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.