{"id":"https://openalex.org/W4360980779","doi":"https://doi.org/10.1186/s13635-023-00137-0","title":"Gaussian class-conditional simplex loss for accurate, adversarially robust deep classifier training","display_name":"Gaussian class-conditional simplex loss for accurate, adversarially robust deep classifier training","publication_year":2023,"publication_date":"2023-03-10","ids":{"openalex":"https://openalex.org/W4360980779","doi":"https://doi.org/10.1186/s13635-023-00137-0"},"language":"en","primary_location":{"id":"doi:10.1186/s13635-023-00137-0","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13635-023-00137-0","pdf_url":"https://jis-eurasipjournals.springeropen.com/counter/pdf/10.1186/s13635-023-00137-0","source":{"id":"https://openalex.org/S5820498","display_name":"EURASIP Journal on Information Security","issn_l":"1687-4161","issn":["1687-4161","1687-417X","2510-523X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EURASIP Journal on Information Security","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://jis-eurasipjournals.springeropen.com/counter/pdf/10.1186/s13635-023-00137-0","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101469785","display_name":"Arslan Ali","orcid":"https://orcid.org/0000-0003-0282-0726"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Arslan Ali","raw_affiliation_strings":["DET - Department of Electronics and Telecommunications, Politecnico di Torino, Turin, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DET - Department of Electronics and Telecommunications, Politecnico di Torino, Turin, Italy","institution_ids":["https://openalex.org/I177477856"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018841739","display_name":"Andrea Migliorati","orcid":"https://orcid.org/0000-0001-9239-0568"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Andrea Migliorati","raw_affiliation_strings":["DET - Department of Electronics and Telecommunications, Politecnico di Torino, Turin, Italy"],"raw_orcid":"https://orcid.org/0000-0001-9239-0568","affiliations":[{"raw_affiliation_string":"DET - Department of Electronics and Telecommunications, Politecnico di Torino, Turin, Italy","institution_ids":["https://openalex.org/I177477856"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054395599","display_name":"Tiziano Bianchi","orcid":"https://orcid.org/0000-0002-3965-3522"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Tiziano Bianchi","raw_affiliation_strings":["DET - Department of Electronics and Telecommunications, Politecnico di Torino, Turin, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DET - Department of Electronics and Telecommunications, Politecnico di Torino, Turin, Italy","institution_ids":["https://openalex.org/I177477856"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034486931","display_name":"Enrico Magli","orcid":"https://orcid.org/0000-0002-0901-0251"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Enrico Magli","raw_affiliation_strings":["DET - Department of Electronics and Telecommunications, Politecnico di Torino, Turin, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DET - Department of Electronics and Telecommunications, Politecnico di Torino, Turin, Italy","institution_ids":["https://openalex.org/I177477856"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5018841739"],"corresponding_institution_ids":["https://openalex.org/I177477856"],"apc_list":{"value":1040,"currency":"USD","value_usd":1040},"apc_paid":{"value":1040,"currency":"USD","value_usd":1040},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02514883,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2023","issue":"1","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":0.9868000149726868,"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/T11515","display_name":"Bacillus and Francisella bacterial research","score":0.95169997215271,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7188951373100281},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.6676881313323975},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6237829327583313},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.6064822673797607},{"id":"https://openalex.org/keywords/adversarial-system","display_name":"Adversarial system","score":0.5149415135383606},{"id":"https://openalex.org/keywords/classifier","display_name":"Classifier (UML)","score":0.4762980043888092},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.47541433572769165},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.46465104818344116},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.4631919264793396},{"id":"https://openalex.org/keywords/feature-vector","display_name":"Feature vector","score":0.42129719257354736},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3680746853351593},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34641456604003906},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33287689089775085},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.23433548212051392}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7188951373100281},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6676881313323975},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6237829327583313},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6064822673797607},{"id":"https://openalex.org/C37736160","wikidata":"https://www.wikidata.org/wiki/Q1801315","display_name":"Adversarial system","level":2,"score":0.5149415135383606},{"id":"https://openalex.org/C95623464","wikidata":"https://www.wikidata.org/wiki/Q1096149","display_name":"Classifier (UML)","level":2,"score":0.4762980043888092},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.47541433572769165},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.46465104818344116},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.4631919264793396},{"id":"https://openalex.org/C83665646","wikidata":"https://www.wikidata.org/wiki/Q42139305","display_name":"Feature vector","level":2,"score":0.42129719257354736},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3680746853351593},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34641456604003906},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33287689089775085},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23433548212051392},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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},{"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1186/s13635-023-00137-0","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13635-023-00137-0","pdf_url":"https://jis-eurasipjournals.springeropen.com/counter/pdf/10.1186/s13635-023-00137-0","source":{"id":"https://openalex.org/S5820498","display_name":"EURASIP