RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions

[2501.17518] RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2501.17518 (cs) [Submitted on 29 Jan 2025 ( v1 ), last revised 13 Apr 2026 (this version, v3)] Title: RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions Authors: Hui Yang , Jiaoyan Chen View a PDF of the paper titled RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions, by Hui Yang and 1 other authors View PDF HTML (experimental) Abstract: Hierarchical data is common in many domains like life sciences and e-commerce, and its embeddings often play a critical role. While hyperbolic embeddings offer a theoretically grounded approach to representing hierarchies in low-dimensional spaces, current methods often rely on specific geometric constructs as embedding candidates. This reliance limits their generalizability and makes it difficult to integrate with techniques that model semantic relationships beyond pure hierarchies, such as ontology embeddings. In this paper, we present RegD, a flexible Euclidean framework that supports the use of arbitrary geometric regions -- such as boxes and balls -- as embedding representations. Although RegD operates entirely in Euclidean space, we formally prove that it achieves hyperbolic-like expressiveness by incorporating a depth-based dissimilarity between regions, enabling it to emulate key properties of hyperbolic geometry, including exponential growth. Our empirical evaluation on diverse real-world datasets shows consistent performance gains over state-of-the-art methods and demonstrates RegD's potential for broader applications such as the ontology embedding task that goes beyond hierarchy. Subjects: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI) Cite as: arXiv:2501.17518 [cs.LG] (or arXiv:2501.17518v3 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2501.17518 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Hui Yang [ view email ] [v1] Wed, 29 Jan 2025 09:44:03 UTC (59 KB) [v2] Wed, 8 Oct 2025 08:26:07 UTC (93 KB) [v3] Mon, 13 Apr 2026 19:35:10 UTC (109 KB) Full-text links: Access Paper: View a PDF of the paper titled RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions, by Hui Yang and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2025-01 Change to browse by: cs cs.AI References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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