{"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/aligning-hyperbolic-representations-an","title":"Aligning Hyperbolic Representations: an Optimal Transport-based approach","arxiv_id":"2012.01089","date":"2020-12-02","proceeding":null,"authors":["Andrés Hoyos-Idrobo"],"abstract":"Hyperbolic-spaces are better suited to represent data with underlying hierarchical relationships, e.g., tree-like data. However, it is often necessary to incorporate, through alignment, different but related representations meaningfully. This aligning is an important class of machine learning problems, with applications as ontology matching and cross-lingual alignment. Optimal transport (OT)-based approaches are a natural choice to tackle the alignment problem as they aim to find a transformation of the source dataset to match a target dataset, subject to some distribution constraints. This work proposes a novel approach based on OT of embeddings on the Poincar\\'e model of hyperbolic spaces. Our method relies on the gyrobarycenter mapping on M\\\"obius gyrovector spaces. As a result of this formalism, we derive extensions to some existing Euclidean methods of OT-based domain adaptation to their hyperbolic counterparts. Empirically, we show that both Euclidean and hyperbolic methods have similar performances in the context of retrieval.","url_abs":"https://arxiv.org/abs/2012.01089v1","url_pdf":"https://arxiv.org/pdf/2012.01089v1.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":"aligning-hyperbolic-representations-an","repo_url":"https://github.com/ahoyosid/hyperbolic_alignment","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"domain-adaptation","task_name":"Domain Adaptation"},{"task_slug":"ontology-matching","task_name":"Ontology Matching"},{"task_slug":"retrieval","task_name":"Retrieval"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2012.01089","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2012.01089"}},"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. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/ahoyosid/hyperbolic_alignment","reach":null}],"summary":{"ran_honours":2},"by_repo_kind":{"official":{"samples":2,"ran":2,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":2,"samples":[{"code_sha256_prefix":"47029fec9dccdf55","entry":"to_float","repo":"ahoyosid/hyperbolic_alignment","repo_kind":"official","path":"hyperbolic_domain_adaptation.py","file_url":"https://github.com/ahoyosid/hyperbolic_alignment/blob/HEAD/hyperbolic_domain_adaptation.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"47029fec9dccdf55"}},{"code_sha256_prefix":"f6cfcf9ee77607a2","entry":"to_np","repo":"ahoyosid/hyperbolic_alignment","repo_kind":"official","path":"hyperbolic_domain_adaptation.py","file_url":"https://github.com/ahoyosid/hyperbolic_alignment/blob/HEAD/hyperbolic_domain_adaptation.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"f6cfcf9ee77607a2"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}