# NQE: N-ary Query Embedding for Complex Query Answering over Hyper-Relational Knowledge Graphs

arXiv: https://arxiv.org/abs/2211.13469 · HTML: https://mlsanity.com/paper/2211.13469/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 22 of its 41 references that are in the map.
- First posted on arXiv 24 Nov 2022.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [Heterogeneous Graph Attention Network](https://mlsanity.com/paper/1903.07293/) (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)
- [Query2box: Reasoning over Knowledge Graphs in Vector Space using Box Embeddings](https://mlsanity.com/paper/2002.05969/) (2020)
- [Beta Embeddings for Multi-Hop Logical Reasoning in Knowledge Graphs](https://mlsanity.com/paper/2010.11465/) (2020)
- [Embedding Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/1806.01445/) (2018)
- [BoxE: A Box Embedding Model for Knowledge Base Completion](https://mlsanity.com/paper/2007.06267/) (2020)
- [Complex Query Answering with Neural Link Predictors](https://mlsanity.com/paper/2011.03459/) (2020)
- [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)
- [Neural-Symbolic Models for Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/2205.10128/) (2022)
- [On the representation and embedding of knowledge bases beyond binary relations](https://mlsanity.com/paper/1604.08642/) (2016)
- [Generalizing Tensor Decomposition for N-ary Relational Knowledge Bases](https://mlsanity.com/paper/2007.03988/) (2020)
- [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)
- [Answering Complex Queries in Knowledge Graphs with Bidirectional Sequence Encoders](https://mlsanity.com/paper/2004.02596/) (2020)
- [Probabilistic Entity Representation Model for Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2110.13522/) (2021)
- [Query Embedding on Hyper-relational Knowledge Graphs](https://mlsanity.com/paper/2106.08166/) (2021)
- [Message Passing Query Embedding](https://mlsanity.com/paper/2002.02406/) (2020)
- [FLEX: Feature-Logic Embedding Framework for CompleX Knowledge Graph Reasoning](https://mlsanity.com/paper/2205.11039/) (2022)

## Built on by (most cited first, 9 of 9)

- [Neural Graph Reasoning: Complex Logical Query Answering Meets Graph Databases](https://mlsanity.com/paper/2303.14617/) (2023)
- [Top Ten Challenges Towards Agentic Neural Graph Databases](https://mlsanity.com/paper/2501.14224/) (2025)
- [EFOk-CQA: Towards Knowledge Graph Complex Query Answering beyond Set Operation](https://mlsanity.com/paper/2307.13701/) (2023)
- [Effective Instruction Parsing Plugin for Complex Logical Query Answering on Knowledge Graphs](https://mlsanity.com/paper/2410.20321/) (2024)
- [A Neuro-Symbolic Framework for Answering Graph Pattern Queries in Knowledge Graphs](https://mlsanity.com/paper/2310.04598/) (2023)
- [Cardinality Estimation on Hyper-relational Knowledge Graphs](https://mlsanity.com/paper/2405.15231/) (2024)
- [RConE: Rough Cone Embedding for Multi-Hop Logical Query Answering on Multi-Modal Knowledge Graphs](https://mlsanity.com/paper/2408.11526/) (2024)
- [Transformers for Complex Query Answering over Knowledge Hypergraphs](https://mlsanity.com/paper/2504.16537/) (2025)
- [GTA: Graph Theory Agent and Benchmark for Algorithmic Graph Reasoning with LLMs](https://mlsanity.com/paper/2609.12265/) (2026)

## Abstract (arXiv)

Complex query answering (CQA) is an essential task for multi-hop and logical reasoning on knowledge graphs (KGs). Currently, most approaches are limited to queries among binary relational facts and pay less attention to n-ary facts (n>=2) containing more than two entities, which are more prevalent in the real world. Moreover, previous CQA methods can only make predictions for a few given types of queries and cannot be flexibly extended to more complex logical queries, which significantly limits their applications. To overcome these challenges, in this work, we propose a novel N-ary Query Embedding (NQE) model for CQA over hyper-relational knowledge graphs (HKGs), which include massive n-ary facts. The NQE utilizes a dual-heterogeneous Transformer encoder and fuzzy logic theory to satisfy all n-ary FOL queries, including existential quantifiers, conjunction, disjunction, and negation. We also propose a parallel processing algorithm that can train or predict arbitrary n-ary FOL queries in a single batch, regardless of the kind of each query, with good flexibility and extensibility. In addition, we generate a new CQA dataset WD50K-NFOL, including diverse n-ary FOL queries over WD50K. Experimental results on WD50K-NFOL and other standard CQA datasets show that NQE is the state-of-the-art CQA method over HKGs with good generalization capability. Our code and dataset are publicly available.