# Shrinking Embeddings for Hyper-Relational Knowledge Graphs

arXiv: https://arxiv.org/abs/2306.02199 · HTML: https://mlsanity.com/paper/2306.02199/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 48 references that are in the map.
- First posted on arXiv 3 Jun 2023.

## Builds on (most cited first, 28 of 28)

- [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)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [SimplE Embedding for Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/1802.04868/) (2018)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Query2box: Reasoning over Knowledge Graphs in Vector Space using Box Embeddings](https://mlsanity.com/paper/2002.05969/) (2020)
- [BoxE: A Box Embedding Model for Knowledge Base Completion](https://mlsanity.com/paper/2007.06267/) (2020)
- [Knowledge Graph Completion via Complex Tensor Factorization](https://mlsanity.com/paper/1702.06879/) (2017)
- [Message Passing for Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2009.10847/) (2020)
- [ConE: Cone Embeddings for Multi-Hop Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2110.13715/) (2021)
- [Fairness-Aware Explainable Recommendation over Knowledge Graphs](https://mlsanity.com/paper/2006.02046/) (2020)
- [Probabilistic Embedding of Knowledge Graphs with Box Lattice Measures](https://mlsanity.com/paper/1805.06627/) (2018)
- [On the representation and embedding of knowledge bases beyond binary relations](https://mlsanity.com/paper/1604.08642/) (2016)
- [EL Embeddings: Geometric construction of models for the Description Logic EL ++](https://mlsanity.com/paper/1902.10499/) (2019)
- [Generalizing Tensor Decomposition for N-ary Relational Knowledge Bases](https://mlsanity.com/paper/2007.03988/) (2020)
- [Modeling Scale-free Graphs with Hyperbolic Geometry for Knowledge-aware Recommendation](https://mlsanity.com/paper/2108.06468/) (2021)
- [Role-Aware Modeling for N-ary Relational Knowledge Bases](https://mlsanity.com/paper/2104.09780/) (2021)
- [Link Prediction on N-ary Relational Facts: A Graph-based Approach](https://mlsanity.com/paper/2105.08476/) (2021)
- [Faithiful Embeddings for EL++ Knowledge Bases](https://mlsanity.com/paper/2201.09919/) (2022)
- [Ultrahyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2206.00449/) (2022)
- [Improving Hyper-Relational Knowledge Graph Completion](https://mlsanity.com/paper/2104.08167/) (2021)
- [Link Prediction on N-ary Relational Data Based on Relatedness Evaluation](https://mlsanity.com/paper/2104.10424/) (2021)
- [Searching to Sparsify Tensor Decomposition for N-ary Relational Data](https://mlsanity.com/paper/2104.10625/) (2021)
- [HiPrompt: Few-Shot Biomedical Knowledge Fusion via Hierarchy-Oriented Prompting](https://mlsanity.com/paper/2304.05973/) (2023)
- [Geometric Relational Embeddings: A Survey](https://mlsanity.com/paper/2304.11949/) (2023)
- [Learning Representations for Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2208.14322/) (2022)
- [Modeling Relational Patterns for Logical Query Answering over Knowledge Graphs](https://mlsanity.com/paper/2303.11858/) (2023)

## Built on by (most cited first, 12 of 12)

- [A Survey on Temporal Knowledge Graph Completion: Taxonomy, Progress, and Prospects](https://mlsanity.com/paper/2308.02457/) (2023)
- [Temporal Fact Reasoning over Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2307.10219/) (2023)
- [Link Prediction with Relational Hypergraphs](https://mlsanity.com/paper/2402.04062/) (2024)
- [Predictive Multiplicity of Knowledge Graph Embeddings in Link Prediction](https://mlsanity.com/paper/2408.08226/) (2024)
- [A Survey of Link Prediction in N-ary Knowledge Graphs](https://mlsanity.com/paper/2506.08970/) (2025)
- [Cardinality Estimation on Hyper-relational Knowledge Graphs](https://mlsanity.com/paper/2405.15231/) (2024)
- [UniHR: Hierarchical Representation Learning for Unified Knowledge Graph Link Prediction](https://mlsanity.com/paper/2411.07019/) (2024)
- [HyperMono: A Monotonicity-aware Approach to Hyper-Relational Knowledge Representation](https://mlsanity.com/paper/2404.09848/) (2024)
- [Two-dimensional Taxonomy for N-ary Knowledge Representation Learning Methods](https://mlsanity.com/paper/2506.05626/) (2025)
- [Understanding the Embedding Models on Hyper-relational Knowledge Graph](https://mlsanity.com/paper/2508.03280/) (2025)
- [AlertStar: Path-Aware Alert Prediction on Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2604.03104/) (2026)
- [Generative Representation Learning on Hyper-relational Knowledge Graphs via Masked Discrete Diffusion](https://mlsanity.com/paper/2605.24064/) (2026)

## Abstract (arXiv)

Link prediction on knowledge graphs (KGs) has been extensively studied on binary relational KGs, wherein each fact is represented by a triple. A significant amount of important knowledge, however, is represented by hyper-relational facts where each fact is composed of a primal triple and a set of qualifiers comprising a key-value pair that allows for expressing more complicated semantics. Although some recent works have proposed to embed hyper-relational KGs, these methods fail to capture essential inference patterns of hyper-relational facts such as qualifier monotonicity, qualifier implication, and qualifier mutual exclusion, limiting their generalization capability. To unlock this, we present ShrinkE, a geometric hyper-relational KG embedding method aiming to explicitly model these patterns. ShrinkE models the primal triple as a spatial-functional transformation from the head into a relation-specific box. Each qualifier ``shrinks'' the box to narrow down the possible answer set and, thus, realizes qualifier monotonicity. The spatial relationships between the qualifier boxes allow for modeling core inference patterns of qualifiers such as implication and mutual exclusion. Experimental results demonstrate ShrinkE's superiority on three benchmarks of hyper-relational KGs.