{"id":"https://openalex.org/W4403706136","doi":"https://doi.org/10.48550/arxiv.2409.10967","title":"Relative Representations: Topological and Geometric Perspectives","display_name":"Relative Representations: Topological and Geometric Perspectives","publication_year":2024,"publication_date":"2024-09-17","ids":{"openalex":"https://openalex.org/W4403706136","doi":"https://doi.org/10.48550/arxiv.2409.10967"},"language":"en","primary_location":{"id":"pmh:oai:dare.uva.nl:openaire/4451562d-f43b-44c1-90d9-860bf089c65b","is_oa":true,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/relative-representations(4451562d-f43b-44c1-90d9-860bf089c65b).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Garc\u00eda-Castellanos, A, Marchetti, G L, Kragic, D & Scolamiero, M 2024, 'Relative Representations : Topological and Geometric Perspectives', Proceedings of Machine Learning Research, vol. 285, pp. 219-231. https://doi.org/10.48550/arXiv.2409.10967","raw_type":"info:eu-repo/semantics/publishedVersion"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://handle.uba.uva.nl/personal/pure/en/publications/relative-representations(4451562d-f43b-44c1-90d9-860bf089c65b).html","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114352574","display_name":"Alejandro Garc\u00eda-Castellanos","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Garc\u00eda-Castellanos, Alejandro","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090524248","display_name":"Giovanni Luca Marchetti","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marchetti, Giovanni Luca","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023792180","display_name":"Danica Kragi\u0107","orcid":"https://orcid.org/0000-0003-2965-2953"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kragic, Danica","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5049927421","display_name":"Martina Scolamiero","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Scolamiero, Martina","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5114352574"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.34119999408721924,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.34119999408721924,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4771551489830017},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42241108417510986},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4071204662322998},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3326869606971741},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1534038484096527}],"concepts":[{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4771551489830017},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42241108417510986},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4071204662322998},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3326869606971741},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1534038484096527}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:dare.uva.nl:openaire/4451562d-f43b-44c1-90d9-860bf089c65b","is_oa":true,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/relative-representations(4451562d-f43b-44c1-90d9-860bf089c65b).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Garc\u00eda-Castellanos, A, Marchetti, G L, Kragic, D & Scolamiero, M 2024, 'Relative Representations : Topological and Geometric Perspectives', Proceedings of Machine Learning Research, vol. 285, pp. 219-231. https://doi.org/10.48550/arXiv.2409.10967","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:2409.10967","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2409.10967","pdf_url":"https://arxiv.org/pdf/2409.10967","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2409.10967","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2409.10967","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:dare.uva.nl:openaire/4451562d-f43b-44c1-90d9-860bf089c65b","is_oa":true,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/relative-representations(4451562d-f43b-44c1-90d9-860bf089c65b).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Garc\u00eda-Castellanos, A, Marchetti, G L, Kragic, D & Scolamiero, M 2024, 'Relative Representations : Topological and Geometric Perspectives', Proceedings of Machine Learning Research, vol. 285, pp. 219-231. https://doi.org/10.48550/arXiv.2409.10967","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"},{"id":"https://openalex.org/F4320322327","display_name":"Knut och Alice Wallenbergs Stiftelse","ror":"https://ror.org/004hzzk67"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"Relative":[0],"representations":[1],"are":[2],"an":[3,92],"established":[4],"approach":[5],"to":[6,36,52,74],"zero-shot":[7,109],"model":[8,110],"stitching,":[9],"consisting":[10],"of":[11,15,19,27],"a":[12,20,42,82,96],"non-trainable":[13],"transformation":[14],"the":[16,46,61,102],"latent":[17],"space":[18,65],"deep":[21],"neural":[22],"network.":[23],"Based":[24],"on":[25,95,108],"insights":[26],"topological":[28,76,83],"and":[29,55],"geometric":[30],"nature,":[31],"we":[32,40,72],"propose":[33,73],"two":[34],"improvements":[35],"relative":[37,47,80],"representations.":[38],"First,":[39],"introduce":[41],"normalization":[43],"procedure":[44],"in":[45,50,63],"transformation,":[48],"resulting":[49],"invariance":[51],"non-isotropic":[53],"rescalings":[54],"permutations.":[56],"The":[57],"latter":[58],"coincides":[59],"with":[60],"symmetries":[62],"parameter":[64],"induced":[66],"by":[67],"common":[68],"activation":[69],"functions.":[70],"Second,":[71],"deploy":[75],"densification":[77],"when":[78],"fine-tuning":[79],"representations,":[81],"regularization":[84],"loss":[85],"encouraging":[86],"clustering":[87],"within":[88],"classes.":[89],"We":[90],"provide":[91],"empirical":[93],"investigation":[94],"natural":[97],"language":[98],"task,":[99],"where":[100],"both":[101],"proposed":[103],"variations":[104],"yield":[105],"improved":[106],"performance":[107],"stitching.":[111]},"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
