# Rot-Pro: Modeling Transitivity by Projection in Knowledge Graph Embedding

arXiv: https://arxiv.org/abs/2110.14450 · HTML: https://mlsanity.com/paper/2110.14450/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 29 references that are in the map.
- First posted on arXiv 27 Oct 2021.

## Builds on (most cited first, 12 of 12)

- [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)
- [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)
- [A Novel Embedding Model for Knowledge Base Completion Based on Convolutional Neural Network](https://mlsanity.com/paper/1712.02121/) (2017)
- [Learning Attention-based Embeddings for Relation Prediction in Knowledge Graphs](https://mlsanity.com/paper/1906.01195/) (2019)
- [BoxE: A Box Embedding Model for Knowledge Base Completion](https://mlsanity.com/paper/2007.06267/) (2020)
- [Orthogonal Relation Transforms with Graph Context Modeling for Knowledge Graph Embedding](https://mlsanity.com/paper/1911.04910/) (2019)
- [Relation Embedding with Dihedral Group in Knowledge Graph](https://mlsanity.com/paper/1906.00687/) (2019)
- [TransA: An Adaptive Approach for Knowledge Graph Embedding](https://mlsanity.com/paper/1509.05490/) (2015)

## Built on by (most cited first, 15 of 15)

- [HousE: Knowledge Graph Embedding with Householder Parameterization](https://mlsanity.com/paper/2202.07919/) (2022)
- [Knowledge Graph Reasoning with Logics and Embeddings: Survey and Perspective](https://mlsanity.com/paper/2202.07412/) (2022)
- [Multi-task Pre-training Language Model for Semantic Network Completion](https://mlsanity.com/paper/2201.04843/) (2022)
- [A Review of Knowledge Graph Completion](https://mlsanity.com/paper/2208.11652/) (2022)
- [Large Language Model Enhanced Knowledge Representation Learning: A Survey](https://mlsanity.com/paper/2407.00936/) (2024)
- [Analogical Inference Enhanced Knowledge Graph Embedding](https://mlsanity.com/paper/2301.00982/) (2023)
- [Knowledge Graph Embedding with 3D Compound Geometric Transformations](https://mlsanity.com/paper/2304.00378/) (2023)
- [Knowledge Graph Reasoning with Self-supervised Reinforcement Learning](https://mlsanity.com/paper/2405.13640/) (2024)
- [To Copy Rather Than Memorize: A Vertical Learning Paradigm for Knowledge Graph Completion](https://mlsanity.com/paper/2305.14126/) (2023)
- [KG-BiLM: Knowledge Graph Embedding via Bidirectional Language Models](https://mlsanity.com/paper/2506.03576/) (2025)
- [Flow-Modulated Scoring for Semantic-Aware Knowledge Graph Completion](https://mlsanity.com/paper/2506.23137/) (2025)
- [Improving Enzyme Prediction with Chemical Reaction Equations by Hypergraph-Enhanced Knowledge Graph Embeddings](https://mlsanity.com/paper/2601.05330/) (2026)
- [Simple Rule Injection for ComplEx Embeddings](https://mlsanity.com/paper/2308.03269/) (2023)
- [Fully Geometric Multi-Hop Reasoning on Knowledge Graphs with Transitive Relations](https://mlsanity.com/paper/2505.12369/) (2025)
- [RSCF: Relation-Semantics Consistent Filter for Entity Embedding of Knowledge Graph](https://mlsanity.com/paper/2505.20813/) (2025)

## Abstract (arXiv)

Knowledge graph embedding models learn the representations of entities and relations in the knowledge graphs for predicting missing links (relations) between entities. Their effectiveness are deeply affected by the ability of modeling and inferring different relation patterns such as symmetry, asymmetry, inversion, composition and transitivity. Although existing models are already able to model many of these relations patterns, transitivity, a very common relation pattern, is still not been fully supported. In this paper, we first theoretically show that the transitive relations can be modeled with projections. We then propose the Rot-Pro model which combines the projection and relational rotation together. We prove that Rot-Pro can infer all the above relation patterns. Experimental results show that the proposed Rot-Pro model effectively learns the transitivity pattern and achieves the state-of-the-art results on the link prediction task in the datasets containing transitive relations.