{"id":"https://openalex.org/W3010476364","doi":null,"title":"When can Wasserstein GANs minimize Wasserstein Distance","display_name":"When can Wasserstein GANs minimize Wasserstein Distance","publication_year":2020,"publication_date":"2020-03-09","ids":{"openalex":"https://openalex.org/W3010476364","mag":"3010476364"},"language":"en","primary_location":{"id":"mag:3010476364","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2003.04033","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2003.04033","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101879892","display_name":"Yuanzhi Li","orcid":"https://orcid.org/0000-0002-4604-0468","observed_orcids":["https://orcid.org/0000-0002-4604-0468","https://orcid.org/0009-0004-4418-9308"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuanzhi Li","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0004-4418-9308","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5020541874","display_name":"Zehao Dou","orcid":"https://orcid.org/0000-0002-0426-2740","observed_orcids":["https://orcid.org/0000-0002-0426-2740"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zehao Dou","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-0426-2740","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":6,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.8705999851226807,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.8705999851226807,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.07980000227689743,"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/T10320","display_name":"Neural Networks and Applications","score":0.012799999676644802,"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/wasserstein-gan","display_name":"Wasserstein GAN","score":0.9670000076293945},{"id":"https://openalex.org/keywords/wasserstein-distance","display_name":"Wasserstein distance","score":0.8230000138282776},{"id":"https://openalex.org/keywords/generative-adversarial-networks","display_name":"generative adversarial networks","score":0.8600000143051147},{"id":"https://openalex.org/keywords/two-layer-neural-networks","display_name":"two-layer neural networks","score":0.8659999966621399},{"id":"https://openalex.org/keywords/relu-activation-function","display_name":"ReLU activation","score":0.8460000157356262}],"concepts":[{"id":"https://openalex.org/C2779803651","wikidata":"https://www.wikidata.org/wiki/Q5282088","display_name":"Discriminator","level":3,"score":0.9563655853271484},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.8426165580749512},{"id":"https://openalex.org/C2779545769","wikidata":"https://www.wikidata.org/wiki/Q5135364","display_name":"Closeness","level":2,"score":0.7405847907066345},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7327315807342529},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5613529086112976},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.5353019833564758},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.521794319152832},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5170977115631104},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.47012126445770264},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4357495903968811},{"id":"https://openalex.org/C37736160","wikidata":"https://www.wikidata.org/wiki/Q1801315","display_name":"Adversarial system","level":2,"score":0.4347570538520813},{"id":"https://openalex.org/C2777211547","wikidata":"https://www.wikidata.org/wiki/Q17141490","display_name":"Training (meteorology)","level":2,"score":0.4326246678829193},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3996816873550415},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3629213571548462},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24513742327690125},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.11418405175209045},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06031501293182373},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.059469074010849},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.059365034103393555},{"id":"https://openalex.org/C94915269","wikidata":"https://www.wikidata.org/wiki/Q1834857","display_name":"Detector","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:3010476364","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2003.04033","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:3010476364","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2003.04033","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":77,"referenced_works":["https://openalex.org/W21261423","https://openalex.org/W658559791","https://openalex.org/W1489604929","https://openalex.org/W1697075315","https://openalex.org/W1873349594","https://openalex.org/W1980018091","https://openalex.org/W2105724942","https://openalex.org/W2166116275","https://openalex.org