{"id":"https://openalex.org/W4391013550","doi":"https://doi.org/10.48550/arxiv.2401.09191","title":"An Optimal Transport Approach for Computing Adversarial Training Lower Bounds in Multiclass Classification","display_name":"An Optimal Transport Approach for Computing Adversarial Training Lower Bounds in Multiclass Classification","publication_year":2024,"publication_date":"2024-01-17","ids":{"openalex":"https://openalex.org/W4391013550","doi":"https://doi.org/10.48550/arxiv.2401.09191"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2401.09191","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2401.09191","pdf_url":"https://arxiv.org/pdf/2401.09191","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/2401.09191","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058626346","display_name":"Nicol\u00e1s Garc\u00eda Trillos","orcid":"https://orcid.org/0000-0002-7711-5901"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Trillos, Nicolas Garcia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045055371","display_name":"Matt Jacobs","orcid":"https://orcid.org/0000-0001-9306-6495"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jacobs, Matt","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021482008","display_name":"Jakwang Kim","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kim, Jakwang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5061903774","display_name":"Matthew Werenski","orcid":"https://orcid.org/0000-0003-3633-9893"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Werenski, Matthew","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9998999834060669,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9998999834060669,"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":0.972000002861023,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.9164000153541565,"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/mnist-database","display_name":"MNIST database","score":0.7792527675628662},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.684804379940033},{"id":"https://openalex.org/keywords/adversarial-system","display_name":"Adversarial system","score":0.6753854155540466},{"id":"https://openalex.org/keywords/leverage","display_name":"Leverage (statistics)","score":0.6753776669502258},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5614352822303772},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5512166023254395},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.527823269367218},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.5045038461685181},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5010683536529541},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.46822115778923035},{"id":"https://openalex.org/keywords/multiclass-classification","display_name":"Multiclass classification","score":0.43930381536483765},{"id":"https://openalex.org/keywords/deep-neural-networks","display_name":"Deep neural networks","score":0.4245126247406006},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.40460050106048584},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2064201533794403},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.09015139937400818}],"concepts":[{"id":"https://openalex.org/C190502265","wikidata":"https://www.wikidata.org/wiki/Q17069496","display_name":"MNIST database","level":3,"score":0.7792527675628662},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.684804379940033},{"id":"https://openalex.org/C37736160","wikidata":"https://www.wikidata.org/wiki/Q1801315","display_name":"Adversarial system","level":2,"score":0.6753854155540466},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.6753776669502258},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5614352822303772},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5512166023254395},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.527823269367218},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.5045038461685181},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5010683536529541},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.46822115778923035},{"id":"https://openalex.org/C123860398","wikidata":"https://www.wikidata.org/wiki/Q6934605","display_name":"Multiclass classification","level":3,"score":0.43930381536483765},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.4245126247406006},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.40460050106048584},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2064201533794403},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.09015139937400818},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2401.09191","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2401.09191","pdf_url":"https://arxiv.org/pdf/2401.09191","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":"doi:10.48550/arxiv.2401.09191","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2401.09191","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:2401.09191","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2401.09191","pdf_url":"https://arxiv.org/pdf/2401.09191","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":[{"id":"https://openalex.org/G1243439379","display_name":null,"funder_award_id":"1641020","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2196136972","display_name":"CAREER: Adversarial Robustness through the Lens of Mathematical Analysis and Geometry","funder_award_id":"2236447","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2845557239","display_name":"Pacific Interdisciplinary Hub on Optimal Transport","funder_award_id":"2133244","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5899227995","display_name":"Interfacial problems in data science and PDEs","funder_award_id":"2308217","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7727778866","display_name":null,"funder_award_id":"DMS 1641020","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334626","display_name":"Medical Research Council","ror":"https://ror.org/03x94j517"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4391013550.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2950183588","https://openalex.org/W3080754722","https://openalex.org/W4383221314","https://openalex.org/W2618574054","https://openalex.org/W3093978547","https://openalex.org/W2953536436","https://openalex.org/W3203790781","https://openalex.org/W4313346231","https://openalex.org/W2738001131","https://openalex.org/W4285785480"],"abstract_inverted_index":{"Despite":[0],"the":[1,46,70,85,116,123,144],"success":[2],"of":[3,59,146],"deep":[4],"learning-based":[5],"algorithms,":[6],"it":[7],"is":[8,25,110],"widely":[9],"known":[10],"that":[11,111],"neural":[12],"networks":[13],"may":[14],"fail":[15],"to":[16,22,61,73],"be":[17],"robust.":[18],"A":[19],"popular":[20],"paradigm":[21],"enforce":[23],"robustness":[24],"adversarial":[26,87],"training":[27],"(AT),":[28],"however,":[29],"this":[30,63,66],"introduces":[31],"many":[32],"computational":[33],"and":[34,50,89,103,140],"theoretical":[35],"difficulties.":[36],"Recent":[37],"works":[38],"have":[39],"developed":[40],"a":[41,56],"connection":[42,72],"between":[43,120],"AT":[44],"in":[45,129],"multiclass":[47],"classification":[48],"setting":[49],"multimarginal":[51],"optimal":[52,86,91],"transport":[53],"(MOT),":[54],"unlocking":[55],"new":[57],"set":[58],"tools":[60],"study":[62],"problem.":[64],"In":[65],"paper,":[67],"we":[68],"leverage":[69],"MOT":[71,130],"propose":[74,94],"computationally":[75],"tractable":[76],"numerical":[77],"algorithms":[78,97],"for":[79],"computing":[80],"universal":[81],"lower":[82],"bounds":[83],"on":[84,99,138],"risk":[88],"identifying":[90],"classifiers.":[92],"We":[93,132],"two":[95],"main":[96],"based":[98],"linear":[100],"programming":[101],"(LP)":[102],"entropic":[104],"regularization":[105],"(Sinkhorn).":[106],"Our":[107],"key":[108],"insight":[109],"one":[112],"can":[113],"harmlessly":[114],"truncate":[115],"higher":[117],"order":[118],"interactions":[119],"classes,":[121],"preventing":[122],"combinatorial":[124],"run":[125],"times":[126],"typically":[127],"encountered":[128],"problems.":[131],"validate":[133],"these":[134],"results":[135],"with":[136],"experiments":[137],"MNIST":[139],"CIFAR-$10$,":[141],"which":[142],"demonstrate":[143],"tractability":[145],"our":[147],"approach.":[148]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2024-01-19T00:00:00"}
