{"id":"https://openalex.org/W7130697288","doi":"https://doi.org/10.48550/arxiv.2602.17155","title":"Powering Up Zeroth-Order Training via Subspace Gradient Orthogonalization","display_name":"Powering Up Zeroth-Order Training via Subspace Gradient Orthogonalization","publication_year":2026,"publication_date":"2026-02-19","ids":{"openalex":"https://openalex.org/W7130697288","doi":"https://doi.org/10.48550/arxiv.2602.17155"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2602.17155","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2602.17155","pdf_url":"https://arxiv.org/pdf/2602.17155","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2602.17155","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111235146","display_name":"Yicheng Lang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lang, Yicheng","raw_affiliation_strings":["Michigan State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Michigan State University","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126511298","display_name":"Changsheng Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wang, Changsheng","raw_affiliation_strings":["Michigan State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Michigan State University","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126490882","display_name":"Yihua Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhang, Yihua","raw_affiliation_strings":["Michigan State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Michigan State University","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100633783","display_name":"Mingyi Hong","orcid":"https://orcid.org/0000-0003-1263-9365","observed_orcids":["https://orcid.org/0000-0003-1263-9365"]},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hong, Mingyi","raw_affiliation_strings":["University of Minnesota"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Minnesota","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100459107","display_name":"Zheng Zhang","orcid":"https://orcid.org/0000-0002-2292-0030","observed_orcids":["https://orcid.org/0000-0002-2292-0030","https://orcid.org/0000-0001-6216-6872"]},"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":"Zhang, Zheng","raw_affiliation_strings":["University of California , Santa Barbara"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California , Santa Barbara","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126467383","display_name":"Wotao Yin","orcid":"https://orcid.org/0000-0001-6697-9731","observed_orcids":["https://orcid.org/0000-0001-6697-9731"]},"institutions":[{"id":"https://openalex.org/I4210086143","display_name":"Alibaba Group (Cayman Islands)","ror":"https://ror.org/00mnrxf72","country_code":"KY","type":"company","lineage":["https://openalex.org/I4210086143","https://openalex.org/I45928872"]}],"countries":["KY"],"is_corresponding":false,"raw_author_name":"Yin, Wotao","raw_affiliation_strings":["DAMO Academy , Alibaba Group US"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DAMO Academy , Alibaba Group US","institution_ids":["https://openalex.org/I4210086143"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5126488092","display_name":"Sijia Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]},{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Liu, Sijia","raw_affiliation_strings":["IBM Research , USA","Michigan State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM Research , USA","institution_ids":["https://openalex.org/I1341412227"]},{"raw_affiliation_string":"Michigan State University","institution_ids":["https://openalex.org/I87216513"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9937000274658203,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9937000274658203,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.0013000000035390258,"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":0.0007999999797903001,"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/derivative-free-optimization","display_name":"derivative-free optimization","score":0.9990000128746033},{"id":"https://openalex.org/keywords/subspace-projection","display_name":"subspace projection","score":0.7960000038146973},{"id":"https://openalex.org/keywords/spectral-optimization","display_name":"spectral optimization","score":0.7279999852180481},{"id":"https://openalex.org/keywords/muon-optimizer","display_name":"Muon optimizer","score":0.8889999985694885},{"id":"https://openalex.org/keywords/low-rank-optimization","display_name":"low-rank optimization","score":0.6449999809265137},{"id":"https://openalex.org/keywords/llm-fine-tuning","display_name":"LLM fine-tuning","score":0.8790000081062317},{"id":"https://openalex.org/keywords/query-efficiency","display_name":"query efficiency","score":0.8109999895095825},{"id":"https://openalex.org/keywords/convergence-acceleration","display_name":"convergence