{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/neste-modeling-nested-relational-structures","title":"NestE: Modeling Nested Relational Structures for Knowledge Graph Reasoning","arxiv_id":"2312.09219","date":"2023-12-14","proceeding":null,"authors":["Bo Xiong","Mojtaba Nayyeri","Linhao Luo","ZiHao Wang","Shirui Pan","Steffen Staab"],"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 \\emph{atomic facts}, which describe a single piece of information. This paper extends beyond \\emph{atomic facts} and delves into \\emph{nested facts}, represented by quoted triples where subjects and objects are triples themselves (e.g., ((\\emph{BarackObama}, \\emph{holds\\_position}, \\emph{President}), \\emph{succeed\\_by}, (\\emph{DonaldTrump}, \\emph{holds\\_position}, \\emph{President}))). These nested facts enable the expression of complex semantics like \\emph{situations} over time and \\emph{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 $1\\times3$ matrix, and each nested relation is modeled as a $3\\times3$ matrix that rotates the $1\\times3$ 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.","url_abs":"https://arxiv.org/abs/2312.09219v1","url_pdf":"https://arxiv.org/pdf/2312.09219v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"neste-modeling-nested-relational-structures","repo_url":"https://github.com/xiongbo010/neste","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"knowledge-graphs","task_name":"Knowledge Graphs"},{"task_slug":"link-prediction","task_name":"Link Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}