Geometric Relational Embeddings

TL;DR

This paper introduces geometric relational embeddings that better capture complex, symbolic, and structured properties of relational data, improving upon traditional vector-based methods.

Contribution

It proposes new geometric models for relational embeddings that effectively encode hierarchies, logical constraints, and high-order structures in relational data.

Findings

Effective in capturing hierarchies and cycles in networks

Able to encode logical structures and constraints

Demonstrated superior performance on benchmark datasets

Abstract

Relational representation learning transforms relational data into continuous and low-dimensional vector representations. However, vector-based representations fall short in capturing crucial properties of relational data that are complex and symbolic. We propose geometric relational embeddings, a paradigm of relational embeddings that respect the underlying symbolic structures. Specifically, this dissertation introduces various geometric relational embedding models capable of capturing: 1) complex structured patterns like hierarchies and cycles in networks and knowledge graphs; 2) logical structures in ontologies and logical constraints applicable for constraining machine learning model outputs; and 3) high-order structures between entities and relations. Our results obtained from benchmark and real-world datasets demonstrate the efficacy of geometric relational embeddings in adeptly capturing these discrete, symbolic, and structured properties inherent in relational data.