# RulE: Knowledge Graph Reasoning with Rule Embedding

arXiv: https://arxiv.org/abs/2210.14905 · HTML: https://mlsanity.com/paper/2210.14905/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 52 references that are in the map.
- First posted on arXiv 24 Oct 2022.

## Builds on (most cited first, 26 of 26)

- [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)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Neural-Symbolic VQA: Disentangling Reasoning from Vision and Language Understanding](https://mlsanity.com/paper/1810.02338/) (2018)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Prediction](https://mlsanity.com/paper/2106.06935/) (2021)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Inductive Relation Prediction by Subgraph Reasoning](https://mlsanity.com/paper/1911.06962/) (2019)
- [DRUM: End-To-End Differentiable Rule Mining On Knowledge Graphs](https://mlsanity.com/paper/1911.00055/) (2019)
- [RippleNet: Propagating User Preferences on the Knowledge Graph for Recommender Systems](https://mlsanity.com/paper/1803.03467/) (2018)
- [Beta Embeddings for Multi-Hop Logical Reasoning in Knowledge Graphs](https://mlsanity.com/paper/2010.11465/) (2020)
- [RNNLogic: Learning Logic Rules for Reasoning on Knowledge Graphs](https://mlsanity.com/paper/2010.04029/) (2020)
- [BoxE: A Box Embedding Model for Knowledge Base Completion](https://mlsanity.com/paper/2007.06267/) (2020)
- [Neuro-Symbolic Program Synthesis](https://mlsanity.com/paper/1611.01855/) (2016)
- [Question Answering with Subgraph Embeddings](https://mlsanity.com/paper/1406.3676/) (2014)
- [Knowledge Graph Embedding with Iterative Guidance from Soft Rules](https://mlsanity.com/paper/1711.11231/) (2017)
- [Efficient Probabilistic Logic Reasoning with Graph Neural Networks](https://mlsanity.com/paper/2001.11850/) (2020)
- [Ontology Reasoning with Deep Neural Networks](https://mlsanity.com/paper/1808.07980/) (2018)
- [Improving Knowledge Graph Embedding Using Simple Constraints](https://mlsanity.com/paper/1805.02408/) (2018)
- [TensorLog: Deep Learning Meets Probabilistic DBs](https://mlsanity.com/paper/1707.05390/) (2017)
- [Are Message Passing Neural Networks Really Helpful for Knowledge Graph Completion?](https://mlsanity.com/paper/2205.10652/) (2022)

## Built on by (most cited first, 5 of 5)

- [Punctuation and Predicates in Language Models](https://mlsanity.com/paper/2508.14067/) (2025)
- [Faithful Differentiable Reasoning with Reshuffled Region-based Embeddings](https://mlsanity.com/paper/2406.09529/) (2024)
- [Emulating the Human Mind: A Neural-symbolic Link Prediction Model with Fast and Slow Reasoning and Filtered Rules](https://mlsanity.com/paper/2310.13996/) (2023)
- [MPRM: A Markov Path-based Rule Miner for Efficient and Interpretable Knowledge Graph Reasoning](https://mlsanity.com/paper/2505.12329/) (2025)
- [Inferring Sensitive Attributes from Knowledge Graph Embeddings: Attack and Defense Strategies](https://mlsanity.com/paper/2605.19644/) (2026)

## Abstract (arXiv)

Knowledge graph (KG) reasoning is an important problem for knowledge graphs. In this paper, we propose a novel and principled framework called RulE (stands for Rule Embedding) to effectively leverage logical rules to enhance KG reasoning. Unlike knowledge graph embedding (KGE) methods, RulE learns rule embeddings from existing triplets and first-order rules by jointly representing entities, relations and logical rules in a unified embedding space. Based on the learned rule embeddings, a confidence score can be calculated for each rule, reflecting its consistency with the observed triplets. This allows us to perform logical rule inference in a soft way, thus alleviating the brittleness of logic. On the other hand, RulE injects prior logical rule information into the embedding space, enriching and regularizing the entity/relation embeddings. This makes KGE alone perform better too. RulE is conceptually simple and empirically effective. We conduct extensive experiments to verify each component of RulE. Results on multiple benchmarks reveal that our model outperforms the majority of existing embedding-based and rule-based approaches.