{"id":"https://openalex.org/W7133235158","doi":"https://doi.org/10.48550/arxiv.2602.24283","title":"Taming Momentum: Rethinking Optimizer States Through Low-Rank Approximation","display_name":"Taming Momentum: Rethinking Optimizer States Through Low-Rank Approximation","publication_year":2026,"publication_date":"2026-02-27","ids":{"openalex":"https://openalex.org/W7133235158","doi":"https://doi.org/10.48550/arxiv.2602.24283"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.24283","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.24283","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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2602.24283","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074836725","display_name":"Zhengbo Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Wang, Zhengbo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127826179","display_name":"Jian Liang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liang, Jian","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112749024","display_name":"Ran He","orcid":"https://orcid.org/0000-0002-3807-991X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"He, Ran","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114909809","display_name":"Zilei Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Zilei","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5127863705","display_name":"Tieniu Tan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tan, Tieniu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5074836725"],"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":0.63919997215271,"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":0.63919997215271,"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":0.06759999692440033,"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/T12303","display_name":"Tensor decomposition and applications","score":0.045499999076128006,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/memory-footprint","display_name":"Memory footprint","score":0.724399983882904},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.6711000204086304},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5426999926567078},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.44920000433921814},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.3779999911785126},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.3709999918937683},{"id":"https://openalex.org/keywords/language-model","display_name":"Language model","score":0.3422999978065491},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.3310000002384186},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.319599986076355}],"concepts":[{"id":"https://openalex.org/C74912251","wikidata":"https://www.wikidata.org/wiki/Q6815727","display_name":"Memory footprint","level":2,"score":0.724399983882904},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.6711000204086304},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6193000078201294},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5426999926567078},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4607999920845032},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.44920000433921814},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4334000051021576},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.3779999911785126},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3709999918937683},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3603000044822693},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3465999960899353},{"id":"https://openalex.org/C137293760","wikidata":"https://www.wikidata.org/wiki/Q3621696","display_name":"Language model","level":2,"score":0.3422999978065491},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3370000123977661},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.3310000002384186},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.319599986076355},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.29670000076293945},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2937999963760376},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.2924000024795532},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.29010000824928284},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.2838999927043915},{"id":"https://openalex.org/C17305859","wikidata":"https://www.wikidata.org/wiki/Q382944","display_name":"Soar","level":2,"score":0.27900001406669617},{"id":"https://openalex.org/C113775141","wikidata":"https://www.wikidata.org/wiki/Q428691","display_name":"Computer engineering","level":1,"score":0.27869999408721924},{"id":"https://openalex.org/C29081049","wikidata":"https://www.wikidata.org/wiki/Q1364242","display_name":"Image stitching","level":2,"score":0.2727000117301941},{"id":"https://openalex.org/C170122806","wikidata":"https://www.wikidata.org/wiki/Q1914828","display_name":"Linear scale","level":2,"score":0.26570001244544983},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.25920000672340393},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.25870001316070557},{"id":"https://openalex.org/C60718061","wikidata":"https://www.wikidata.org/wiki/Q1414747","display_name":"Momentum (technical analysis)","level":2,"score":0.25699999928474426},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.2526000142097473},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.25049999356269836}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.24283","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.24283","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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2602.24283","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.24283","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":false,"raw_source_name":null,"raw_type":"article"},"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":{"Modern":[0],"optimizers":[1],"like":[2],"Adam":[3],"and":[4,18,28,183,195],"Muon":[5],"are":[6],"central":[7],"to":[8,118,171],"training":[9,47],"large":[10],"language":[11],"models,":[12],"but":[13],"their":[14],"reliance":[15],"on":[16,57,181,186],"first-":[17],"second-order":[19],"momenta":[20,44],"introduces":[21],"significant":[22],"memory":[23,76,100],"overhead,":[24],"which":[25],"constrains":[26],"scalability":[27],"computational":[29],"efficiency.":[30,101],"In":[31],"this":[32,58],"work,":[33],"we":[34,60,151],"reframe":[35],"the":[36,46,74,80,90,111,123,144,159],"exponential":[37],"moving":[38],"average":[39],"(EMA)":[40],"used":[41],"in":[42,155],"these":[43],"as":[45],"of":[48,146,178],"a":[49,63,85],"linear":[50,92],"regressor":[51],"via":[52],"online":[53,91],"gradient":[54],"flow.":[55],"Building":[56],"equivalence,":[59],"introduce":[61],"LoRA-Pre,":[62],"novel":[64],"low-rank":[65,87],"optimizer":[66],"designed":[67],"for":[68],"efficient":[69,166],"pre-training.":[70],"Specifically,":[71,169],"LoRA-Pre":[72,121,131,162,174],"reduces":[73],"optimizer's":[75],"footprint":[77],"by":[78,107],"decomposing":[79],"full":[81],"momentum":[82],"matrix":[83],"into":[84],"compact":[86],"subspace":[88],"within":[89],"learner,":[93],"thereby":[94],"maintaining":[95],"optimization":[96],"performance":[97,125],"while":[98],"improving":[99],"We":[102],"empirically":[103],"validate":[104],"LoRA-Pre's":[105,153],"efficacy":[106],"pre-training":[108,194],"models":[109],"from":[110,116],"Llama":[112],"architecture":[113],"family,":[114],"scaling":[115],"60M":[117],"1B":[119],"parameters.":[120],"achieves":[122,175],"highest":[124],"across":[126,192],"all":[127,165],"model":[128],"sizes.":[129],"Notably,":[130],"demonstrates":[132],"remarkable":[133],"rank":[134,145],"efficiency,":[135],"achieving":[136],"comparable":[137],"or":[138],"superior":[139],"results":[140],"using":[141],"only":[142],"1/8":[143],"baseline":[147],"methods.":[148],"Beyond":[149],"pre-training,":[150],"evaluate":[152],"effectiveness":[154,191],"fine-tuning":[156,167,196],"scenarios.":[157],"With":[158],"same":[160],"rank,":[161],"consistently":[163],"outperforms":[164],"baselines.":[168],"compared":[170],"standard":[172],"LoRA,":[173],"substantial":[176],"improvements":[177],"3.14":[179],"points":[180,185],"Llama-3.1-8B":[182],"6.17":[184],"Llama-2-7B,":[187],"validating":[188],"our":[189],"approach's":[190],"both":[193],"paradigms.":[197],"Our":[198],"code":[199],"is":[200],"publicly":[201],"available":[202],"at":[203],"https://github.com/mrflogs/LoRA-Pre.":[204]},"counts_by_year":[],"updated_date":"2026-03-03T06:18:10.843953","created_date":"2026-03-03T00:00:00"}