# HyperMono: A Monotonicity-aware Approach to Hyper-Relational Knowledge Representation

arXiv: https://arxiv.org/abs/2404.09848 · HTML: https://mlsanity.com/paper/2404.09848/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 69 references that are in the map.
- First posted on arXiv 15 Apr 2024.

## Builds on (most cited first, 30 of 37)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [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)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Learning Hierarchy-Aware Knowledge Graph Embeddings for Link Prediction](https://mlsanity.com/paper/1911.09419/) (2019)
- [Beta Embeddings for Multi-Hop Logical Reasoning in Knowledge Graphs](https://mlsanity.com/paper/2010.11465/) (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)
- [Knowledge Graph Contrastive Learning for Recommendation](https://mlsanity.com/paper/2205.00976/) (2022)
- [On the representation and embedding of knowledge bases beyond binary relations](https://mlsanity.com/paper/1604.08642/) (2016)
- [L2-GCN: Layer-Wise and Learned Efficient Training of Graph Convolutional Networks](https://mlsanity.com/paper/2003.13606/) (2020)
- [Mask and Reason: Pre-Training Knowledge Graph Transformers for Complex Logical Queries](https://mlsanity.com/paper/2208.07638/) (2022)
- [Generalizing Tensor Decomposition for N-ary Relational Knowledge Bases](https://mlsanity.com/paper/2007.03988/) (2020)
- [A Capsule Network-based Embedding Model for Knowledge Graph Completion and Search Personalization](https://mlsanity.com/paper/1808.04122/) (2018)
- [Multi-level Cross-view Contrastive Learning for Knowledge-aware Recommender System](https://mlsanity.com/paper/2204.08807/) (2022)
- [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)
- [HousE: Knowledge Graph Embedding with Householder Parameterization](https://mlsanity.com/paper/2202.07919/) (2022)
- [GammaE: Gamma Embeddings for Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/2210.15578/) (2022)
- [Improving Hyper-Relational Knowledge Graph Completion](https://mlsanity.com/paper/2104.08167/) (2021)
- [Representation Learning on Hyper-Relational and Numeric Knowledge Graphs with Transformers](https://mlsanity.com/paper/2305.18256/) (2023)
- [Link Prediction on N-ary Relational Data Based on Relatedness Evaluation](https://mlsanity.com/paper/2104.10424/) (2021)
- [I Know What You Do Not Know: Knowledge Graph Embedding via Co-distillation Learning](https://mlsanity.com/paper/2208.09828/) (2022)
- [Searching to Sparsify Tensor Decomposition for N-ary Relational Data](https://mlsanity.com/paper/2104.10625/) (2021)
- [Type-aware Embeddings for Multi-Hop Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2205.00782/) (2022)
- [Transformer-based Entity Typing in Knowledge Graphs](https://mlsanity.com/paper/2210.11151/) (2022)

## Built on by (most cited first, 2 of 2)

- [A Survey of Link Prediction in N-ary Knowledge Graphs](https://mlsanity.com/paper/2506.08970/) (2025)
- [Two-dimensional Taxonomy for N-ary Knowledge Representation Learning Methods](https://mlsanity.com/paper/2506.05626/) (2025)

## Abstract (arXiv)

In a hyper-relational knowledge graph (HKG), each fact is composed of a main triple associated with attribute-value qualifiers, which express additional factual knowledge. The hyper-relational knowledge graph completion (HKGC) task aims at inferring plausible missing links in a HKG. Most existing approaches to HKGC focus on enhancing the communication between qualifier pairs and main triples, while overlooking two important properties that emerge from the monotonicity of the hyper-relational graphs representation regime. Stage Reasoning allows for a two-step reasoning process, facilitating the integration of coarse-grained inference results derived solely from main triples and fine-grained inference results obtained from hyper-relational facts with qualifiers. In the initial stage, coarse-grained results provide an upper bound for correct predictions, which are subsequently refined in the fine-grained step. More generally, Qualifier Monotonicity implies that by attaching more qualifier pairs to a main triple, we may only narrow down the answer set, but never enlarge it. This paper proposes the HyperMono model for hyper-relational knowledge graph completion, which realizes stage reasoning and qualifier monotonicity. To implement qualifier monotonicity HyperMono resorts to cone embeddings. Experiments on three real-world datasets with three different scenario conditions demonstrate the strong performance of HyperMono when compared to the SoTA.