{"id":"https://openalex.org/W7140182119","doi":"https://doi.org/10.48550/arxiv.2603.20632","title":"Optimal low-rank stochastic gradient estimation for LLM training","display_name":"Optimal low-rank stochastic gradient estimation for LLM training","publication_year":2026,"publication_date":"2026-03-21","ids":{"openalex":"https://openalex.org/W7140182119","doi":"https://doi.org/10.48550/arxiv.2603.20632"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.20632","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.20632","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.20632","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Li, Zehao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Zehao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Ren, Tao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ren, Tao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Zhang, Zishi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Zishi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Chen, Xi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Xi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Peng, Yijie","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peng, Yijie","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":0.8564000129699707,"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":0.8564000129699707,"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":0.02019999921321869,"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":0.014499999582767487,"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/estimator","display_name":"Estimator","score":0.7595000267028809},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.6172000169754028},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5231999754905701},{"id":"https://openalex.org/keywords/autoregressive-model","display_name":"Autoregressive model","score":0.48840001225471497},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4431000053882599},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.4000999927520752},{"id":"https://openalex.org/keywords/lift","display_name":"Lift (data mining)","score":0.3774000108242035},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.3476000130176544},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.3465999960899353},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.3276999890804291}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7595000267028809},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.6172000169754028},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5662999749183655},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5231999754905701},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49889999628067017},{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.48840001225471497},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45239999890327454},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4431000053882599},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.423799991607666},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.4000999927520752},{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.3774000108242035},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3476000130176544},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.3465999960899353},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.3276999890804291},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.3255000114440918},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.3190000057220459},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.31630000472068787},{"id":"https://openalex.org/C2777036070","wikidata":"https://www.wikidata.org/wiki/Q18393452","display_name":"Random projection","level":2,"score":0.31349998712539673},{"id":"https://openalex.org/C165646398","wikidata":"https://www.wikidata.org/wiki/Q3755281","display_name":"Minimum-variance unbiased estimator","level":3,"score":0.3093000054359436},{"id":"https://openalex.org/C2986577269","wikidata":"https://www.wikidata.org/wiki/Q11306265","display_name":"Random noise","level":2,"score":0.2912999987602234},{"id":"https://openalex.org/C35594927","wikidata":"https://www.wikidata.org/wiki/Q2265984","display_name":"Efficient estimator","level":4,"score":0.28519999980926514},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.2761000096797943},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.27239999175071716},{"id":"https://openalex.org/C39425265","wikidata":"https://www.wikidata.org/wiki/Q7098944","display_name":"Optimal estimation","level":2,"score":0.27230000495910645},{"id":"https://openalex.org/C133939421","wikidata":"https://www.wikidata.org/wiki/Q6865379","display_name":"Minimax estimator","level":4,"score":0.27059999108314514},{"id":"https://openalex.org/C164172150","wikidata":"https://www.wikidata.org/wiki/Q1782585","display_name":"Consistent estimator","level":4,"score":0.2703999876976013},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.26969999074935913},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.2678999900817871},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.2678999900817871},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.26489999890327454},{"id":"https://openalex.org/C175694140","wikidata":"https://www.wikidata.org/wiki/Q980329","display_name":"Orthographic projection","level":2,"score":0.2603999972343445},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.25679999589920044}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.20632","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.20632","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,"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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.20632","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.20632","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,"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"},"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":{"Large":[0],"language":[1],"model":[2],"(LLM)":[3],"training":[4,129],"is":[5,47,58,98],"often":[6],"bottlenecked":[7],"by":[8,21,100],"memory":[9,76,125,141],"constraints":[10],"and":[11,71,82,127],"stochastic":[12,51,63],"gradient":[13,27,52,64,120],"noise":[14],"in":[15,155,157],"extremely":[16],"high-dimensional":[17,62],"parameter":[18],"spaces.":[19],"Motivated":[20],"empirical":[22],"evidence":[23],"that":[24,46,112],"many":[25],"LLM":[26,159],"matrices":[28],"are":[29],"effectively":[30],"low-rank":[31,39,119],"during":[32],"training,":[33],"we":[34],"present":[35],"an":[36,87,108],"unbiased,":[37],"memory-efficient,":[38],"matrix":[40],"estimator":[41,65,80],"with":[42],"the":[43,79,117,137,165,169,172],"lowest":[44,138],"variance":[45],"applicable":[48],"across":[49],"common":[50],"estimation":[53],"paradigms.":[54],"The":[55,95],"core":[56],"idea":[57],"to":[59],"project":[60],"a":[61,67,102],"onto":[66],"random":[68,110],"low-dimensional":[69],"subspace":[70],"lift":[72],"it":[73],"back,":[74],"reducing":[75],"while":[77,152],"keeping":[78],"unbiased":[81],"controlling":[83],"mean-squared":[84],"error":[85],"via":[86],"optimally":[88],"designed":[89],"projection":[90,96,175],"distribution,":[91],"including":[92],"Haar--Stiefel":[93],"projections.":[94],"distribution":[97],"derived":[99],"solving":[101],"constrained":[103],"functional":[104],"optimization":[105],"problem,":[106],"yielding":[107],"optimal":[109,174],"projector":[111],"guides":[113],"algorithm":[114],"design.":[115],"Empirically,":[116],"resulting":[118],"estimators":[121],"deliver":[122],"both":[123],"practical":[124],"savings":[126],"improved":[128],"behavior.":[130],"In":[131],"RoBERTa-large":[132],"fine-tuning,":[133],"our":[134,162],"method":[135,163],"attains":[136],"peak":[139],"GPU":[140],"among":[142],"compared":[143],"methods":[144],"(e.g.,":[145],"3.83GB":[146],"versus":[147],"16.7GB":[148],"for":[149],"full":[150],"BP)":[151],"remaining":[153],"competitive":[154],"accuracy;":[156],"autoregressive":[158],"pretraining":[160],"(LLaMA-20M/60M/100M),":[161],"outperforms":[164],"traditional":[166],"methods,":[167],"supporting":[168],"benefit":[170],"of":[171],"proposed":[173],"strategy.":[176]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-03-25T00:00:00"}