Journal on Information Security","issn_l":"1687-4161","issn":["1687-4161","1687-417X","2510-523X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EURASIP Journal on Information Security","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:b0ad3f4b7c7946e8b71a6fcc9cca422f","is_oa":true,"landing_page_url":"https://doaj.org/article/b0ad3f4b7c7946e8b71a6fcc9cca422f","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"EURASIP Journal on Information Security, Vol 2023, Iss 1, Pp 1-17 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1186/s13635-023-00137-0","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13635-023-00137-0","pdf_url":"https://jis-eurasipjournals.springeropen.com/counter/pdf/10.1186/s13635-023-00137-0","source":{"id":"https://openalex.org/S5820498","display_name":"EURASIP Journal on Information Security","issn_l":"1687-4161","issn":["1687-4161","1687-417X","2510-523X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EURASIP Journal on Information Security","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7699999809265137}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4360980779.pdf","grobid_xml":"https://content.openalex.org/works/W4360980779.grobid-xml"},"referenced_works_count":50,"referenced_works":["https://openalex.org/W1981276685","https://openalex.org/W2075851722","https://openalex.org/W2112796928","https://openalex.org/W2124289529","https://openalex.org/W2125908420","https://openalex.org/W2167998037","https://openalex.org/W2180612164","https://openalex.org/W2194775991","https://openalex.org/W2243397390","https://openalex.org/W2293768274","https://openalex.org/W2296452361","https://openalex.org/W2535873859","https://openalex.org/W2543927648","https://openalex.org/W2767471303","https://openalex.org/W2768346313","https://openalex.org/W2798302089","https://openalex.org/W2924551358","https://openalex.org/W2928157547","https://openalex.org/W2937223285","https://openalex.org/W2962821226","https://openalex.org/W2963026800","https://openalex.org/W2963166243","https://openalex.org/W2963501948","https://openalex.org/W2963516603","https://openalex.org/W2963564844","https://openalex.org/W2963855547","https://openalex.org/W2963952467","https://openalex.org/W2964082701","https://openalex.org/W2988331694","https://openalex.org/W2992667408","https://openalex.org/W3034214559","https://openalex.org/W3034537217","https://openalex.org/W3098920376","https://openalex.org/W3107115938","https://openalex.org/W3118608800","https://openalex.org/W3157825581","https://openalex.org/W6600176753","https://openalex.org/W6600281463","https://openalex.org/W6600466347","https://openalex.org/W6600679772","https://openalex.org/W6601802196","https://openalex.org/W6603287499","https://openalex.org/W6607666538","https://openalex.org/W6609410732","https://openalex.org/W6629201165","https://openalex.org/W6677908715","https://openalex.org/W6701041153","https://openalex.org/W6757381326","https://openalex.org/W6815268342","https://openalex.org/W6821127250"],"related_works":["https://openalex.org/W4311734044","https://openalex.org/W3046843850","https://openalex.org/W2563096758","https://openalex.org/W4386716251","https://openalex.org/W4386053843","https://openalex.org/W4286899967","https://openalex.org/W3158004940","https://openalex.org/W3205128835","https://openalex.org/W4379258830","https://openalex.org/W4293092754"],"abstract_inverted_index":{"Abstract":[0],"In":[1,161],"this":[2],"work,":[3],"we":[4],"present":[5],"the":[6,24,48,67,74,86,104,110,121,131,134,171],"Gaussian":[7,52],"Class-Conditional":[8],"Simplex":[9],"(GCCS)":[10],"loss:":[11],"a":[12,45,56,61,113,166,182],"novel":[13],"approach":[14,140],"for":[15,38,79,196],"training":[16,159],"deep":[17],"robust":[18],"multiclass":[19],"classifiers":[20],"that":[21,60,116,130,169,186],"improves":[22],"over":[23,193],"state-of-the-art":[25,191],"in":[26,55,208],"terms":[27,209],"of":[28,47,72,76,103,112,133,173,210],"classification":[29,143,211],"accuracy":[30,212],"and":[31,96,198,213],"adversarial":[32,151,158,205,214],"robustness,":[33],"with":[34,156],"little":[35],"extra":[36],"cost":[37],"network":[39,87],"training.":[40],"The":[41,100],"proposed":[42],"method":[43],"learns":[44,165],"mapping":[46],"input":[49],"classes":[50],"onto":[51],"target":[53,77],"distributions":[54,91,106],"latent":[57,135],"space":[58,136,168],"such":[59,115],"hyperplane":[62],"can":[63],"be":[64],"used":[65],"as":[66,201,203],"optimal":[68],"decision":[69,167,178],"surface.":[70],"Instead":[71],"maximizing":[73],"likelihood":[75],"labels":[78],"individual":[80],"samples,":[81],"our":[82,139,163],"loss":[83],"function":[84],"pushes":[85],"to":[88],"produce":[89],"feature":[90],"yielding":[92],"high":[93],"inter-class":[94],"separation":[95],"low":[97],"intra-class":[98],"separation.":[99],"mean":[101],"values":[102],"learned":[105],"are":[107],"centered":[108],"on":[109,138],"vertices":[111],"simplex":[114],"each":[117],"class":[118],"is":[119],"at":[120],"same":[122],"distance":[123],"from":[124],"every":[125],"other":[126],"class.":[127],"We":[128,180],"show":[129],"regularization":[132],"based":[137],"yields":[141],"excellent":[142],"accuracy.":[144],"Moreover,":[145],"GCCS":[146,189],"provides":[147],"improved":[148],"robustness":[149],"against":[150],"perturbations,":[152],"outperforming":[153],"models":[154],"trained":[155],"conventional":[157],"(AT).":[160],"particular,":[162],"model":[164],"minimizes":[170],"presence":[172],"short":[174],"paths":[175],"toward":[176],"neighboring":[177],"regions.":[179],"provide":[181],"comprehensive":[183],"empirical":[184],"evaluation":[185],"shows":[187],"how":[188],"outperforms":[190],"approaches":[192],"challenging":[194],"datasets":[195],"targeted":[197],"untargeted":[199],"gradient-based,":[200],"well":[202],"gradient-free":[204],"attacks,":[206],"both":[207],"robustness.":[215]},"counts_by_year":[],"updated_date":"2026-07-23T05:56:39.545243","created_date":"2025-10-10T00:00:00"}