Knowledge Graph Embeddings in Geometric Algebras

TL;DR

This paper introduces GeomE, a novel geometric algebra-based framework for knowledge graph embedding that models entities and relations with multivectors, capturing complex relation patterns and outperforming existing models on benchmarks.

Contribution

The paper presents GeomE, a new geometric algebra framework that unifies and extends existing KG embedding methods with enhanced modeling capabilities.

Findings

Outperforms state-of-the-art models on link prediction benchmarks.

Effectively models various relation patterns including symmetry and inversion.

Provides higher expressiveness and better generalization.

Abstract

Knowledge graph (KG) embedding aims at embedding entities and relations in a KG into a lowdimensional latent representation space. Existing KG embedding approaches model entities andrelations in a KG by utilizing real-valued , complex-valued, or hypercomplex-valued (Quaternionor Octonion) representations, all of which are subsumed into a geometric algebra. In this work,we introduce a novel geometric algebra-based KG embedding framework, GeomE, which uti-lizes multivector representations and the geometric product to model entities and relations. Ourframework subsumes several state-of-the-art KG embedding approaches and is advantageouswith its ability of modeling various key relation patterns, including (anti-)symmetry, inversionand composition, rich expressiveness with higher degree of freedom as well as good general-ization capacity. Experimental results on multiple benchmark knowledge graphs show that theproposed approach outperforms existing state-of-the-art models for link prediction.