# Logical Entity Representation in Knowledge-Graphs for Differentiable Rule Learning

arXiv: https://arxiv.org/abs/2305.12738 · HTML: https://mlsanity.com/paper/2305.12738/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 83 references that are in the map.
- First posted on arXiv 22 May 2023.

## Builds on (most cited first, 30 of 42)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision](https://mlsanity.com/paper/1904.12584/) (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)
- [DeepPath: A Reinforcement Learning Method for Knowledge Graph Reasoning](https://mlsanity.com/paper/1707.06690/) (2017)
- [Inductive Relation Prediction by Subgraph Reasoning](https://mlsanity.com/paper/1911.06962/) (2019)
- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [Holographic Embeddings of Knowledge Graphs](https://mlsanity.com/paper/1510.04935/) (2015)
- [DRUM: End-To-End Differentiable Rule Mining On Knowledge Graphs](https://mlsanity.com/paper/1911.00055/) (2019)
- [Query2box: Reasoning over Knowledge Graphs in Vector Space using Box Embeddings](https://mlsanity.com/paper/2002.05969/) (2020)
- [Go for a Walk and Arrive at the Answer: Reasoning Over Paths in Knowledge Bases using Reinforcement Learning](https://mlsanity.com/paper/1711.05851/) (2017)
- [Neural Logic Machines](https://mlsanity.com/paper/1904.11694/) (2019)
- [Harnessing Deep Neural Networks with Logic Rules](https://mlsanity.com/paper/1603.06318/) (2016)
- [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)
- [Multi-Hop Knowledge Graph Reasoning with Reward Shaping](https://mlsanity.com/paper/1808.10568/) (2018)
- [Probabilistic Logic Neural Networks for Reasoning](https://mlsanity.com/paper/1906.08495/) (2019)
- [Hinge-Loss Markov Random Fields and Probabilistic Soft Logic](https://mlsanity.com/paper/1505.04406/) (2015)
- [KBGAN: Adversarial Learning for Knowledge Graph Embeddings](https://mlsanity.com/paper/1711.04071/) (2017)
- [Communicative Message Passing for Inductive Relation Reasoning](https://mlsanity.com/paper/2012.08911/) (2020)
- [Efficient Probabilistic Logic Reasoning with Graph Neural Networks](https://mlsanity.com/paper/2001.11850/) (2020)
- [Learn to Explain Efficiently via Neural Logic Inductive Learning](https://mlsanity.com/paper/1910.02481/) (2019)
- [Modeling Fine-Grained Entity Types with Box Embeddings](https://mlsanity.com/paper/2101.00345/) (2021)
- [M-Walk: Learning to Walk over Graphs using Monte Carlo Tree Search](https://mlsanity.com/paper/1802.04394/) (2018)
- [NeuPSL: Neural Probabilistic Soft Logic](https://mlsanity.com/paper/2205.14268/) (2022)

## Built on by (most cited first, 8 of 8)

- [CaLa: Complementary Association Learning for Augmenting Composed Image Retrieval](https://mlsanity.com/paper/2405.19149/) (2024)
- [Applications of Generative AI (GAI) for Mobile and Wireless Networking: A Survey](https://mlsanity.com/paper/2405.20024/) (2024)
- [KERMIT: Knowledge Graph Completion of Enhanced Relation Modeling with Inverse Transformation](https://mlsanity.com/paper/2309.14770/) (2023)
- [LogicCBMs: Logic-Enhanced Concept-Based Learning](https://mlsanity.com/paper/2512.07383/) (2025)
- [Systematic Relational Reasoning With Epistemic Graph Neural Networks](https://mlsanity.com/paper/2407.17396/) (2024)
- [Block-Diagonal Orthogonal Relation and Matrix Entity for Knowledge Graph Embedding](https://mlsanity.com/paper/2401.05967/) (2024)
- [Cross-Document Contextual Coreference Resolution in Knowledge Graphs](https://mlsanity.com/paper/2504.05767/) (2025)
- [Deep Sparse Latent Feature Models for Knowledge Graph Completion](https://mlsanity.com/paper/2411.15694/) (2024)

## Abstract (arXiv)

Probabilistic logical rule learning has shown great strength in logical rule mining and knowledge graph completion. It learns logical rules to predict missing edges by reasoning on existing edges in the knowledge graph. However, previous efforts have largely been limited to only modeling chain-like Horn clauses such as R1(x,z)land R2(z,y)Rightarrow H(x,y). This formulation overlooks additional contextual information from neighboring sub-graphs of entity variables x, y and z. Intuitively, there is a large gap here, as local sub-graphs have been found to provide important information for knowledge graph completion. Inspired by these observations, we propose Logical Entity RePresentation (LERP) to encode contextual information of entities in the knowledge graph. A LERP is designed as a vector of probabilistic logical functions on the entity's neighboring sub-graph. It is an interpretable representation while allowing for differentiable optimization. We can then incorporate LERP into probabilistic logical rule learning to learn more expressive rules. Empirical results demonstrate that with LERP, our model outperforms other rule learning methods in knowledge graph completion and is comparable or even superior to state-of-the-art black-box methods. Moreover, we find that our model can discover a more expressive family of logical rules. LERP can also be further combined with embedding learning methods like TransE to make it more interpretable.