NestE: Modeling Nested Relational Structures for Knowledge Graph Reasoning

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 atomic facts, which describe a single piece of information. This paper extends beyond atomic facts and delves into nested facts, represented by quoted triples where subjects and objects are triples themselves (e.g., ((BarackObama, holds_position, President), succeed_by, (DonaldTrump, holds_position, President))). These nested facts enable the expression of complex semantics like situations over time and 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. The code and pre-trained models are open available at https://github.com/xiongbo010/NestE.