{"id":"https://openalex.org/W4410950114","doi":"https://doi.org/10.1109/tpami.2025.3575618","title":"Analyzing the Implicit Bias of Adversarial Training From a Generalized Margin Perspective","display_name":"Analyzing the Implicit Bias of Adversarial Training From a Generalized Margin Perspective","publication_year":2025,"publication_date":"2025-06-02","ids":{"openalex":"https://openalex.org/W4410950114","doi":"https://doi.org/10.1109/tpami.2025.3575618","pmid":"https://pubmed.ncbi.nlm.nih.gov/40456063"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2025.3575618","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2025.3575618","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Pattern Analysis and Machine Intelligence","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/A5108122268","display_name":"Bin Lyu","orcid":"https://orcid.org/0009-0005-1150-7637"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Bochen Lyu","raw_affiliation_strings":["University of Southampton, Southampton, U.K","University of Southampton, U.K"],"affiliations":[{"raw_affiliation_string":"University of Southampton, Southampton, U.K","institution_ids":["https://openalex.org/I43439940"]},{"raw_affiliation_string":"University of Southampton, U.K","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045305860","display_name":"Zhanxing Zhu","orcid":"https://orcid.org/0000-0002-2141-6553"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Zhanxing Zhu","raw_affiliation_strings":["University of Southampton, Southampton, U.K","University of Southampton, U.K"],"affiliations":[{"raw_affiliation_string":"University of Southampton, Southampton, U.K","institution_ids":["https://openalex.org/I43439940"]},{"raw_affiliation_string":"University of Southampton, U.K","institution_ids":["https://openalex.org/I43439940"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5108122268"],"corresponding_institution_ids":["https://openalex.org/I43439940"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12543138,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"47","issue":"9","first_page":"8025","last_page":"8039"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.8366000056266785,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.8366000056266785,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/adversarial-system","display_name":"Adversarial system","score":0.8684504628181458},{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.7680675983428955},{"id":"https://openalex.org/keywords/margin","display_name":"Margin (machine learning)","score":0.7182996273040771},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.6451659798622131},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6436985731124878},{"id":"https://openalex.org/keywords/training","display_name":"Training (meteorology)","score":0.5256116390228271},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.413252592086792},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.4065920412540436},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3282053470611572}],"concepts":[{"id":"https://openalex.org/C37736160","wikidata":"https://www.wikidata.org/wiki/Q1801315","display_name":"Adversarial system","level":2,"score":0.8684504628181458},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.7680675983428955},{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.7182996273040771},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6451659798622131},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6436985731124878},{"id":"https://openalex.org/C2777211547","wikidata":"https://www.wikidata.org/wiki/Q17141490","display_name":"Training (meteorology)","level":2,"score":0.5256116390228271},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.413252592086792},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4065920412540436},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3282053470611572},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tpami.2025.3575618","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2025.3575618","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:40456063","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40456063","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 pattern analysis and machine