{"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/hyperbolic-entailment-cones-for-learning","title":"Hyperbolic Entailment Cones for Learning Hierarchical Embeddings","arxiv_id":"1804.01882","date":"2018-04-03","proceeding":"ICML 2018 7","authors":["Octavian-Eugen Ganea","Gary Bécigneul","Thomas Hofmann"],"abstract":"Learning graph representations via low-dimensional embeddings that preserve\nrelevant network properties is an important class of problems in machine\nlearning. We here present a novel method to embed directed acyclic graphs.\nFollowing prior work, we first advocate for using hyperbolic spaces which\nprovably model tree-like structures better than Euclidean geometry. Second, we\nview hierarchical relations as partial orders defined using a family of nested\ngeodesically convex cones. We prove that these entailment cones admit an\noptimal shape with a closed form expression both in the Euclidean and\nhyperbolic spaces, and they canonically define the embedding learning process.\nExperiments show significant improvements of our method over strong recent\nbaselines both in terms of representational capacity and generalization.","url_abs":"http://arxiv.org/abs/1804.01882v3","url_pdf":"http://arxiv.org/pdf/1804.01882v3.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":"hyperbolic-entailment-cones-for-learning","repo_url":"https://github.com/dalab/hyperbolic_cones","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"hyperbolic-entailment-cones-for-learning","repo_url":"https://github.com/dinobby/hypemo","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"hyperbolic-entailment-cones-for-learning","repo_url":"https://github.com/iesl/geometric_graph_embedding","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[{"task_slug":"graph-embedding","task_name":"Graph Embedding"},{"task_slug":"hypernym-discovery","task_name":"Hypernym Discovery"},{"task_slug":"link-prediction","task_name":"Link Prediction"},{"task_slug":"representation-learning","task_name":"Representation Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/link-prediction-on-wordnet","task":"Link Prediction","dataset":"WordNet","model":"Hyperbolic Entailment Cones","rank_in_archive_order":1,"of":7,"metrics":{"Accuracy":"94.4"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1804.01882","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}