# Probabilistic Entity Representation Model for Reasoning over Knowledge Graphs

arXiv: https://arxiv.org/abs/2110.13522 · HTML: https://mlsanity.com/paper/2110.13522/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 31 references that are in the map.
- First posted on arXiv 26 Oct 2021.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [Adversarial Attacks on Neural Networks for Graph Data](https://mlsanity.com/paper/1805.07984/) (2018)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [Adversarial Attack on Graph Structured Data](https://mlsanity.com/paper/1806.02371/) (2018)
- [Query2box: Reasoning over Knowledge Graphs in Vector Space using Box Embeddings](https://mlsanity.com/paper/2002.05969/) (2020)
- [Beta Embeddings for Multi-Hop Logical Reasoning in Knowledge Graphs](https://mlsanity.com/paper/2010.11465/) (2020)
- [Embedding Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/1806.01445/) (2018)
- [Complex Query Answering with Neural Link Predictors](https://mlsanity.com/paper/2011.03459/) (2020)
- [Word Representations via Gaussian Embedding](https://mlsanity.com/paper/1412.6623/) (2014)
- [Probabilistic Embedding of Knowledge Graphs with Box Lattice Measures](https://mlsanity.com/paper/1805.06627/) (2018)
- [Chains of Reasoning over Entities, Relations, and Text using Recurrent Neural Networks](https://mlsanity.com/paper/1607.01426/) (2016)
- [Self-Supervised Hyperboloid Representations from Logical Queries over Knowledge Graphs](https://mlsanity.com/paper/2012.13023/) (2020)
- [AutoKnow: Self-Driving Knowledge Collection for Products of Thousands of Types](https://mlsanity.com/paper/2006.13473/) (2020)

## Built on by (most cited first, 28 of 28)

- [Neural Graph Reasoning: Complex Logical Query Answering Meets Graph Databases](https://mlsanity.com/paper/2303.14617/) (2023)
- [Logical Message Passing Networks with One-hop Inference on Atomic Formulas](https://mlsanity.com/paper/2301.08859/) (2023)
- [Complex Logical Reasoning over Knowledge Graphs using Large Language Models](https://mlsanity.com/paper/2305.01157/) (2023)
- [Inductive Logical Query Answering in Knowledge Graphs](https://mlsanity.com/paper/2210.08008/) (2022)
- [GammaE: Gamma Embeddings for Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/2210.15578/) (2022)
- [SMORE: Knowledge Graph Completion and Multi-hop Reasoning in Massive Knowledge Graphs](https://mlsanity.com/paper/2110.14890/) (2021)
- [Wasserstein-Fisher-Rao Embedding: Logical Query Embeddings with Local Comparison and Global Transport](https://mlsanity.com/paper/2305.04034/) (2023)
- [Type-aware Embeddings for Multi-Hop Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2205.00782/) (2022)
- [TFLEX: Temporal Feature-Logic Embedding Framework for Complex Reasoning over Temporal Knowledge Graph](https://mlsanity.com/paper/2205.14307/) (2022)
- [Sequential Query Encoding For Complex Query Answering on Knowledge Graphs](https://mlsanity.com/paper/2302.13114/) (2023)
- [Rethinking Complex Queries on Knowledge Graphs with Neural Link Predictors](https://mlsanity.com/paper/2304.07063/) (2023)
- [Knowledge Graph Reasoning over Entities and Numerical Values](https://mlsanity.com/paper/2306.01399/) (2023)
- [NQE: N-ary Query Embedding for Complex Query Answering over Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2211.13469/) (2022)
- [Geometric Relational Embeddings: A Survey](https://mlsanity.com/paper/2304.11949/) (2023)
- [Privacy-Preserved Neural Graph Databases](https://mlsanity.com/paper/2312.15591/) (2023)
- [Conditional Logical Message Passing Transformer for Complex Query Answering](https://mlsanity.com/paper/2402.12954/) (2024)
- [Learning Federated Neural Graph Databases for Answering Complex Queries from Distributed Knowledge Graphs](https://mlsanity.com/paper/2402.14609/) (2024)
- [FLEX: Feature-Logic Embedding Framework for CompleX Knowledge Graph Reasoning](https://mlsanity.com/paper/2205.11039/) (2022)
- [Query Structure Modeling for Inductive Logical Reasoning Over Knowledge Graphs](https://mlsanity.com/paper/2305.13585/) (2023)
- [Improving Multi-hop Logical Reasoning in Knowledge Graphs with Context-Aware Query Representation Learning](https://mlsanity.com/paper/2406.07034/) (2024)
- [Meta Operator for Complex Query Answering on Knowledge Graphs](https://mlsanity.com/paper/2403.10110/) (2024)
- [Efficient and Scalable Neural Symbolic Search for Knowledge Graph Complex Query Answering](https://mlsanity.com/paper/2505.08155/) (2025)
- [Role Support in Knowledge-Graph Error Ranking: Predictor Regimes and Evaluation Policies](https://mlsanity.com/paper/2512.22318/) (2025)
- [Logic Diffusion for Knowledge Graph Reasoning](https://mlsanity.com/paper/2306.03515/) (2023)
- [Learning Visual-Semantic Subspace Representations](https://mlsanity.com/paper/2405.16213/) (2024)
- [A Survey on Semantic Communication for Vision: Categories, Frameworks, Enabling Techniques, and Applications](https://mlsanity.com/paper/2601.22202/) (2026)
- [Neural Scalable Symbolic Search Framework for Complex Logical Queries with Multiple Free Variables](https://mlsanity.com/paper/2605.25985/) (2026)
- [Spectral Initialization and Scheduled Graph Smoothness for Uncertain Knowledge Graph Completion](https://mlsanity.com/paper/2609.02519/) (2026)

## Abstract (arXiv)

Logical reasoning over Knowledge Graphs (KGs) is a fundamental technique that can provide efficient querying mechanism over large and incomplete databases. Current approaches employ spatial geometries such as boxes to learn query representations that encompass the answer entities and model the logical operations of projection and intersection. However, their geometry is restrictive and leads to non-smooth strict boundaries, which further results in ambiguous answer entities. Furthermore, previous works propose transformation tricks to handle unions which results in non-closure and, thus, cannot be chained in a stream. In this paper, we propose a Probabilistic Entity Representation Model (PERM) to encode entities as a Multivariate Gaussian density with mean and covariance parameters to capture its semantic position and smooth decision boundary, respectively. Additionally, we also define the closed logical operations of projection, intersection, and union that can be aggregated using an end-to-end objective function. On the logical query reasoning problem, we demonstrate that the proposed PERM significantly outperforms the state-of-the-art methods on various public benchmark KG datasets on standard evaluation metrics. We also evaluate PERM's competence on a COVID-19 drug-repurposing case study and show that our proposed work is able to recommend drugs with substantially better F1 than current methods. Finally, we demonstrate the working of our PERM's query answering process through a low-dimensional visualization of the Gaussian representations.