# MQuinE: a cure for "Z-paradox" in knowledge graph embedding models

arXiv: https://arxiv.org/abs/2402.03583 · HTML: https://mlsanity.com/paper/2402.03583/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 51 references that are in the map.
- First posted on arXiv 5 Feb 2024.

## Builds on (most cited first, 23 of 23)

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [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)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [KGAT: Knowledge Graph Attention Network for Recommendation](https://mlsanity.com/paper/1905.07854/) (2019)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Prediction](https://mlsanity.com/paper/2106.06935/) (2021)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [DKN: Deep Knowledge-Aware Network for News Recommendation](https://mlsanity.com/paper/1801.08284/) (2018)
- [Learning Hierarchy-Aware Knowledge Graph Embeddings for Link Prediction](https://mlsanity.com/paper/1911.09419/) (2019)
- [Learning Attention-based Embeddings for Relation Prediction in Knowledge Graphs](https://mlsanity.com/paper/1906.01195/) (2019)
- [BoxE: A Box Embedding Model for Knowledge Base Completion](https://mlsanity.com/paper/2007.06267/) (2020)
- [CoDEx: A Comprehensive Knowledge Graph Completion Benchmark](https://mlsanity.com/paper/2009.07810/) (2020)
- [Jointly Learning Explainable Rules for Recommendation with Knowledge Graph](https://mlsanity.com/paper/1903.03714/) (2019)
- [Orthogonal Relation Transforms with Graph Context Modeling for Knowledge Graph Embedding](https://mlsanity.com/paper/1911.04910/) (2019)
- [HousE: Knowledge Graph Embedding with Householder Parameterization](https://mlsanity.com/paper/2202.07919/) (2022)
- [Relation Embedding with Dihedral Group in Knowledge Graph](https://mlsanity.com/paper/1906.00687/) (2019)
- [ExpressivE: A Spatio-Functional Embedding For Knowledge Graph Completion](https://mlsanity.com/paper/2206.04192/) (2022)
- [SEEK: Segmented Embedding of Knowledge Graphs](https://mlsanity.com/paper/2005.00856/) (2020)
- [HopfE: Knowledge Graph Representation Learning using Inverse Hopf Fibrations](https://mlsanity.com/paper/2108.05774/) (2021)

## Built on by (most cited first, 3 of 3)

- [Entity Alignment with Noisy Annotations from Large Language Models](https://mlsanity.com/paper/2405.16806/) (2024)
- [Neuro-Symbolic Entity Alignment via Variational Inference](https://mlsanity.com/paper/2410.04153/) (2024)
- [CL4KGE: A Curriculum Learning Method for Knowledge Graph Embedding](https://mlsanity.com/paper/2408.14840/) (2024)

## Abstract (arXiv)

Knowledge graph embedding (KGE) models achieved state-of-the-art results on many knowledge graph tasks including link prediction and information retrieval. Despite the superior performance of KGE models in practice, we discover a deficiency in the expressiveness of some popular existing KGE models called Z-paradox. Motivated by the existence of Z-paradox, we propose a new KGE model called MQuinE that does not suffer from Z-paradox while preserves strong expressiveness to model various relation patterns including symmetric/asymmetric, inverse, 1-N/N-1/N-N, and composition relations with theoretical justification. Experiments on real-world knowledge bases indicate that Z-paradox indeed degrades the performance of existing KGE models, and can cause more than 20% accuracy drop on some challenging test samples. Our experiments further demonstrate that MQuinE can mitigate the negative impact of Z-paradox and outperform existing KGE models by a visible margin on link prediction tasks.