{"id":"https://openalex.org/W7164564891","doi":"https://doi.org/10.48550/arxiv.2606.12921","title":"LoRA-Muon: Spectral Steepest Descent on the Low-Rank Manifold","display_name":"LoRA-Muon: Spectral Steepest Descent on the Low-Rank Manifold","publication_year":2026,"publication_date":"2026-06-11","ids":{"openalex":"https://openalex.org/W7164564891","doi":"https://doi.org/10.48550/arxiv.2606.12921"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.12921","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.12921","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":"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.12921","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138530369","display_name":"Franz Louis Cesista","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cesista, Franz Louis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060316364","display_name":"Katherine Crowson","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Crowson, Katherine","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5120048196","display_name":"C\u00e9dric Simal","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Simal, C\u00e9dric","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5138504094","display_name":"Stella Biderman","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Biderman, Stella","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":false,"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":0.22269999980926514,"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":0.22269999980926514,"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/T10048","display_name":"Particle physics theoretical and experimental studies","score":0.11990000307559967,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13650","display_name":"Computational Physics and Python Applications","score":0.08900000154972076,"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/initialization","display_name":"Initialization","score":0.7282999753952026},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6092000007629395},{"id":"https://openalex.org/keywords/proxy","display_name":"Proxy (statistics)","score":0.4187000095844269},{"id":"https://openalex.org/keywords/transfer-of-learning","display_name":"Transfer of learning","score":0.400299996137619},{"id":"https://openalex.org/keywords/domain-adaptation","display_name":"Domain adaptation","score":0.37389999628067017},{"id":"https://openalex.org/keywords/spectral-gap","display_name":"Spectral gap","score":0.36550000309944153},{"id":"https://openalex.org/keywords/fraction","display_name":"Fraction (chemistry)","score":0.36070001125335693},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.33550000190734863}],"concepts":[{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.7282999753952026},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6092000007629395},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.513700008392334},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43810001015663147},{"id":"https://openalex.org/C2780148112","wikidata":"https://www.wikidata.org/wiki/Q1432581","display_name":"Proxy (statistics)","level":2,"score":0.4187000095844269},{"id":"https://openalex.org/C150899416","wikidata":"https://www.wikidata.org/wiki/Q1820378","display_name":"Transfer of learning","level":2,"score":0.400299996137619},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3991999924182892},{"id":"https://openalex.org/C2776434776","wikidata":"https://www.wikidata.org/wiki/Q19246213","display_name":"Domain adaptation","level":3,"score":0.37389999628067017},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.36550000309944153},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.36070001125335693},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.35040000081062317},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.33550000190734863},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.3255000114440918},{"id":"https://openalex.org/C2987249920","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectral representation","level":2,"score":0.3188999891281128},{"id":"https://openalex.org/C2776175482","wikidata":"https://www.wikidata.org/wiki/Q1195816","display_name":"Transfer (computing)","level":2,"score":0.31040000915527344},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.2842999994754791},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.265500009059906},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.25679999589920044},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C12725497","wikidata":"https://www.wikidata.org/wiki/Q810247","display_name":"Baseline (sea)","level":2,"score":0.2540000081062317}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.12921","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.12921","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.12921","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.12921","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":"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Low-Rank":[0],"Adaptation":[1],"(LoRA)":[2],"significantly":[3],"reduces":[4],"compute":[5],"and":[6,44,87,99,116,161,178,187],"memory":[7],"costs":[8],"for":[9,84],"finetuning":[10,155],"Deep":[11],"Learning":[12],"models":[13],"but":[14],"is":[15,31,76,79],"often":[16,46],"harder":[17],"to":[18,33,48,63],"tune":[19],"than":[20,126],"dense":[21,50,111,128],"training:":[22],"when":[23,154],"using":[24],"factor-wise":[25],"optimizers":[26],"such":[27],"as":[28],"AdamW,":[29],"it":[30,45,147,184],"sensitive":[32],"initialization":[34],"choices,":[35],"its":[36],"optimal":[37,91],"learning":[38,92,114],"rates":[39,93],"transfer":[40,94],"poorly":[41],"across":[42,95],"ranks,":[43],"fails":[47],"beat":[49],"baselines.":[51],"We":[52,134],"derive":[53],"LoRA-Muon":[54,78,119,172],"by":[55],"applying":[56],"the":[57,64,110,127,131,138,168],"Muon":[58,86],"optimizer's":[59],"spectral":[60,170],"steepest-descent":[61],"rule":[62],"low-rank":[65,82],"setting.":[66],"Along":[67],"with":[68],"our":[69,73,102],"split":[70],"weight-decay":[71],"rule,":[72],"main":[74],"claim":[75],"that":[77,137,162,174],"a":[80,106,117,151],"good":[81],"proxy":[83,108],"full-rank":[85],"Shampoo-family":[88],"optimizers.":[89],"Its":[90],"rank,":[96],"width,":[97],"depth,":[98],"factor-rescaling.":[100],"In":[101],"compute-matched":[103],"TinyShakespeare":[104],"study,":[105],"rank-$2$":[107],"recovers":[109],"best":[112],"tested":[113],"rate,":[115],"rank-$32$":[118],"run":[120],"attains":[121],"lower":[122],"mean":[123],"validation":[124],"loss":[125],"baseline":[129],"in":[130],"seed-averaged":[132],"sweep.":[133],"further":[135],"show":[136],"Spectron":[139],"optimizer":[140],"depends":[141],"on":[142],"arbitrary":[143],"factor":[144],"scaling,":[145],"so":[146],"would":[148],"likely":[149],"be":[150],"poor":[152],"fit":[153],"starts":[156],"from":[157],"badly":[158],"imbalanced":[159],"factors,":[160],"LoRA-RITE's":[163],"simplified":[164],"QR-coordinate":[165],"core":[166],"implements":[167],"same":[169],"update.":[171],"computes":[173],"update":[175],"without":[176],"QR-decomposition":[177],"avoids":[179],"storing":[180],"second":[181],"moments,":[182],"making":[183],"more":[185],"accelerator-friendly":[186],"memory-efficient.":[188]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-13T00:00:00"}
