Quaternion Knowledge Graph Embeddings

TL;DR

This paper introduces quaternion-based hypercomplex embeddings for knowledge graphs, offering more expressive and geometrically interpretable representations that outperform previous models on standard benchmarks.

Contribution

It presents a novel quaternion embedding framework that generalizes ComplEx, capturing complex relational patterns with improved expressiveness and interpretability.

Findings

Achieves state-of-the-art results on four benchmarks

Models symmetry, anti-symmetry, and inversion effectively

Provides a more compact and expressive representation of entities and relations

Abstract

In this work, we move beyond the traditional complex-valued representations, introducing more expressive hypercomplex representations to model entities and relations for knowledge graph embeddings. More specifically, quaternion embeddings, hypercomplex-valued embeddings with three imaginary components, are utilized to represent entities. Relations are modelled as rotations in the quaternion space. The advantages of the proposed approach are: (1) Latent inter-dependencies (between all components) are aptly captured with Hamilton product, encouraging a more compact interaction between entities and relations; (2) Quaternions enable expressive rotation in four-dimensional space and have more degree of freedom than rotation in complex plane; (3) The proposed framework is a generalization of ComplEx on hypercomplex space while offering better geometrical interpretations, concurrently satisfying the key desiderata of relational representation learning (i.e., modeling symmetry, anti-symmetry and inversion). Experimental results demonstrate that our method achieves state-of-the-art performance on four well-established knowledge graph completion benchmarks.