intelligence","raw_type":null},{"id":"pmh:oai:eprints.soton.ac.uk:509649","is_oa":false,"landing_page_url":"http://doi.org/10.1109/TPAMI.2025.3575618>).","pdf_url":null,"source":{"id":"https://openalex.org/S4306401020","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W1551360398","https://openalex.org/W1677182931","https://openalex.org/W1932198206","https://openalex.org/W2000985550","https://openalex.org/W2073429525","https://openalex.org/W2117130368","https://openalex.org/W2155858901","https://openalex.org/W2156985405","https://openalex.org/W2964210434","https://openalex.org/W3028525609","https://openalex.org/W3035656068","https://openalex.org/W4230471307","https://openalex.org/W4251616545","https://openalex.org/W4293846201","https://openalex.org/W6637162671","https://openalex.org/W6637373629","https://openalex.org/W6640425456","https://openalex.org/W6682388183","https://openalex.org/W6684191040","https://openalex.org/W6684701998","https://openalex.org/W6730161283","https://openalex.org/W6745272055","https://openalex.org/W6745276634","https://openalex.org/W6746402973","https://openalex.org/W6748475379","https://openalex.org/W6748581759","https://openalex.org/W6748742374","https://openalex.org/W6752274886","https://openalex.org/W6752591435","https://openalex.org/W6754642193","https://openalex.org/W6755310938","https://openalex.org/W6755511848","https://openalex.org/W6759129252","https://openalex.org/W6762806779","https://openalex.org/W6762989574","https://openalex.org/W6763334048","https://openalex.org/W6763621065","https://openalex.org/W6764007832","https://openalex.org/W6764891227","https://openalex.org/W6773538819","https://openalex.org/W6773877805","https://openalex.org/W6779259321","https://openalex.org/W6780154528","https://openalex.org/W6780430711","https://openalex.org/W6790651642","https://openalex.org/W6790874890","https://openalex.org/W6792068788","https://openalex.org/W6809874921","https://openalex.org/W6838477436","https://openalex.org/W7047792466"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2502115930","https://openalex.org/W2482350142","https://openalex.org/W4246396837","https://openalex.org/W3126451824","https://openalex.org/W1561927205","https://openalex.org/W3191453585","https://openalex.org/W4297672492","https://openalex.org/W4310988119","https://openalex.org/W4285226279"],"abstract_inverted_index":{"Adversarial":[0],"training":[1,50,61,141,208,258,278],"has":[2],"been":[3],"empirically":[4],"demonstrated":[5],"as":[6,101,184],"an":[7,114,185,215],"effective":[8],"strategy":[9],"to":[10,165,176,238,267],"improve":[11,268],"the":[12,23,44,87,91,106,156,159,178,221,223,226,231,246,249,260],"robustness":[13],"of":[14,26,81,93,105,145,158,162,169,187,228],"deep":[15,69],"neural":[16],"networks":[17,71,199],"(DNNs)":[18],"against":[19],"adversarial":[20,49,60,94,140,146,181,207,257,265],"examples.":[21,182],"However,":[22],"underlying":[24],"reason":[25],"its":[27],"effectiveness":[28],"is":[29],"still":[30],"non-transparent.":[31],"In":[32,65],"this":[33,188],"paper":[34],"we":[35,76,138,153,204],"conduct":[36],"both":[37,133],"extensive":[38],"theoretical":[39,240],"and":[40,86,120,135,200,225,270],"empirical":[41],"analysis":[42],"on":[43,59,220],"implicit":[45],"bias":[46],"induced":[47],"by":[48,113,263],"from":[51],"a":[52,102,143,149,166,170],"generalized":[53,103],"margin":[54,92,104,179],"perspective.":[55],"Our":[56,242],"results":[57,243],"focus":[58],"for":[62,180,191,248,274],"homogeneous":[63,130,195],"DNNs.":[64],"particular,":[66],"(i)":[67],"For":[68,128],"linear":[70,134,194,198,201],"with":[72,142,209],"$\\ell":[73,118,121,210],"_{p}$\u2113p-norm":[74,211],"perturbation,":[75],"show":[77,154,205],"that":[78,109,155,174,206,218,256],"weight":[79],"matrices":[80],"adjacent":[82],"layers":[83],"get":[84],"aligned":[85],"converged":[88],"parameters":[89,163],"maximize":[90,177],"examples,":[95],"which":[96],"can":[97,110],"be":[98,111],"further":[99],"viewed":[100],"original":[107],"dataset":[108],"achieved":[112],"interpolation":[115,216],"solution":[116],"between":[117],"_{2}$\u21132-SVM":[119],"_{q}$\u2113q-SVM":[122],"where":[123],"$1/p":[124],"+":[125],"1/q=1$1/p+1/q=1.":[126],"(ii)":[127],"general":[129,189],"DNNs,":[131,196],"including":[132],"nonlinear":[136],"ones,":[137],"investigate":[139],"variety":[144],"perturbations":[147],"in":[148,230],"unified":[150],"manner.":[151],"Specifically,":[152],"direction":[157],"limit":[160],"point":[161,168],"converges":[164],"KKT":[167],"constrained":[171],"optimization":[172],"problem":[173],"aims":[175],"Additionally,":[183],"application":[186],"result":[190],"two":[192],"special":[193],"diagonal":[197],"convolutional":[202],"networks,":[203],"perturbation":[212],"equivalently":[213],"minimizes":[214],"norm":[217],"depends":[219],"depth,":[222],"architecture,":[224],"value":[227],"$p$p":[229],"predictor":[232],"space.":[233],"Extensive":[234],"experiments":[235],"are":[236],"conducted":[237],"verify":[239],"claims.":[241],"theoretically":[244],"provide":[245,272],"basis":[247],"longstanding":[250],"folklore":[251],"Madry":[252],"et":[253],"al.":[254],"2018":[255],"modifies":[259],"decision":[261],"boundary":[262],"utilizing":[264],"examples":[266],"robustness,":[269],"potentially":[271],"insights":[273],"designing":[275],"new":[276],"robust":[277],"strategies.":[279]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}