{"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-neural-networks","title":"Hyperbolic Neural Networks","arxiv_id":"1805.09112","date":"2018-05-23","proceeding":"NeurIPS 2018 12","authors":["Octavian-Eugen Ganea","Gary Bécigneul","Thomas Hofmann"],"abstract":"Hyperbolic spaces have recently gained momentum in the context of machine\nlearning due to their high capacity and tree-likeliness properties. However,\nthe representational power of hyperbolic geometry is not yet on par with\nEuclidean geometry, mostly because of the absence of corresponding hyperbolic\nneural network layers. This makes it hard to use hyperbolic embeddings in\ndownstream tasks. Here, we bridge this gap in a principled manner by combining\nthe formalism of M\\\"obius gyrovector spaces with the Riemannian geometry of the\nPoincar\\'e model of hyperbolic spaces. As a result, we derive hyperbolic\nversions of important deep learning tools: multinomial logistic regression,\nfeed-forward and recurrent neural networks such as gated recurrent units. This\nallows to embed sequential data and perform classification in the hyperbolic\nspace. Empirically, we show that, even if hyperbolic optimization tools are\nlimited, hyperbolic sentence embeddings either outperform or are on par with\ntheir Euclidean variants on textual entailment and noisy-prefix recognition\ntasks.","url_abs":"http://arxiv.org/abs/1805.09112v2","url_pdf":"http://arxiv.org/pdf/1805.09112v2.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-neural-networks","repo_url":"https://github.com/dalab/hyperbolic_nn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"hyperbolic-neural-networks","repo_url":"https://github.com/HazyResearch/hgcn","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"hyperbolic-neural-networks","repo_url":"https://github.com/mtbarta/hyperbolic","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}}],"tasks":[{"task_slug":"graph-representation-learning","task_name":"Graph Representation Learning"},{"task_slug":"natural-language-inference","task_name":"Natural Language Inference"},{"task_slug":"sentence","task_name":"Sentence"},{"task_slug":"sentence-embeddings","task_name":"Sentence Embeddings"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1805.09112","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1805.09112"}},"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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