete missing links. Most of the existing works are to find patterns between relationships and effectively model them to accomplish this task. Previous works have mainly discovered 6 important patterns like non-commutativity. Although some bilinear methods succeed in modeling these patterns, they neglect to handle 1-to-N, N-to-1, and N-to-N relations (or complex relations) concurrently, which hurts their expressiveness. To this end, we integrate scaling, the combination of translation and rotation that can solve complex relations and patterns, respectively, where scaling is a simplification of projection. Therefore, we propose a corresponding bilinear model Scaling Translation and Rotation (STaR) consisting of the above two parts. Besides, since translation cannot be incorporated into the bilinear model directly, we introduce translation matrix as the equivalent. Theoretical analysis proves that STaR is capable of modeling all patterns and handling complex relations simultaneously, and experiments demonstrate its effectiveness on commonly used benchmarks for link prediction.