{"id":"https://openalex.org/W2217490359","doi":"https://doi.org/10.1109/tnnls.2017.2672978","title":"Preconditioned Stochastic Gradient Descent","display_name":"Preconditioned Stochastic Gradient Descent","publication_year":2017,"publication_date":"2017-03-10","ids":{"openalex":"https://openalex.org/W2217490359","doi":"https://doi.org/10.1109/tnnls.2017.2672978","mag":"2217490359","pmid":"https://pubmed.ncbi.nlm.nih.gov/28362591"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2017.2672978","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2017.2672978","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1512.04202","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100639664","display_name":"Xi-Lin Li","orcid":"https://orcid.org/0000-0002-3853-2702"},"institutions":[{"id":"https://openalex.org/I4210121988","display_name":"Film Independent","ror":"https://ror.org/036cy3843","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210121988"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Xi-Lin Li","raw_affiliation_strings":["Independent Researcher, San Jose, CA, USA"],"raw_orcid":"https://orcid.org/0000-0002-3853-2702","affiliations":[{"raw_affiliation_string":"Independent Researcher, San Jose, CA, USA","institution_ids":["https://openalex.org/I4210121988"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100639664"],"corresponding_institution_ids":["https://openalex.org/I4210121988"],"apc_list":null,"apc_paid":null,"fwci":11.1187,"has_fulltext":false,"cited_by_count":110,"citation_normalized_percentile":{"value":0.99413029,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"29","issue":"5","first_page":"1454","last_page":"1466"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9994999766349792,"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/T12676","display_name":"Machine Learning and ELM","score":0.9991999864578247,"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/preconditioner","display_name":"Preconditioner","score":0.9450666904449463},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.7618379592895508},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.7385768294334412},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5261366367340088},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5191766023635864},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5128150582313538},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.503102719783783},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5005884170532227},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4136591851711273},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.411325603723526},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35929039120674133},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.22384944558143616},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1347382366657257}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.9450666904449463},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.7618379592895508},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.7385768294334412},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5261366367340088},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5191766023635864},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5128150582313538},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.503102719783783},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5005884170532227},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4136591851711273},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.411325603723526},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35929039120674133},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.22384944558143616},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1347382366657257},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tnnls.2017.2672978","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2017.2672978","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:28362591","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28362591","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks and learning systems","raw_type":null},{"id":"pmh:oai:arXiv.org:1512.04202","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1512.04202","pdf_url":"https://arxiv.org/pdf/1512.04202","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1512.04202","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1512.04202","pdf_url":"https://arxiv.org/pdf/1512.04202","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W71081281","https://openalex.org/W1491622225","https://openalex.org/W1498436455","https://openalex.org/W1737237432","https://openalex.org/W1772464306","https://openalex.org/W1779452081","https://openalex.org/W1968020335","https://openalex.org/W1970789124","https://openalex.org/W1977067929","https://openalex.org/W2064675550","https://openalex.org/W2097987904","https://openalex.org/W2098082088","https://openalex.org/W2107878631","https://openalex.org/W2112514080","https://openalex.org/W2112796928","https://openalex.org/W2137515395","https://openalex.org/W2150355110","https://openalex.org/W2155894447","https://openalex.org/W2157791002","https://openalex.org/W2238987678","https://openalex.org/W2438680196","https://openalex.org/W2613332842","https://openalex.org/W2950351588","https://openalex.org/W2950942124","https://openalex.org/W2963941964","https://openalex.org/W2964125128","https://openalex.org/W3004533406","https://openalex.org/W4297797495","https://openalex.org/W6629379589","https://openalex.org/W6637940777","https://openalex.org/W6637947871","https://openalex.org/W6638005537","https://openalex.org/W6682953061","https://openalex.org/W6683107984","https://openalex.org/W6690138163"],"related_works":["https://openalex.org/W2355987247","https://openalex.org/W3143650729","https://openalex.org/W3177326532","https://openalex.org/W4297883503","https://openalex.org/W2042173174","https://openalex.org/W4206903459","https://openalex.org/W2754816816","https://openalex.org/W4366280654","https://openalex.org/W3160167280","https://openalex.org/W4231621013"],"abstract_inverted_index":{"Stochastic":[0],"gradient":[1,74,137,145],"descent":[2],"(SGD)":[3],"still":[4],"is":[5,23,138],"the":[6,67,78,96,118,144,172,188],"workhorse":[7],"for":[8,92,124],"many":[9,34,184],"practical":[10],"problems.":[11,165],"However,":[12],"it":[13,140],"converges":[14],"slow,":[15],"and":[16,114,127,156],"can":[17,141,181],"be":[18,83],"difficult":[19],"to":[20,25,28,60,82,89,147,163],"tune.":[21],"It":[22],"possible":[24],"precondition":[26],"SGD":[27,180],"accelerate":[29],"its":[30,116],"convergence":[31],"remarkably.":[32],"But":[33],"attempts":[35],"in":[36,47,85,105],"this":[37],"direction":[38],"either":[39],"aim":[40],"at":[41],"solving":[42],"specialized":[43],"problems,":[44],"or":[45,132,195],"result":[46],"significantly":[48],"more":[49],"complicated":[50],"methods":[51,153],"than":[52],"SGD.":[53,149],"This":[54],"paper":[55],"proposes":[56],"a":[57,63,86,191,196],"new":[58,119,173],"method":[59,91],"adaptively":[61],"estimate":[62],"preconditioner,":[64,174],"such":[65],"that":[66,76,169],"amplitudes":[68],"of":[69,71,77,80,190],"perturbations":[70,79],"preconditioned":[72,179],"stochastic":[73,136],"match":[75],"parameters":[81],"optimized":[84],"way":[87],"comparable":[88],"Newton":[90],"deterministic":[93,106],"optimization.":[94],"Unlike":[95],"preconditioners":[97],"based":[98],"on":[99],"secant":[100],"equation":[101],"fitting":[102],"as":[103],"done":[104],"quasi-Newton":[107],"methods,":[108],"which":[109],"assume":[110],"positive":[111],"definite":[112],"Hessian":[113],"approximate":[115],"inverse,":[117],"preconditioner":[120,151],"works":[121],"equally":[122],"well":[123],"both":[125],"convex":[126],"nonconvex":[128],"optimizations":[129],"with":[130,157,171],"exact":[131],"noisy":[133],"gradients.":[134],"When":[135],"used,":[139],"naturally":[142],"damp":[143],"noise":[146],"stabilize":[148],"Efficient":[150],"estimation":[152],"are":[154,161],"developed,":[155],"reasonable":[158],"simplifications,":[159],"they":[160],"applicable":[162],"large-scale":[164],"Experimental":[166],"results":[167],"demonstrate":[168],"equipped":[170],"without":[175],"any":[176],"tuning":[177],"effort,":[178],"efficiently":[182],"solve":[183],"challenging":[185],"problems":[186],"like":[187],"training":[189],"deep":[192],"neural":[193,198],"network":[194,199],"recurrent":[197],"requiring":[200],"extremely":[201],"long-term":[202],"memories.":[203]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":15},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":23},{"year":2019,"cited_by_count":20},{"year":2018,"cited_by_count":10},{"year":2016,"cited_by_count":1}],"updated_date":"2026-08-12T21:12:35.861297","created_date":"2025-10-10T00:00:00"}
