NestE: Modeling Nested Relational Structures for Knowledge Graph Reasoning

Abstract

Reasoning with knowledge graphs (KGs) has primarily focused on triple-shaped facts. Recent advancements have been explored to enhance the semantics of these facts by incorporating more potent representations, such as hyper-relational facts. However, these approaches are limited to mph{atomic facts}, which describe a single piece of information. This paper extends beyond mph{atomic facts} and delves into mph{nested facts}, represented by quoted triples where subjects and objects are triples themselves (e.g., ((mph{BarackObama}, mph{holds position}, mph{President}), mph{succeed by}, (mph{DonaldTrump}, mph{holds position}, mph{President}))). These nested facts enable the expression of complex semantics like mph{situations} over time and mph{logical patterns} over entities and relations. In response, we introduce NestE, a novel KG embedding approach that captures the semantics of both atomic and nested factual knowledge. NestE represents each atomic fact as a 1×3 matrix, and each nested relation is modeled as a 3×3 matrix that rotates the 1×3 atomic fact matrix through matrix multiplication. Each element of the matrix is represented as a complex number in the generalized 4D hypercomplex space, including (spherical) quaternions, hyperbolic quaternions, and split-quaternions. Through thorough analysis, we demonstrate the embedding’s efficacy in capturing diverse logical patterns over nested facts, surpassing the confines of first-order logic-like expressions. Our experimental results showcase NestE’s significant performance gains over current baselines in triple prediction and conditional link prediction.

Bo Xiong

Postdoc

My research interests mainly focus on machine learning on relational data (e.g., knowledge graphs).

Linhao Luo

PhD Student @ Monash (02/2022-)

My research interests mainly focus on the areas of artificial intelligence and data mining, especially for the graph neural network and recommendation.

Shirui Pan

Professor and ARC Future Fellow

My research interests include data mining, machine learning, and graph analysis.