/W2170648111","https://openalex.org/W2173520492","https://openalex.org/W2294384375","https://openalex.org/W2295508206","https://openalex.org/W2399994860","https://openalex.org/W2404068508","https://openalex.org/W2488153767","https://openalex.org/W2518186251","https://openalex.org/W2548275288","https://openalex.org/W2557139899","https://openalex.org/W2585305991","https://openalex.org/W2591714514","https://openalex.org/W2593709294","https://openalex.org/W2593729559","https://openalex.org/W2605135824","https://openalex.org/W2614119628","https://openalex.org/W2624823827","https://openalex.org/W2625063094","https://openalex.org/W2626994141","https://openalex.org/W2739160792","https://openalex.org/W2765701314","https://openalex.org/W2766371994","https://openalex.org/W2766527293","https://openalex.org/W2785678896","https://openalex.org/W2785838823","https://openalex.org/W2788004794","https://openalex.org/W2788671554","https://openalex.org/W2789048837","https://openalex.org/W2800987155","https://openalex.org/W2803583880","https://openalex.org/W2804078698","https://openalex.org/W2809090039","https://openalex.org/W2810203579","https://openalex.org/W2848500096","https://openalex.org/W2863175877","https://openalex.org/W2886067286","https://openalex.org/W2891416231","https://openalex.org/W2894604724","https://openalex.org/W2898324627","https://openalex.org/W2898871740","https://openalex.org/W2899748887","https://openalex.org/W2900959181","https://openalex.org/W2911867426","https://openalex.org/W2913473169","https://openalex.org/W2941057241","https://openalex.org/W2942052807","https://openalex.org/W2946840143","https://openalex.org/W2947996939","https://openalex.org/W2950934461","https://openalex.org/W2951567597","https://openalex.org/W2952817981","https://openalex.org/W2962698540","https://openalex.org/W2962848977","https://openalex.org/W2962939986","https://openalex.org/W2963519230","https://openalex.org/W2963981733","https://openalex.org/W2970241199","https://openalex.org/W2970330753","https://openalex.org/W2970388773","https://openalex.org/W2970443625","https://openalex.org/W2972392510","https://openalex.org/W2980328027","https://openalex.org/W2992906545","https://openalex.org/W3000127803","https://openalex.org/W3022507773","https://openalex.org/W3028525609","https://openalex.org/W3037593317","https://openalex.org/W3042003204","https://openalex.org/W3113303810"],"related_works":["https://openalex.org/W4225786113","https://openalex.org/W2810203579","https://openalex.org/W3134644013","https://openalex.org/W3080419721","https://openalex.org/W3130725574","https://openalex.org/W2938251438","https://openalex.org/W6913035407","https://openalex.org/W3033050199","https://openalex.org/W4388295184","https://openalex.org/W3164017636"],"abstract_inverted_index":{"Generative":[0],"Adversarial":[1],"Networks":[2],"(GANs)":[3],"are":[4],"widely":[5],"used":[6],"models":[7,87],"to":[8,56,132,164],"learn":[9],"complex":[10],"real-world":[11],"distributions.":[12],"In":[13,95],"GANs,":[14],"the":[15,18,23,29,33,46,50,57,79,85,93,102,114,130,150,153,165],"training":[16,36,47,147,151,175],"of":[17,35,41,84,101,119],"generator":[19,80,115,154,180],"usually":[20],"stops":[21],"when":[22,45,71,113,149],"discriminator":[24,131],"can":[25,67,88,176],"no":[26],"longer":[27],"distinguish":[28],"generator's":[30],"output":[31,157],"from":[32],"set":[34],"examples.":[37],"A":[38],"central":[39],"question":[40],"GANs":[42,174],"is":[43,53,73,116,125,161],"that":[44,64,112,160],"stops,":[48,152],"whether":[49],"generated":[51],"distribution":[52,159],"actually":[54],"close":[55,163],"target":[58],"distribution.":[59],"Previously,":[60],"it":[61,124],"was":[62],"found":[63],"such":[65,178],"closeness":[66],"only":[68],"be":[69,89,133],"achieved":[70],"there":[72],"a":[74,117,134,158,179],"strict":[75],"capacity":[76],"trade-off":[77],"between":[78],"and":[81,127],"discriminator:":[82],"Neither":[83],"two":[86],"too":[90],"powerful":[91],"than":[92],"other.":[94],"this":[96,108,142],"paper,":[97],"we":[98],"established":[99],"one":[100],"first":[103],"theoretical":[104],"results":[105],"in":[106],"explaining":[107],"trade-off.":[109],"We":[110],"show":[111],"class":[118],"two-layer":[120],"neural":[121],"networks,":[122],"then":[123],"necessary":[126],"sufficient":[128],"for":[129],"one-layer":[135],"network":[136],"with":[137],"ReLU-type":[138],"activation":[139],"functions.":[140],"With":[141],"trade-off,":[143],"using":[144],"polynomially":[145],"many":[146],"examples,":[148],"will":[155],"indeed":[156],"inverse-polynomially":[162],"target.":[166],"Our":[167],"result":[168],"also":[169],"sheds":[170],"light":[171],"on":[172],"how":[173],"find":[177],"efficiently.":[181]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2020-03-13T00:00:00"}