{"id":"https://openalex.org/W4392678142","doi":"https://doi.org/10.48550/arxiv.2403.05033","title":"Quantifying Manifolds: Do the manifolds learned by Generative Adversarial Networks converge to the real data manifold","display_name":"Quantifying Manifolds: Do the manifolds learned by Generative Adversarial Networks converge to the real data manifold","publication_year":2024,"publication_date":"2024-03-08","ids":{"openalex":"https://openalex.org/W4392678142","doi":"https://doi.org/10.48550/arxiv.2403.05033"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2403.05033","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2403.05033","pdf_url":"https://arxiv.org/pdf/2403.05033","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2403.05033","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5104103753","display_name":"Anupam Chaudhuri","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chaudhuri, Anupam","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024537636","display_name":"Anj Simmons","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Simmons, Anj","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5068173669","display_name":"Mohamed Abdelrazek","orcid":"https://orcid.org/0000-0003-3812-9785"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Abdelrazek, Mohamed","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5104103753"],"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/T10320","display_name":"Neural Networks and Applications","score":0.9465000033378601,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10320","display_name":"Neural Networks and Applications","score":0.9465000033378601,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11512","display_name":"Anomaly Detection Techniques and Applications","score":0.9391999840736389,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/manifold","display_name":"Manifold (fluid mechanics)","score":0.7914597392082214},{"id":"https://openalex.org/keywords/generative-grammar","display_name":"Generative grammar","score":0.7366684079170227},{"id":"https://openalex.org/keywords/adversarial-system","display_name":"Adversarial system","score":0.7151983380317688},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42748820781707764},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4168745279312134},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39734748005867004},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3647066354751587},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.329146146774292},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18708467483520508},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.13536950945854187}],"concepts":[{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.7914597392082214},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.7366684079170227},{"id":"https://openalex.org/C37736160","wikidata":"https://www.wikidata.org/wiki/Q1801315","display_name":"Adversarial system","level":2,"score":0.7151983380317688},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42748820781707764},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4168745279312134},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39734748005867004},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3647066354751587},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.329146146774292},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18708467483520508},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.13536950945854187},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2403.05033","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2403.05033","pdf_url":"https://arxiv.org/pdf/2403.05033","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:figshare.com:article/28216778","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Conference contribution"},{"id":"doi:10.48550/arxiv.2403.05033","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2403.05033","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2403.05033","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2403.05033","pdf_url":"https://arxiv.org/pdf/2403.05033","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4392678142.pdf","grobid_xml":"https://content.openalex.org/works/W4392678142.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2502115930","https://openalex.org/W2482350142","https://openalex.org/W4246396837","https://openalex.org/W3176240006","https://openalex.org/W3126451824","https://openalex.org/W1561927205","https://openalex.org/W3191453585","https://openalex.org/W4297672492","https://openalex.org/W4288019534","https://openalex.org/W4310988119"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"our":[3,14],"experiments":[4],"to":[5,32,67,81],"quantify":[6,41],"the":[7,26,33,37,46,53,57,69,77,82,85],"manifolds":[8,27,35],"learned":[9,28,55],"by":[10,56],"ML":[11,58],"models":[12],"(in":[13],"experiment,":[15],"we":[16,44,65],"use":[17],"a":[18,42],"GAN":[19],"model)":[20],"as":[21,64],"they":[22],"train.":[23],"We":[24],"compare":[25],"at":[29],"each":[30],"epoch":[31],"real":[34,38,86],"representing":[36],"data.":[39],"To":[40],"manifold,":[43],"study":[45],"intrinsic":[47],"dimensions":[48],"and":[49,71],"topological":[50],"features":[51],"of":[52,79,84],"manifold":[54],"model,":[59,70],"how":[60],"these":[61,73],"metrics":[62,74,83],"change":[63],"continue":[66],"train":[68],"whether":[72],"convergence":[75],"over":[76],"course":[78],"training":[80],"data":[87],"manifold.":[88]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
