# Link Prediction on N-ary Relational Facts: A Graph-based Approach

arXiv: https://arxiv.org/abs/2105.08476 · HTML: https://mlsanity.com/paper/2105.08476/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 41 references that are in the map.
- First posted on arXiv 18 May 2021.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://mlsanity.com/paper/1906.08237/) (2019)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [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)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [A Survey on Knowledge Graphs: Representation, Acquisition and Applications](https://mlsanity.com/paper/2002.00388/) (2020)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [A Review of Relational Machine Learning for Knowledge Graphs](https://mlsanity.com/paper/1503.00759/) (2015)
- [Message Passing for Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2009.10847/) (2020)
- [Linguistically-Informed Self-Attention for Semantic Role Labeling](https://mlsanity.com/paper/1804.08199/) (2018)
- [Tree Transformer: Integrating Tree Structures into Self-Attention](https://mlsanity.com/paper/1909.06639/) (2019)
- [Entity Structure Within and Throughout: Modeling Mention Dependencies for Document-Level Relation Extraction](https://mlsanity.com/paper/2102.10249/) (2021)
- [FLAT: Chinese NER Using Flat-Lattice Transformer](https://mlsanity.com/paper/2004.11795/) (2020)
- [On the representation and embedding of knowledge bases beyond binary relations](https://mlsanity.com/paper/1604.08642/) (2016)
- [HittER: Hierarchical Transformers for Knowledge Graph Embeddings](https://mlsanity.com/paper/2008.12813/) (2020)
- [Generalizing Tensor Decomposition for N-ary Relational Knowledge Bases](https://mlsanity.com/paper/2007.03988/) (2020)
- [CoKE: Contextualized Knowledge Graph Embedding](https://mlsanity.com/paper/1911.02168/) (2019)
- [Role-Aware Modeling for N-ary Relational Knowledge Bases](https://mlsanity.com/paper/2104.09780/) (2021)
- [Extracting Multiple-Relations in One-Pass with Pre-Trained Transformers](https://mlsanity.com/paper/1902.01030/) (2019)
- [Improving Hyper-Relational Knowledge Graph Completion](https://mlsanity.com/paper/2104.08167/) (2021)

## Built on by (most cited first, 29 of 29)

- [HyperGraphRAG: Retrieval-Augmented Generation via Hypergraph-Structured Knowledge Representation](https://mlsanity.com/paper/2503.21322/) (2025)
- [What is Event Knowledge Graph: A Survey](https://mlsanity.com/paper/2112.15280/) (2021)
- [Representation Learning on Hyper-Relational and Numeric Knowledge Graphs with Transformers](https://mlsanity.com/paper/2305.18256/) (2023)
- [Shrinking Embeddings for Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2306.02199/) (2023)
- [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)
- [Temporal Fact Reasoning over Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2307.10219/) (2023)
- [NQE: N-ary Query Embedding for Complex Query Answering over Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2211.13469/) (2022)
- [Learning Representations for Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2208.14322/) (2022)
- [DHGE: Dual-View Hyper-Relational Knowledge Graph Embedding for Link Prediction and Entity Typing](https://mlsanity.com/paper/2207.08562/) (2022)
- [HyperFormer: Enhancing Entity and Relation Interaction for Hyper-Relational Knowledge Graph Completion](https://mlsanity.com/paper/2308.06512/) (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)
- [Cardinality Estimation on Hyper-relational Knowledge Graphs](https://mlsanity.com/paper/2405.15231/) (2024)
- [Replacing Paths with Connection-Biased Attention for Knowledge Graph Completion](https://mlsanity.com/paper/2410.00876/) (2024)
- [UniHR: Hierarchical Representation Learning for Unified Knowledge Graph Link Prediction](https://mlsanity.com/paper/2411.07019/) (2024)
- [Inductive Link Prediction on N-ary Relational Facts via Semantic Hypergraph Reasoning](https://mlsanity.com/paper/2503.20676/) (2025)
- [Fact-Tree Reasoning for N-ary Question Answering over Knowledge Graphs](https://mlsanity.com/paper/2108.08297/) (2021)
- [Few-shot Link Prediction on N-ary Facts](https://mlsanity.com/paper/2305.06104/) (2023)
- [HyperMono: A Monotonicity-aware Approach to Hyper-Relational Knowledge Representation](https://mlsanity.com/paper/2404.09848/) (2024)
- [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)
- [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)
- [VITA: Versatile Time Representation Learning for Temporal Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2505.11803/) (2025)
- [Mixture Policy based Multi-Hop Reasoning over N-tuple Temporal Knowledge Graphs](https://mlsanity.com/paper/2505.12788/) (2025)
- [THOR: Inductive Link Prediction over Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2602.05424/) (2026)
- [Life-Bench: A Benchmark and Knowledge Graph Framework for Multimodal Personalization Beyond Concept Recognition](https://mlsanity.com/paper/2602.19001/) (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) is a key research topic. Previous work mainly focused on binary relations, paying less attention to higher-arity relations although they are ubiquitous in real-world KGs. This paper considers link prediction upon n-ary relational facts and proposes a graph-based approach to this task. The key to our approach is to represent the n-ary structure of a fact as a small heterogeneous graph, and model this graph with edge-biased fully-connected attention. The fully-connected attention captures universal inter-vertex interactions, while with edge-aware attentive biases to particularly encode the graph structure and its heterogeneity. In this fashion, our approach fully models global and local dependencies in each n-ary fact, and hence can more effectively capture associations therein. Extensive evaluation verifies the effectiveness and superiority of our approach. It performs substantially and consistently better than current state-of-the-art across a variety of n-ary relational benchmarks. Our code is publicly available.