Multi-relational Poincaré Graph Embeddings

2019/05/23 by Ivana Balažević, Carl Allen, Balažević, Ivana +4 · 29 citations
Computer Science · Mathematics · #Advanced Graph Neural Networks #Algebra over a field #Artificial intelligence #Bayesian Modeling and Causal Inference #Computer science #Curse of dimensionality #Data mining #Embedding #Euclidean geometry #Euclidean space #FOS: Computer and information sciences #Graph #Hyperbolic space #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematics #Poincaré conjecture #Pure mathematics #Relational database #Statistical relational learning #Theoretical computer science #Topic Modeling #Vector space #cs.LG #stat.ML

paper · pdf · doi:10.48550/arxiv.1905.09791

published in arXiv (Cornell University) 32, 4465-4475 (Cornell University)

openalex publication_date 2019/05/23 · arxiv created 2019/10/27 · arxiv updated 2019/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Hyperbolic embeddings have recently gained attention in machine learning due to their ability to represent hierarchical data more accurately and succinctly than their Euclidean analogues. However, multi-relational knowledge graphs often exhibit multiple simultaneous hierarchies, which current hyperbolic models do not capture. To address this, we propose a model that embeds multi-relational graph data in the Poincaré ball model of hyperbolic space. Our Multi-Relational Poincaré model (MuRP) learns relation-specific parameters to transform entity embeddings by Möbius matrix-vector multiplication and Möbius addition. Experiments on the hierarchical WN18RR knowledge graph show that our Poincaré embeddings outperform their Euclidean counterpart and existing embedding methods on the link prediction task, particularly at lower dimensionality.

Citations

• Embedding Entities and Relations for Learning and Inference in Knowledge Bases
• Distributed Representations of Words and Phrases and their Compositionality
• M-Walk: Learning to Walk over Graphs using Monte Carlo Tree Search
• RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space
• Analogies Explained: Towards Understanding Word Embeddings

Cited by

• HyperComplEx: Adaptive Multi-Space Knowledge Graph Embeddings
• OntoAligner Meets Knowledge Graph Embedding Aligners
• SMART: Relation-Aware Learning of Geometric Representations for Knowledge Graphs
• DuetGraph: Coarse-to-Fine Knowledge Graph Reasoning with Dual-Pathway Global-Local Fusion
• Platform for Representation and Integration of multimodal Molecular Embeddings
• Multi-Hop Reasoning for Question Answering with Hyperbolic Representations
• A Set-to-Set Distance Measure in Hyperbolic Space
• Affective-CARA: A Knowledge Graph Driven Framework for Culturally Adaptive Emotional Intelligence in HCI
• GGBall: Graph Generative Model on Poincaré Ball
• RSCF: Relation-Semantics Consistent Filter for Entity Embedding of Knowledge Graph
• MEDMKG: Benchmarking Medical Knowledge Exploitation with Multimodal Knowledge Graph
• Hyperbolic Residual Quantization: Discrete Representations for Data with Latent Hierarchies
• A Hyperbolic-to-Hyperbolic Graph Convolutional Network
• Knowledge-augmented Pre-trained Language Models for Biomedical Relation Extraction
• Neural-Symbolic Logic Query Answering in Non-Euclidean Space
• A Survey of Task-Oriented Knowledge Graph Reasoning: Status, Applications, and Prospects
• Hyperbolic Graph Wavelet Neural Network
• CHAINSFORMER: Numerical Reasoning on Knowledge Graphs from a Chain Perspective
• Graph-based Approaches and Functionalities in Retrieval-Augmented Generation: A Comprehensive Survey

Related

• HYPER²: Hyperbolic Poincare Embedding for Hyper-Relational Link Prediction
• FFHR: Fully and Flexible Hyperbolic Representation for Knowledge Graph Completion
• Low-Dimensional Hyperbolic Knowledge Graph Embeddings
• Poincaré Embeddings for Learning Hierarchical Representations
• Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry