Knowledge Base Embeddings: Semantics and Theoretical Properties

TL;DR

This paper analyzes recent knowledge base embedding methods, focusing on their geometric semantics and theoretical properties, to understand how they incorporate conceptual knowledge into vector space models.

Contribution

It provides a unified theoretical framework for understanding the geometric and semantic properties of knowledge base embeddings in description logics.

Findings

Identification of key theoretical properties of embedding methods

Analysis of how embedding techniques align with geometric semantics

Generalization and unification of existing theoretical frameworks

Abstract

Research on knowledge graph embeddings has recently evolved into knowledge base embeddings, where the goal is not only to map facts into vector spaces but also constrain the models so that they take into account the relevant conceptual knowledge available. This paper examines recent methods that have been proposed to embed knowledge bases in description logic into vector spaces through the lens of their geometric-based semantics. We identify several relevant theoretical properties, which we draw from the literature and sometimes generalize or unify. We then investigate how concrete embedding methods fit in this theoretical framework.