# On the representation and embedding of knowledge bases beyond binary relations

arXiv: https://arxiv.org/abs/1604.08642 · HTML: https://mlsanity.com/paper/1604.08642/

## Key facts

- Cited by 55 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Apr 2016.

## Built on by (most cited first, 30 of 55)

- [HyperGraphRAG: Retrieval-Augmented Generation via Hypergraph-Structured Knowledge Representation](https://mlsanity.com/paper/2503.21322/) (2025)
- [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)
- [How Expressive are Knowledge Graph Foundation Models?](https://mlsanity.com/paper/2502.13339/) (2025)
- [What is Event Knowledge Graph: A Survey](https://mlsanity.com/paper/2112.15280/) (2021)
- [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)
- [Searching to Sparsify Tensor Decomposition for N-ary Relational Data](https://mlsanity.com/paper/2104.10625/) (2021)
- [HEAT: Hyperedge Attention Networks](https://mlsanity.com/paper/2201.12113/) (2022)
- [A Dataset for Hyper-Relational Extraction and a Cube-Filling Approach](https://mlsanity.com/paper/2211.10018/) (2022)
- [SMiLE: Schema-augmented Multi-level Contrastive Learning for Knowledge Graph Link Prediction](https://mlsanity.com/paper/2210.04870/) (2022)
- [Shrinking Embeddings for Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2306.02199/) (2023)
- [Knowledge Hypergraph Embedding Meets Relational Algebra](https://mlsanity.com/paper/2102.09557/) (2021)
- [Text2NKG: Fine-Grained N-ary Relation Extraction for N-ary relational Knowledge Graph Construction](https://mlsanity.com/paper/2310.05185/) (2023)
- [HAHE: Hierarchical Attention for Hyper-Relational Knowledge Graphs in Global and Local Level](https://mlsanity.com/paper/2305.06588/) (2023)
- [NQE: N-ary Query Embedding for Complex Query Answering over Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2211.13469/) (2022)
- [Link Prediction with Relational Hypergraphs](https://mlsanity.com/paper/2402.04062/) (2024)
- [Learning Representations for Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2208.14322/) (2022)
- [A Survey on Visual Transfer Learning using Knowledge Graphs](https://mlsanity.com/paper/2201.11794/) (2022)
- [DHGE: Dual-View Hyper-Relational Knowledge Graph Embedding for Link Prediction and Entity Typing](https://mlsanity.com/paper/2207.08562/) (2022)
- [HYPER: A Foundation Model for Inductive Link Prediction with Knowledge Hypergraphs](https://mlsanity.com/paper/2506.12362/) (2025)
- [HyCubE: Efficient Knowledge Hypergraph 3D Circular Convolutional Embedding](https://mlsanity.com/paper/2402.08961/) (2024)
- [HyperFormer: Enhancing Entity and Relation Interaction for Hyper-Relational Knowledge Graph Completion](https://mlsanity.com/paper/2308.06512/) (2023)
- [Automating construction contract review using knowledge graph-enhanced large language models](https://mlsanity.com/paper/2309.12132/) (2023)
- [A Survey of Link Prediction in N-ary Knowledge Graphs](https://mlsanity.com/paper/2506.08970/) (2025)
- [IntelliGraphs: Datasets for Benchmarking Knowledge Graph Generation](https://mlsanity.com/paper/2307.06698/) (2023)
- [RDF-star2Vec: RDF-star Graph Embeddings for Data Mining](https://mlsanity.com/paper/2312.15626/) (2023)
- [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)

## Abstract (arXiv)

The models developed to date for knowledge base embedding are all based on the assumption that the relations contained in knowledge bases are binary. For the training and testing of these embedding models, multi-fold (or n-ary) relational data are converted to triples (e.g., in FB15K dataset) and interpreted as instances of binary relations. This paper presents a canonical representation of knowledge bases containing multi-fold relations. We show that the existing embedding models on the popular FB15K datasets correspond to a sub-optimal modelling framework, resulting in a loss of structural information. We advocate a novel modelling framework, which models multi-fold relations directly using this canonical representation. Using this framework, the existing TransH model is generalized to a new model, m-TransH. We demonstrate experimentally that m-TransH outperforms TransH by a large margin, thereby establishing a new state of the art.