# Knowledge Hypergraph Embedding Meets Relational Algebra

arXiv: https://arxiv.org/abs/2102.09557 · HTML: https://mlsanity.com/paper/2102.09557/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 39 references that are in the map.
- First posted on arXiv 18 Feb 2021.

## Builds on (most cited first, 18 of 18)

- [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)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [TextWorld: A Learning Environment for Text-based Games](https://mlsanity.com/paper/1806.11532/) (2018)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [Inductive Relation Prediction by Subgraph Reasoning](https://mlsanity.com/paper/1911.06962/) (2019)
- [SimplE Embedding for Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/1802.04868/) (2018)
- [Canonical Tensor Decomposition for Knowledge Base Completion](https://mlsanity.com/paper/1806.07297/) (2018)
- [BoxE: A Box Embedding Model for Knowledge Base Completion](https://mlsanity.com/paper/2007.06267/) (2020)
- [Message Passing for Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2009.10847/) (2020)
- [On the representation and embedding of knowledge bases beyond binary relations](https://mlsanity.com/paper/1604.08642/) (2016)
- [Knowledge Base Completion: Baselines Strike Back](https://mlsanity.com/paper/1705.10744/) (2017)
- [Generalizing Tensor Decomposition for N-ary Relational Knowledge Bases](https://mlsanity.com/paper/2007.03988/) (2020)
- [Evaluating Logical Generalization in Graph Neural Networks](https://mlsanity.com/paper/2003.06560/) (2020)
- [Improved Knowledge Graph Embedding using Background Taxonomic Information](https://mlsanity.com/paper/1812.03235/) (2018)
- [HyperGCN: A New Method of Training Graph Convolutional Networks on Hypergraphs](https://mlsanity.com/paper/1809.02589/) (2018)

## Built on by (most cited first, 11 of 11)

- [Link Prediction with Relational Hypergraphs](https://mlsanity.com/paper/2402.04062/) (2024)
- [HyCubE: Efficient Knowledge Hypergraph 3D Circular Convolutional Embedding](https://mlsanity.com/paper/2402.08961/) (2024)
- [Neural Algorithmic Reasoning for Hypergraphs with Looped Transformers](https://mlsanity.com/paper/2501.10688/) (2025)
- [Generalizing Hyperedge Expansion for Hyper-relational Knowledge Graph Modeling](https://mlsanity.com/paper/2411.06191/) (2024)
- [Transformers for Complex Query Answering over Knowledge Hypergraphs](https://mlsanity.com/paper/2504.16537/) (2025)
- [Demystifying Topological Message-Passing with Relational Structures: A Case Study on Oversquashing in Simplicial Message-Passing](https://mlsanity.com/paper/2506.06582/) (2025)
- [Two-dimensional Taxonomy for N-ary Knowledge Representation Learning Methods](https://mlsanity.com/paper/2506.05626/) (2025)
- [Estimation of embedding vectors in high dimensions](https://mlsanity.com/paper/2312.07802/) (2023)
- [HEHRGNN: A Unified Embedding Model for Knowledge Graphs with Hyperedges and Hyper-Relational Edges](https://mlsanity.com/paper/2602.18897/) (2026)
- [Labeled Incidence Structures for Native Transformer Modeling of Text, Knowledge Graphs, and Hypergraphs](https://mlsanity.com/paper/2609.20278/) (2026)
- [QORH: Learning Query-Specific Ordered Rule Hypergraphs for Inductive Knowledge Graph Link Prediction](https://mlsanity.com/paper/2610.18198/) (2026)

## Abstract (arXiv)

Embedding-based methods for reasoning in knowledge hypergraphs learn a representation for each entity and relation. Current methods do not capture the procedural rules underlying the relations in the graph. We propose a simple embedding-based model called ReAlE that performs link prediction in knowledge hypergraphs (generalized knowledge graphs) and can represent high-level abstractions in terms of relational algebra operations. We show theoretically that ReAlE is fully expressive and provide proofs and empirical evidence that it can represent a large subset of the primitive relational algebra operations, namely renaming, projection, set union, selection, and set difference. We also verify experimentally that ReAlE outperforms state-of-the-art models in knowledge hypergraph completion, and in representing each of these primitive relational algebra operations. For the latter experiment, we generate a synthetic knowledge hypergraph, for which we design an algorithm based on the Erdos-R'enyi model for generating random graphs.