{"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/numerically-accurate-hyperbolic-embeddings","title":"Numerically Accurate Hyperbolic Embeddings Using Tiling-Based Models","arxiv_id":null,"date":"2019-12-01","proceeding":"NeurIPS 2019 12","authors":["Tao Yu","Christopher M. De Sa"],"abstract":"Hyperbolic embeddings achieve excellent performance when embedding hierarchical data structures like synonym or type hierarchies, but they can be limited by numerical error when ordinary floating-point numbers are used to represent points in hyperbolic space. Standard models such as the Poincar{\\'e} disk and the Lorentz model have unbounded numerical error as points get far from the origin.\nTo address this, we propose a new model which uses an integer-based tiling to represent \\emph{any} point in hyperbolic space with provably bounded numerical error. This allows us to learn high-precision embeddings without using BigFloats, and enables us to store the resulting embeddings with fewer bits. We evaluate our tiling-based model empirically, and show that it can both compress hyperbolic embeddings (down to $2\\%$ of a Poincar{\\'e} embedding on WordNet Nouns) and learn more accurate embeddings on real-world datasets.","url_abs":"http://papers.nips.cc/paper/8476-numerically-accurate-hyperbolic-embeddings-using-tiling-based-models","url_pdf":"http://papers.nips.cc/paper/8476-numerically-accurate-hyperbolic-embeddings-using-tiling-based-models.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":"numerically-accurate-hyperbolic-embeddings","repo_url":"https://github.com/ydtydr/HyperbolicTiling_Compression","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"numerically-accurate-hyperbolic-embeddings","repo_url":"https://github.com/ydtydr/HyperbolicTiling_Learning","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}