{"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/cartan-networks-group-theoretical-hyperbolic","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","arxiv_id":"2505.24353","date":"2025-05-30","proceeding":null,"authors":["Federico Milanesio","Matteo Santoro","Pietro G. Fré","Guido Sanguinetti"],"abstract":"Hyperbolic deep learning leverages the metric properties of hyperbolic spaces to develop efficient and informative embeddings of hierarchical data. Here, we focus on the solvable group structure of hyperbolic spaces, which follows naturally from their construction as symmetric spaces. This dual nature of Lie group and Riemannian manifold allows us to propose a new class of hyperbolic deep learning algorithms where group homomorphisms are interleaved with metric-preserving diffeomorphisms. The resulting algorithms, which we call Cartan networks, show promising results on various benchmark data sets and open the way to a novel class of hyperbolic deep learning architectures.","url_abs":"https://arxiv.org/abs/2505.24353v1","url_pdf":"https://arxiv.org/pdf/2505.24353v1.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":"cartan-networks-group-theoretical-hyperbolic","repo_url":"https://github.com/cartannetworks/cartan_networks","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null},{"paper_slug":"cartan-networks-group-theoretical-hyperbolic","repo_url":"https://github.com/federicomilanesio/cartannetworks","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"deep-learning","task_name":"Deep Learning"}],"methods":[{"method_slug":"focus","method_name":"Focus"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}