{"id":"https://openalex.org/W4384663134","doi":"https://doi.org/10.1109/tnnls.2023.3290592","title":"Asymptotic Behavior of Adversarial Training in Binary Linear Classification","display_name":"Asymptotic Behavior of Adversarial Training in Binary Linear Classification","publication_year":2023,"publication_date":"2023-07-18","ids":{"openalex":"https://openalex.org/W4384663134","doi":"https://doi.org/10.1109/tnnls.2023.3290592","pmid":"https://pubmed.ncbi.nlm.nih.gov/37463074"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2023.3290592","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2023.3290592","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102777812","display_name":"Hossein Taheri","orcid":"https://orcid.org/0000-0001-9597-995X"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Hossein Taheri","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California at Santa Barbara, Santa Barbara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California at Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040270189","display_name":"Ramtin Pedarsani","orcid":"https://orcid.org/0000-0002-1126-0292"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ramtin Pedarsani","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California at Santa Barbara, Santa Barbara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California at Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024812488","display_name":"Christos Thrampoulidis","orcid":"https://orcid.org/0000-0001-9053-9365"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]},{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["CA","US"],"is_corresponding":false,"raw_author_name":"Christos Thrampoulidis","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California at Santa Barbara, Santa Barbara, CA, USA","Department of Electrical and Computer Engineering, The University of British Columbia, Vancouver, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California at Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, The University of British Columbia, Vancouver, Canada","institution_ids":["https://openalex.org/I141945490"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102777812"],"corresponding_institution_ids":["https://openalex.org/I154570441"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07798147,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"36","issue":"2","first_page":"2004","last_page":"2012"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9595000147819519,"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/adversarial-system","display_name":"Adversarial system","score":0.831157922744751},{"id":"https://openalex.org/keywords/training","display_name":"Training (meteorology)","score":0.6071491837501526},{"id":"https://openalex.org/keywords/binary-classification","display_name":"Binary classification","score":0.5569004416465759},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5541780591011047},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.48709845542907715},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.4293931722640991},{"id":"https://openalex.org/keywords/training-set","display_name":"Training set","score":0.42558449506759644},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4250921607017517},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3567269444465637},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3344811797142029},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.10298493504524231},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.08069390058517456},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.07699543237686157}],"concepts":[{"id":"https://openalex.org/C37736160","wikidata":"https://www.wikidata.org/wiki/Q1801315","display_name":"Adversarial system","level":2,"score":0.831157922744751},{"id":"https://openalex.org/C2777211547","wikidata":"https://www.wikidata.org/wiki/Q17141490","display_name":"Training (meteorology)","level":2,"score":0.6071491837501526},{"id":"https://openalex.org/C66905080","wikidata":"https://www.wikidata.org/wiki/Q17005494","display_name":"Binary classification","level":3,"score":0.5569004416465759},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5541780591011047},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.48709845542907715},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4293931722640991},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.42558449506759644},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4250921607017517},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3567269444465637},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3344811797142029},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.10298493504524231},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.08069390058517456},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.07699543237686157},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2023.3290592","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2023.3290592","