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For this purpose, we study\ndifferent models of hyperbolic space and find that learning embeddings in the\nLorentz model is substantially more efficient than in the Poincar\\'e-ball\nmodel. We show that the proposed approach allows us to learn high-quality\nembeddings of large taxonomies which yield improvements over Poincar\\'e\nembeddings, especially in low dimensions. Lastly, we apply our model to\ndiscover hierarchies in two real-world datasets: we show that an embedding in\nhyperbolic space can reveal important aspects of a company's organizational\nstructure as well as reveal historical relationships between language families.","url_abs":"http://arxiv.org/abs/1806.03417v2","url_pdf":"http://arxiv.org/pdf/1806.03417v2.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":"learning-continuous-hierarchies-in-the","repo_url":"https://github.com/facebookresearch/poincare-embeddings","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null},{"paper_slug":"learning-continuous-hierarchies-in-the","repo_url":"https://github.com/mtbarta/hyperbolic","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}},{"paper_slug":"learning-continuous-hierarchies-in-the","repo_url":"https://github.com/thesage21/lorentz-embeddings","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1806.03417","atlas_url":"https://app.syntology.ai/?focus=1806.03417","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1806.03417"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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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