acceleration","score":0.5950000286102295}],"concepts":[{"id":"https://openalex.org/C47559304","wikidata":"https://www.wikidata.org/wiki/Q1702189","display_name":"Orthogonalization","level":2,"score":0.9301000237464905},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.7998999953269958},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5738999843597412},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5550000071525574},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5008999705314636},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.44200000166893005},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.41670000553131104},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4115999937057495},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.39590001106262207},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.382999986410141},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.37770000100135803},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.3560999929904938},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.3528999984264374},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3425000011920929},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.3165000081062317},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.31630000472068787},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.30219998955726624},{"id":"https://openalex.org/C2987595161","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Optimization algorithm","level":2,"score":0.2809000015258789},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.26899999380111694},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.2676999866962433},{"id":"https://openalex.org/C66322947","wikidata":"https://www.wikidata.org/wiki/Q11658","display_name":"Transformer","level":3,"score":0.2524999976158142},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.250900000333786}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2602.17155","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2602.17155","pdf_url":"https://arxiv.org/pdf/2602.17155","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2602.17155","doi":"https://doi.org/10.48550/arxiv.2602.17155","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.17155","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2602.17155","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2602.17155","pdf_url":"https://arxiv.org/pdf/2602.17155","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G6093649949","display_name":"CAREER: Zeroth-Order Machine Learning: Foundations and Emerging Applications","funder_award_id":"2338068","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6430357324","display_name":"GOALI: SHF:Small: Energy-Efficient and Real-Time Neural Partial Differential Equation Solvers on 2.5D Photonic Chips","funder_award_id":"2419889","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","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/F4320307791","display_name":"Cisco Systems","ror":"https://ror.org/03yt1ez60"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7130697288.pdf","grobid_xml":"https://content.openalex.org/works/W7130697288.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7160956338","https://openalex.org/W4407091248","https://openalex.org/W7203705598","https://openalex.org/W7125831679","https://openalex.org/W7163368891","https://openalex.org/W7221769395","https://openalex.org/W7118489425","https://openalex.org/W7167024477","https://openalex.org/W7221777946","https://openalex.org/W4416036650"],"abstract_inverted_index":{"Zeroth-order":[0],"(ZO)":[1],"optimization":[2,37,54,87],"provides":[3],"a":[4,25,39,65,104,115,120,124,151],"gradient-free":[5],"alternative":[6],"to":[7,92,161,173],"first-order":[8],"(FO)":[9],"methods":[10],"by":[11,32,59,74,185],"estimating":[12],"gradients":[13],"via":[14],"finite":[15],"differences":[16],"of":[17,80,107,170],"function":[18],"evaluations,":[19],"and":[20,44,83,139,149,156,182],"has":[21,38],"recently":[22],"emerged":[23],"as":[24,123],"memory-efficient":[26],"paradigm":[27],"for":[28,179],"fine-tuning":[29,189],"large-scale":[30],"models":[31,137],"avoiding":[33],"backpropagation.":[34],"However,":[35],"ZO":[36,53,99,130],"fundamental":[40],"tension":[41],"between":[42],"accuracy":[43,155,184],"query":[45],"efficiency.":[46,158],"In":[47],"this":[48],"work,":[49],"we":[50,112],"show":[51],"that":[52,69,88,144],"can":[55],"be":[56],"substantially":[57],"improved":[58],"unifying":[60],"two":[61],"complementary":[62],"principles:":[63],"(i)":[64],"projection-based":[66],"subspace":[67,108],"view":[68],"reduces":[70],"gradient":[71,90,109],"estimation":[72],"variance":[73],"exploiting":[75],"the":[76,129,162,171,175],"intrinsic":[77],"low-rank":[78,125],"structure":[79,96],"model":[81],"updates,":[82],"(ii)":[84],"Muon-style":[85],"spectral":[86,95],"applies":[89],"orthogonalization":[91],"extract":[93],"informative":[94],"from":[97],"noisy":[98],"gradients.":[100],"These":[101],"findings":[102],"form":[103],"unified":[105],"framework":[106],"orthogonalization,":[110],"which":[111],"instantiate":[113],"in":[114,128,154],"new":[116],"method,":[117],"ZO-Muon,":[118],"admitting":[119],"natural":[121],"interpretation":[122],"Muon":[126],"optimizer":[127],"setting.":[131],"Extensive":[132],"experiments":[133],"on":[134,187,190],"large":[135],"language":[136],"(LLMs)":[138],"vision":[140],"transformers":[141],"(ViTs)":[142],"demonstrate":[143],"ZO-Muon":[145,166],"significantly":[146],"accelerates":[147],"convergence":[148],"achieves":[150],"win-win":[152],"improvement":[153],"query/runtime":[157],"Notably,":[159],"compared":[160],"popular":[163],"MeZO":[164],"baseline,":[165],"requires":[167],"only":[168],"24.7%":[169],"queries":[172],"reach":[174],"same":[176],"SST-2":[177],"performance":[178],"LLM":[180],"fine-tuning,":[181],"improves":[183],"25.1%":[186],"ViT-L":[188],"CIFAR-100.":[191]},"counts_by_year":[],"updated_date":"2026-11-01T11:40:01.658920","created_date":"2026-02-21T00:00:00"}
