{"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/representation-tradeoffs-for-hyperbolic","title":"Representation Tradeoffs for Hyperbolic Embeddings","arxiv_id":"1804.03329","date":"2018-04-10","proceeding":"ICML 2018 7","authors":["Christopher De Sa","Albert Gu","Christopher Ré","Frederic Sala"],"abstract":"Hyperbolic embeddings offer excellent quality with few dimensions when\nembedding hierarchical data structures like synonym or type hierarchies. Given\na tree, we give a combinatorial construction that embeds the tree in hyperbolic\nspace with arbitrarily low distortion without using optimization. On WordNet,\nour combinatorial embedding obtains a mean-average-precision of 0.989 with only\ntwo dimensions, while Nickel et al.'s recent construction obtains 0.87 using\n200 dimensions. We provide upper and lower bounds that allow us to characterize\nthe precision-dimensionality tradeoff inherent in any hyperbolic embedding. To\nembed general metric spaces, we propose a hyperbolic generalization of\nmultidimensional scaling (h-MDS). We show how to perform exact recovery of\nhyperbolic points from distances, provide a perturbation analysis, and give a\nrecovery result that allows us to reduce dimensionality. The h-MDS approach\noffers consistently low distortion even with few dimensions across several\ndatasets. Finally, we extract lessons from the algorithms and theory above to\ndesign a PyTorch-based implementation that can handle incomplete information\nand is scalable.","url_abs":"http://arxiv.org/abs/1804.03329v2","url_pdf":"http://arxiv.org/pdf/1804.03329v2.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":"representation-tradeoffs-for-hyperbolic","repo_url":"https://github.com/HazyResearch/hyperbolics","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"unanswered"}},{"paper_slug":"representation-tradeoffs-for-hyperbolic","repo_url":"https://github.com/mcneela/mixed-curvature-pathways","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"representation-tradeoffs-for-hyperbolic","repo_url":"https://github.com/nalexai/hyperlib","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1804.03329","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1804.03329"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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