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:37463074","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37463074","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.6899999976158142}],"awards":[{"id":"https://openalex.org/G5580501993","display_name":null,"funder_award_id":"1909320","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6623819417","display_name":null,"funder_award_id":"193464","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6639552142","display_name":null,"funder_award_id":"2009030","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8805048880","display_name":null,"funder_award_id":"2003035","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/F4320322320","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W1673923490","https://openalex.org/W2132235473","https://openalex.org/W2243397390","https://openalex.org/W2893554781","https://openalex.org/W2922153390","https://openalex.org/W2922934758","https://openalex.org/W2923764619","https://openalex.org/W2939822721","https://openalex.org/W2963017107","https://openalex.org/W2963060833","https://openalex.org/W2963518130","https://openalex.org/W2989169642","https://openalex.org/W2994588524","https://openalex.org/W3007237875","https://openalex.org/W3015944005","https://openalex.org/W3028525609","https://openalex.org/W3035656068","https://openalex.org/W3093568497","https://openalex.org/W3109662046","https://openalex.org/W3172995164","https://openalex.org/W4287064111","https://openalex.org/W4287684791","https://openalex.org/W4287704717","https://openalex.org/W4287745534","https://openalex.org/W4288349155","https://openalex.org/W4289713235","https://openalex.org/W4293846201","https://openalex.org/W4295132142","https://openalex.org/W6623408330","https://openalex.org/W6637162671","https://openalex.org/W6637422517","https://openalex.org/W6640425456","https://openalex.org/W6681302627","https://openalex.org/W6750707585","https://openalex.org/W6752495264","https://openalex.org/W6755038706","https://openalex.org/W6755310938","https://openalex.org/W6759129252","https://openalex.org/W6762450911","https://openalex.org/W6762707182","https://openalex.org/W6763427118","https://openalex.org/W6764192614","https://openalex.org/W6767348665","https://openalex.org/W6767692553","https://openalex.org/W6770109230","https://openalex.org/W6773877805","https://openalex.org/W6773981018","https://openalex.org/W6774076947","https://openalex.org/W6774529069","https://openalex.org/W6779553403","https://openalex.org/W6780095956","https://openalex.org/W6782017013","https://openalex.org/W6786769638","https://openalex.org/W6790678048","https://openalex.org/W6798833869"],"related_works":["https://openalex.org/W2502115930","https://openalex.org/W4394050964","https://openalex.org/W3211393740","https://openalex.org/W3208049411","https://openalex.org/W3022908591","https://openalex.org/W4285706568","https://openalex.org/W2551249631","https://openalex.org/W2964083560","https://openalex.org/W2123958887","https://openalex.org/W3117807895"],"abstract_inverted_index":{"Adversarial":[0],"training":[1,41,65,86],"using":[2],"empirical":[3],"risk":[4],"minimization":[5],"(ERM)":[6],"is":[7],"the":[8,36,52,61,73,77,82,85,132,139,142,146,153,164],"state-of-the-art":[9],"method":[10],"for":[11,97],"defense":[12],"against":[13,18],"adversarial":[14,21,40,64,101,133,168],"attacks,":[15],"that":[16],"is,":[17],"small":[19],"additive":[20],"perturbations":[22,108],"applied":[23],"to":[24,28,129,162],"test":[25,102],"data":[26,143],"leading":[27],"misclassification.":[29],"Despite":[30],"being":[31],"successful":[32],"in":[33,42,55,66,111],"practice,":[34],"understanding":[35],"generalization":[37],"properties":[38],"of":[39,63,84,167],"classification":[43],"remains":[44],"widely":[45],"open.":[46],"In":[47],"this":[48,56],"article,":[49],"we":[50,71],"take":[51],"first":[53],"step":[54],"direction":[57],"by":[58,150],"precisely":[59],"characterizing":[60],"robustness":[62],"binary":[67,114],"linear":[68],"classification.":[69],"Specifically,":[70],"consider":[72],"high-dimensional":[74],"regime":[75],"where":[76],"model":[78],"dimension":[79],"grows":[80],"with":[81,120,152],"size":[83],"set":[87],"at":[88],"a":[89],"constant":[90],"ratio.":[91],"Our":[92],"results":[93],"provide":[94],"exact":[95],"asymptotics":[96,159],"both":[98,112],"standard":[99,135],"and":[100,116,134,145],"errors":[103,136],"under":[104],"general":[105],"-norm":[106],"bounded":[107],"(":[109],")":[110],"discriminative":[113],"models":[115,119],"generative":[117],"Gaussian-mixture":[118],"correlated":[121],"features.":[122],"We":[123],"use":[124],"our":[125,157],"sharp":[126,158],"error":[127],"formulae":[128],"explain":[130],"how":[131],"depend":[137],"upon":[138],"over-parameterization":[140],"ratio,":[141],"model,":[144],"attack":[147],"budget.":[148],"Finally,":[149],"comparing":[151],"robust":[154],"Bayes":[155],"estimator,":[156],"allow":[160],"us":[161],"study":[163],"fundamental":[165],"limits":[166],"training.":[169]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
