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Fully Hyperbolic Rotation for Knowledge Graph Embedding

Qiuyu Liang, Weihua Wang, Feilong Bao, Guanglai Gao

TL;DR

A novel fully hyperbolic model designed for knowledge graph embedding that considers each relation in knowledge graphs as a Lorentz rotation from the head entity to the tail entity and adopts the Lorentzian version distance as the scoring function for measuring the plausibility of triplets.

Abstract

Hyperbolic rotation is commonly used to effectively model knowledge graphs and their inherent hierarchies. However, existing hyperbolic rotation models rely on logarithmic and exponential mappings for feature transformation. These models only project data features into hyperbolic space for rotation, limiting their ability to fully exploit the hyperbolic space. To address this problem, we propose a novel fully hyperbolic model designed for knowledge graph embedding. Instead of feature mappings, we define the model directly in hyperbolic space with the Lorentz model. Our model considers each relation in knowledge graphs as a Lorentz rotation from the head entity to the tail entity. We adopt the Lorentzian version distance as the scoring function for measuring the plausibility of triplets. Extensive results on standard knowledge graph completion benchmarks demonstrated that our model achieves competitive results with fewer parameters. In addition, our model get the state-of-the-art performance on datasets of CoDEx-s and CoDEx-m, which are more diverse and challenging than before. Our code is available at https://github.com/llqy123/FHRE.

Fully Hyperbolic Rotation for Knowledge Graph Embedding

TL;DR

A novel fully hyperbolic model designed for knowledge graph embedding that considers each relation in knowledge graphs as a Lorentz rotation from the head entity to the tail entity and adopts the Lorentzian version distance as the scoring function for measuring the plausibility of triplets.

Abstract

Hyperbolic rotation is commonly used to effectively model knowledge graphs and their inherent hierarchies. However, existing hyperbolic rotation models rely on logarithmic and exponential mappings for feature transformation. These models only project data features into hyperbolic space for rotation, limiting their ability to fully exploit the hyperbolic space. To address this problem, we propose a novel fully hyperbolic model designed for knowledge graph embedding. Instead of feature mappings, we define the model directly in hyperbolic space with the Lorentz model. Our model considers each relation in knowledge graphs as a Lorentz rotation from the head entity to the tail entity. We adopt the Lorentzian version distance as the scoring function for measuring the plausibility of triplets. Extensive results on standard knowledge graph completion benchmarks demonstrated that our model achieves competitive results with fewer parameters. In addition, our model get the state-of-the-art performance on datasets of CoDEx-s and CoDEx-m, which are more diverse and challenging than before. Our code is available at https://github.com/llqy123/FHRE.

Paper Structure

This paper contains 18 sections, 1 theorem, 12 equations, 3 figures, 9 tables.

Table of Contents

  1. Related Work
  2. Problem Formulation and Preliminaries
  3. Knowledge graph completion
  4. Hyperbolic geometry
  5. Methodology
  6. Initialization
  7. Lorentz rotation
  8. Scoring function
  9. Loss function
  10. Experiments
  11. Experimental settings
  12. Results
  13. Low-dimensional embedding experiments
  14. High-dimensional embedding experiments
  15. Robustness and generalization experiments
  16. ...and 3 more sections

Key Result

Theorem 1

Lorentz rotation is the rotation of the spatial coordinates. The Lorentz rotation matrix is of the following form: where $\mathrm{\widetilde{R}^T}\mathrm{\widetilde{R}}=\mathrm{I}$ and $\mathbf{det}(\mathrm{\widetilde{R}})=1$. $\mathrm{\widetilde{R}} \in \mathrm{SO}(n)$ is a special orthogonal matrix.

Figures (3)

  • Figure 1: The example of the European entity illustrates how KG presents hierarchies.
  • Figure 2: Rotational transformations based on different spaces in the training phase. Orange dot indicates entity in knowledge graph. Tangent space as subspace of Euclidean space.
  • Figure 3: Embedding of the entities learned with rotation on relation _derivationally_related_form by RotH model and our model .

Theorems & Definitions (1)

  • Theorem 1: Lorentz rotation