{"id":"https://openalex.org/W7204449893","doi":"https://doi.org/10.48550/arxiv.2608.26043","title":"Robust CurveMoE: Multi-Norm Adversarial Defense for Mixture-of-Experts Models via Mode Connectivity","display_name":"Robust CurveMoE: Multi-Norm Adversarial Defense for Mixture-of-Experts Models via Mode Connectivity","publication_year":2026,"publication_date":"2026-08-26","ids":{"openalex":"https://openalex.org/W7204449893","doi":"https://doi.org/10.48550/arxiv.2608.26043"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.26043","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.26043","pdf_url":"https://arxiv.org/pdf/2608.26043","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.26043","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5148438135","display_name":"Xu Zhang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Xu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5136724230","display_name":"Ren Wang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Ren","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":0,"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":1.0,"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":1.0,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.0,"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":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mixture-of-experts","display_name":"mixture of experts","score":0.8700000047683716},{"id":"https://openalex.org/keywords/adversarial-robustness","display_name":"adversarial robustness","score":0.8640000224113464},{"id":"https://openalex.org/keywords/mode-connectivity","display_name":"mode connectivity","score":0.9150000214576721},{"id":"https://openalex.org/keywords/image-classification","display_name":"image classification","score":0.41499999165534973}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7314000129699707},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5852000117301941},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.45840001106262207},{"id":"https://openalex.org/C37736160","wikidata":"https://www.wikidata.org/wiki/Q1801315","display_name":"Adversarial system","level":2,"score":0.45210000872612},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4357999861240387},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4180000126361847},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.40389999747276306},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3393000066280365},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.3131999969482422},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3050000071525574},{"id":"https://openalex.org/C74296488","wikidata":"https://www.wikidata.org/wiki/Q2527392","display_name":"End-to-end principle","level":2,"score":0.2989000082015991},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.29739999771118164},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2971999943256378},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2919999957084656},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.2793000042438507},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.25940001010894775},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2538999915122986},{"id":"https://openalex.org/C31531917","wikidata":"https://www.wikidata.org/wiki/Q915157","display_name":"Robust control","level":3,"score":0.25189998745918274}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.26043","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.26043","pdf_url":"https://arxiv.org/pdf/2608.26043","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.26043","doi":"https://doi.org/10.48550/arxiv.2608.26043","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.26043","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.26043","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.26043","pdf_url":"https://arxiv.org/pdf/2608.26043","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204449893.pdf","grobid_xml":"https://content.openalex.org/works/W7204449893.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3156624478","https://openalex.org/W3186286629","https://openalex.org/W7167693841","https://openalex.org/W4407422870","https://openalex.org/W7131081452","https://openalex.org/W4330336530","https://openalex.org/W4390874353","https://openalex.org/W4415797874","https://openalex.org/W7133245738","https://openalex.org/W4416260964"],"abstract_inverted_index":{"Multi-norm":[0],"adversarial":[1],"defense":[2],"aims":[3],"to":[4,29],"protect":[5],"neural":[6],"networks":[7],"against":[8],"perturbations":[9],"defined":[10],"by":[11,157],"different":[12,50],"norm":[13],"constraints,":[14],"but":[15],"existing":[16],"methods":[17],"typically":[18],"optimize":[19],"competing":[20],"robustness":[21,35,61],"objectives":[22],"within":[23],"a":[24,54],"single":[25],"parameter":[26],"configuration,":[27],"leading":[28],"substantial":[30],"training":[31],"cost":[32],"and":[33,57,72,79,121,128,132,144,149,159,169,183],"unfavorable":[34],"trade-offs.":[36],"We":[37,112],"propose":[38],"Robust":[39,68,138],"CurveMoE,":[40],"an":[41],"efficient":[42],"mixture-of-experts":[43],"framework":[44],"that":[45,137],"connects":[46],"models":[47,64],"specialized":[48],"for":[49],"perturbation":[51],"norms":[52],"through":[53],"low-loss":[55],"path":[56],"exploits":[58],"the":[59,87,116,164,176],"complementary":[60],"profiles":[62],"of":[63,178],"along":[65],"this":[66],"path.":[67],"CurveMoE":[69,139],"derives":[70],"clean":[71],"norm-specialized":[73],"experts":[74],"from":[75],"robustness-constrained":[76,184],"curve":[77,106,123],"locations":[78],"selectively":[80],"expertizes":[81],"only":[82],"influential":[83,105],"layers,":[84],"while":[85],"sharing":[86],"remaining":[88],"parameters":[89,107],"across":[90],"routing":[91],"paths.":[92],"To":[93],"further":[94,174],"reduce":[95],"curve-construction":[96],"cost,":[97],"we":[98],"introduce":[99],"contribution-guided":[100],"partial":[101,120,179],"updating,":[102,180],"which":[103],"selects":[104],"using":[108],"initialization-based":[109],"gradient":[110],"scores.":[111],"also":[113],"theoretically":[114],"bound":[115],"objective":[117],"gap":[118],"between":[119],"full":[122],"optimization.":[124],"Experiments":[125],"on":[126,167],"CIFAR-100":[127,168],"ImageNet-100":[129],"with":[130],"WideResNet":[131],"Vision":[133],"Transformer":[134],"architectures":[135],"show":[136],"consistently":[140],"improves":[141,154],"clean,":[142],"norm-specific,":[143],"Union":[145,155],"accuracy":[146,156],"over":[147,163],"MSD":[148],"ERMC.":[150],"In":[151],"particular,":[152],"it":[153],"2.37":[158],"2.13":[160],"percentage":[161],"points":[162],"strongest":[165],"baseline":[166],"ImageNet-100,":[170],"respectively.":[171],"Extensive":[172],"ablations":[173],"validate":[175],"effectiveness":[177],"selective":[181],"expertization,":[182],"expert":[185],"selection.":[186]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-08-28T00:00:00"}