# Generalizing Tensor Decomposition for N-ary Relational Knowledge Bases

arXiv: https://arxiv.org/abs/2007.03988 · HTML: https://mlsanity.com/paper/2007.03988/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2020.

## Built on by (most cited first, 30 of 38)

- [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)
- [Spatio-Temporal Urban Knowledge Graph Enabled Mobility Prediction](https://mlsanity.com/paper/2111.03465/) (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)
- [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)
- [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)
- [Link Prediction with Relational Hypergraphs](https://mlsanity.com/paper/2402.04062/) (2024)
- [Dynamic Multi-Network Mining of Tensor Time Series](https://mlsanity.com/paper/2402.11773/) (2024)
- [A Survey on Visual Transfer Learning using Knowledge Graphs](https://mlsanity.com/paper/2201.11794/) (2022)
- [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)
- [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)
- [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)
- [Demystifying Topological Message-Passing with Relational Structures: A Case Study on Oversquashing in Simplicial Message-Passing](https://mlsanity.com/paper/2506.06582/) (2025)
- [NestE: Modeling Nested Relational Structures for Knowledge Graph Reasoning](https://mlsanity.com/paper/2312.09219/) (2023)
- [Two-dimensional Taxonomy for N-ary Knowledge Representation Learning Methods](https://mlsanity.com/paper/2506.05626/) (2025)
- [SAG: SQL-Retrieval Augmented Generation with Query-Time Dynamic Hyperedges](https://mlsanity.com/paper/2606.15971/) (2026)

## Abstract (arXiv)

With the rapid development of knowledge bases (KBs), link prediction task, which completes KBs with missing facts, has been broadly studied in especially binary relational KBs (a.k.a knowledge graph) with powerful tensor decomposition related methods. However, the ubiquitous n-ary relational KBs with higher-arity relational facts are paid less attention, in which existing translation based and neural network based approaches have weak expressiveness and high complexity in modeling various relations. Tensor decomposition has not been considered for n-ary relational KBs, while directly extending tensor decomposition related methods of binary relational KBs to the n-ary case does not yield satisfactory results due to exponential model complexity and their strong assumptions on binary relations. To generalize tensor decomposition for n-ary relational KBs, in this work, we propose GETD, a generalized model based on Tucker decomposition and Tensor Ring decomposition. The existing negative sampling technique is also generalized to the n-ary case for GETD. In addition, we theoretically prove that GETD is fully expressive to completely represent any KBs. Extensive evaluations on two representative n-ary relational KB datasets demonstrate the superior performance of GETD, significantly improving the state-of-the-art methods by over 15%. Moreover, GETD further obtains the state-of-the-art results on the benchmark binary relational KB datasets.