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, holdsposition, President), succeedby, (DonaldTrump, holdsposition, 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.