{"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-2","title":"Hyperbolic Neural Networks++","arxiv_id":"2006.08210","date":"2020-06-15","proceeding":"ICLR 2021 1","authors":["Ryohei Shimizu","Yusuke Mukuta","Tatsuya Harada"],"abstract":"Hyperbolic spaces, which have the capacity to embed tree structures without distortion owing to their exponential volume growth, have recently been applied to machine learning to better capture the hierarchical nature of data. In this study, we generalize the fundamental components of neural networks in a single hyperbolic geometry model, namely, the Poincar\\'e ball model. This novel methodology constructs a multinomial logistic regression, fully-connected layers, convolutional layers, and attention mechanisms under a unified mathematical interpretation, without increasing the parameters. Experiments show the superior parameter efficiency of our methods compared to conventional hyperbolic components, and stability and outperformance over their Euclidean counterparts.","url_abs":"https://arxiv.org/abs/2006.08210v3","url_pdf":"https://arxiv.org/pdf/2006.08210v3.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-2","repo_url":"https://github.com/mil-tokyo/hyperbolic_nn_plusplus","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2006.08210","atlas_url":"https://app.syntology.ai/?focus=2006.08210","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}