{"id":"https://openalex.org/W4221147657","doi":"https://doi.org/10.48550/arxiv.2203.06020","title":"Enhancing Adversarial Training with Second-Order Statistics of Weights","display_name":"Enhancing Adversarial Training with Second-Order Statistics of Weights","publication_year":2022,"publication_date":"2022-03-11","ids":{"openalex":"https://openalex.org/W4221147657","doi":"https://doi.org/10.48550/arxiv.2203.06020"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2203.06020","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2203.06020","pdf_url":"https://arxiv.org/pdf/2203.06020","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/2203.06020","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048979254","display_name":"Gaojie Jin","orcid":"https://orcid.org/0000-0003-0240-3033"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jin, Gaojie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112870953","display_name":"Xinping Yi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yi, Xinping","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100352892","display_name":"Wei Huang","orcid":"https://orcid.org/0000-0003-1418-6267"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huang, Wei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041836791","display_name":"Sven Schewe","orcid":"https://orcid.org/0000-0002-9093-9518"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Schewe, Sven","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5020085889","display_name":"Xiaowei Huang","orcid":"https://orcid.org/0000-0001-6267-0366"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huang, Xiaowei","raw_affiliation_strings":[],"raw_orcid":null,"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":true,"cited_by_count":4,"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/T10036","display_name":"Advanced Neural Network Applications","score":0.9929999709129333,"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/T11512","display_name":"Anomaly Detection Techniques and Applications","score":0.992900013923645,"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":0.8213080763816833},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6622011065483093},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.661154568195343},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6333794593811035},{"id":"https://openalex.org/keywords/deep-neural-networks","display_name":"Deep neural networks","score":0.5707507729530334},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5281724333763123},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5102148056030273},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4353019893169403},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4294719099998474},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.42374351620674133},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.42269638180732727},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.41470927000045776},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.41282951831817627},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39606383442878723},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37955042719841003},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.28539353609085083}],"concepts":[{"id":"https://openalex.org/C37736160","wikidata":"https://www.wikidata.org/wiki/Q1801315","display_name":"Adversarial system","level":2,"score":0.8213080763816833},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6622011065483093},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.661154568195343},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6333794593811035},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.5707507729530334},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5281724333763123},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5102148056030273},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4353019893169403},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4294719099998474},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.42374351620674133},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.42269638180732727},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.41470927000045776},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.41282951831817627},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39606383442878723},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37955042719841003},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28539353609085083},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2203.06020","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2203.06020","pdf_url":"https://arxiv.org/pdf/2203.06020","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.2203.06020","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2203.06020","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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2203.06020","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2203.06020","pdf_url":"https://arxiv.org/pdf/2203.06020","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":[{"display_name":"Partnerships for the goals","id":"https://metadata.un.org/sdg/17","score":0.44999998807907104}],"awards":[{"id":"https://openalex.org/G1364539167","display_name":"FOUNDATIONS FOR CONTINUOUS ENGINEERING OF TRUSTWORTHY AUTONOMY","funder_award_id":"956123","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2838024195","display_name":"UK Robotics and Artificial Intelligence Hub for Offshore Energy Asset Integrity Management","funder_award_id":"EP/R026173/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6661291015","display_name":"EnnCore: End-to-End Conceptual Guarding of Neural Architectures","funder_award_id":"EP/T026995/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8602921712","display_name":null,"funder_award_id":"EP/R026173","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320332972","display_name":"Defence Science and Technology Laboratory","ror":"https://ror.org/04jswqb94"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4221147657.pdf","grobid_xml":"https://content.openalex.org/works/W4221147657.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2950183588","https://openalex.org/W3080754722","https://openalex.org/W4383221314","https://openalex.org/W3093978547","https://openalex.org/W2953536436","https://openalex.org/W3203790781","https://openalex.org/W4313346231","https://openalex.org/W2738001131","https://openalex.org/W4285785480","https://openalex.org/W2997056298"],"abstract_inverted_index":{"Adversarial":[0],"training":[1,62,151],"has":[2],"been":[3],"shown":[4],"to":[5,13,70,113,160],"be":[6,38],"one":[7],"of":[8,17,80,104,122,135,164],"the":[9,15,35,71,109,131,136],"most":[10],"effective":[11],"approaches":[12],"improve":[14],"robustness":[16,132],"deep":[18],"neural":[19,138],"networks.":[20],"It":[21],"is":[22,169],"formalized":[23],"as":[24,55],"a":[25,75,161],"min-max":[26],"optimization":[27],"over":[28],"model":[29,53],"weights":[30,36,54,86,105],"and":[31,133,157],"adversarial":[32,61,95,150],"perturbations,":[33],"where":[34],"can":[37,106],"optimized":[39],"through":[40,63],"gradient":[41],"descent":[42],"methods":[43],"like":[44,153],"SGD.":[45],"In":[46,111],"this":[47,114],"paper,":[48],"we":[49,90,117],"show":[50,125],"that":[51,84,100,126],"treating":[52],"random":[56],"variables":[57],"allows":[58],"for":[59],"enhancing":[60],"\\textbf{S}econd-Order":[64],"\\textbf{S}tatistics":[65],"\\textbf{O}ptimization":[66],"(S$^2$O)":[67],"with":[68],"respect":[69],"weights.":[72],"By":[73],"relaxing":[74],"common":[76],"(but":[77],"unrealistic)":[78],"assumption":[79],"previous":[81],"PAC-Bayesian":[82,94],"frameworks":[83],"all":[85],"are":[87],"statistically":[88],"independent,":[89],"derive":[91],"an":[92,119],"improved":[93],"generalization":[96,134],"bound,":[97],"which":[98,124],"suggests":[99],"optimizing":[101],"second-order":[102],"statistics":[103],"effectively":[107],"tighten":[108],"bound.":[110],"addition":[112],"theoretical":[115],"insight,":[116],"conduct":[118],"extensive":[120],"set":[121],"experiments,":[123],"S$^2$O":[127],"not":[128],"only":[129],"improves":[130],"trained":[137],"networks":[139],"when":[140],"used":[141],"in":[142,148],"isolation,":[143],"but":[144],"also":[145],"integrates":[146],"easily":[147],"state-of-the-art":[149],"techniques":[152],"TRADES,":[154],"AWP,":[155],"MART,":[156],"AVMixup,":[158],"leading":[159],"measurable":[162],"improvement":[163],"these":[165],"techniques.":[166],"The":[167],"code":[168],"available":[170],"at":[171],"\\url{https://github.com/Alexkael/S2O}.":[172]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-07-11T18:08:03.149640","created_date":"2025-10-10T00:00:00"}
