Low-Dimensional Hyperbolic Knowledge Graph Embeddings (2005.00545v1)

Abstract: Knowledge graph (KG) embeddings learn low-dimensional representations of entities and relations to predict missing facts. KGs often exhibit hierarchical and logical patterns which must be preserved in the embedding space. For hierarchical data, hyperbolic embedding methods have shown promise for high-fidelity and parsimonious representations. However, existing hyperbolic embedding methods do not account for the rich logical patterns in KGs. In this work, we introduce a class of hyperbolic KG embedding models that simultaneously capture hierarchical and logical patterns. Our approach combines hyperbolic reflections and rotations with attention to model complex relational patterns. Experimental results on standard KG benchmarks show that our method improves over previous Euclidean- and hyperbolic-based efforts by up to 6.1% in mean reciprocal rank (MRR) in low dimensions. Furthermore, we observe that different geometric transformations capture different types of relations while attention-based transformations generalize to multiple relations. In high dimensions, our approach yields new state-of-the-art MRRs of 49.6% on WN18RR and 57.7% on YAGO3-10.

Low-Dimensional Hyperbolic Knowledge Graph Embeddings

Hyperbolic geometry has witnessed increased interest in the field of machine learning, particularly for its utility in representing hierarchically structured data. This essay discusses the contributions of a paper that explores a novel class of hyperbolic embedding models tailored to capture both hierarchical and logical patterns within Knowledge Graphs (KGs). The paper "Low-Dimensional Hyperbolic Knowledge Graph Embeddings" demonstrates advancements in embedding techniques by leveraging hyperbolic space, which inherently supports hierarchical structures while also employing geometric transformations to encode complex relational patterns in KGs.

Summary of Contributions

1. Integration of Hyperbolic Reflections, Rotations, and Attention: The paper introduces an approach that combines hyperbolic reflections and rotations with attention mechanisms. This is strategic for modeling the intricate relational structures in KGs, allowing the model to generalize and capture different relational types during the embedding process.
2. Enhanced Model Performance: Experimental results indicate a substantial improvement, with up to a 6.1% increase in mean reciprocal rank (MRR) when compared to previous Euclidean- and hyperbolic-based embedding methods in low-dimensional space. These improvements are significant when considering the challenging task of effective link prediction in KGs.
3. Dimensional Efficiency and State-of-the-Art Results: Even in higher-dimensional settings, the model achieved new state-of-the-art MRRs of 49.6% on the WN18RR and 57.7% on the YAGO3-10 datasets. This suggests that the proposed model efficiently utilizes dimensions to store hierarchical and logical information pertinent to KGs.

Practical and Theoretical Implications

• Memory Efficiency with Low Dimensionality: The proposed hyperbolic embeddings provide a parsimonious representation of entities and relations, which is critical given the memory-intensive nature of high-dimensional Euclidean embeddings. This characteristic makes the approach computationally attractive in environments constrained by memory.
• Potential for Application in Hierarchically Structured Data: The use of hyperbolic representations could be extended beyond KGs to other domains, such as natural language processing tasks and hierarchical clustering, where data naturally fits into tree-like structures.
• Broader Understanding of Geometric Representations: The integration of different geometric transformations offers insights into how varying geometries can yield different performance characteristics when modeling relational data. This might lead to new lines of research exploring hybrid models that adapt geometries to data dynamics dynamically.

Future Developments and Speculations

Scaling the current findings, future research could explore adaptive embedding techniques that dynamically adjust their geometric properties based on real-time data analysis. Additionally, there exists a potential in exploring embedding spaces that adjust curvature based on localized data structures, allowing even finer-grained adaptability than offered by trainable curvature models.

In conclusion, the work analyzed in the paper fosters a deeper understanding of how hyperbolic spaces can enhance the representation capability of KG embeddings, specifically in capturing hierarchies coupled with logical patterns. It marks a step forward in embedding methodologies by underlining the versatility and efficacy of hyperbolic geometry, further paving the way for new research avenues in hierarchical data modeling.