{"id":"https://openalex.org/W7133200719","doi":"https://doi.org/10.52202/075280-2653","title":"Aiming towards the minimizers: fast convergence of SGD for overparametrized problems","display_name":"Aiming towards the minimizers: fast convergence of SGD for overparametrized problems","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W7133200719","doi":"https://doi.org/10.52202/075280-2653"},"language":"en","primary_location":{"id":"doi:10.52202/075280-2653","doi":"https://doi.org/10.52202/075280-2653","is_oa":false,"landing_page_url":"https://doi.org/10.52202/075280-2653","pdf_url":null,"source":{"id":"https://openalex.org/S4363606243","display_name":"neural information processing systems","issn_l":"1049-5258","issn":["1049-5258"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","norway-2"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Neural Information Processing Systems 36","raw_type":"proceedings-article"},"volume":null,"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2306.02601","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5127845535","display_name":"Chaoyue Liu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chaoyue Liu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033142494","display_name":"Dmitriy Drusvyatskiy","orcid":"https://orcid.org/0000-0001-5245-0458","observed_orcids":["https://orcid.org/0000-0001-5245-0458"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dmitriy Drusvyatskiy","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032670820","display_name":"Misha Belkin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Misha Belkin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011856337","display_name":"Damek Davis","orcid":"https://orcid.org/0000-0003-2105-4641","observed_orcids":["https://orcid.org/0000-0003-2105-4641"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Damek Davis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5004712973","display_name":"Yian Ma","orcid":"https://orcid.org/0000-0001-6074-6638","observed_orcids":["https://orcid.org/0000-0001-6074-6638","https://orcid.org/0009-0000-1096-5410"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yian Ma","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":0.1775,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.48415897,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"60748","last_page":"60767"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9984999895095825,"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":0.9984999895095825,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"stochastic gradient descent","score":0.984000027179718},{"id":"https://openalex.org/keywords/convergence-rate","display_name":"convergence rate","score":0.5},{"id":"https://openalex.org/keywords/minimizers","display_name":"minimizers","score":0.6859999895095825},{"id":"https://openalex.org/keywords/neural-network","display_name":"artificial neural networks","score":0.36500000953674316},{"id":"https://openalex.org/keywords/optimization-dynamics","display_name":"optimization dynamics","score":0.382999986410141}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5712000131607056},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.504800021648407},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4154999852180481},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3287999927997589},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3127000033855438},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2596000134944916},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2587999999523163},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.2574000060558319},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.24779999256134033},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.2475000023841858}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.52202/075280-2653","doi":"https://doi.org/10.52202/075280-2653","is_oa":false,"landing_page_url":"https://doi.org/10.52202/075280-2653","pdf_url":null,"source":{"id":"https://openalex.org/S4363606243","display_name":"neural information processing systems","issn_l":"1049-5258","issn":["1049-5258"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","norway-2"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Neural Information Processing Systems 36","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2306.02601","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2306.02601","pdf_url":"https://arxiv.org/pdf/2306.02601","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2306.02601","doi":"https://doi.org/10.48550/arxiv.2306.02601","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2306.02601","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2306.02601","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2306.02601","pdf_url":"https://arxiv.org/pdf/2306.02601","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":null,"license_id":null,"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/G1154700068","display_name":"CAREER: Nonconvex Optimization for Statistical Estimation and Learning: Conditioning, Dynamics, and Nonsmoothness","funder_award_id":"2047637","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1906418360","display_name":"TRIPODS: Algorithms for Data Science: Complexity, Scalability, and Robustness.","funder_award_id":"1740551","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2647087871","display_name":null,"funder_award_id":"814639","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3638401173","display_name":"Collaboration on the Theoretical Foundations of Deep Learning","funder_award_id":"2031883","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3744848179","display_name":"AI Institute for Learning-Enabled Optimization at Scale (TILOS)","funder_award_id":"2112665","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4275346382","display_name":"Collaborative Research: Robust Deep Learning in Real Physical Space: Generalization, Scalability, and Credibility","funder_award_id":"2134209","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6103245434","display_name":"CAREER: Structure, Complexity, and Conditioning in Nonsmooth Optimization","funder_award_id":"1651851","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/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7133200719.pdf","grobid_xml":"https://content.openalex.org/works/W7133200719.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3089293092","https://openalex.org/W2962712496","https://openalex.org/W2896222303","https://openalex.org/W3122339903","https://openalex.org/W2962916883","https://openalex.org/W4414755698","https://openalex.org/W2945238055","https://openalex.org/W4321392927","https://openalex.org/W3007118755","https://openalex.org/W2963794891"],"abstract_inverted_index":{"Modern":[0],"machine":[1],"learning":[2],"paradigms,":[3],"such":[4],"as":[5,55],"deep":[6],"learning,":[7],"occur":[8],"in":[9,70,89],"or":[10],"close":[11],"to":[12,83],"the":[13,17,26,40,45,50,56,79],"interpolation":[14,41],"regime,":[15],"wherein":[16],"number":[18,27],"of":[19,28,95],"model":[20],"parameters":[21],"is":[22],"much":[23,91],"larger":[24],"than":[25],"data":[29],"samples.":[30],"In":[31,73],"this":[32],"work,":[33],"we":[34,98],"propose":[35],"a":[36,63,68,90,112],"regularity":[37],"condition":[38,102],"within":[39],"regime":[42],"which":[43],"endows":[44],"stochastic":[46,80],"gradient":[47,58,66,81],"method":[48,82],"with":[49,111],"same":[51],"worst-case":[52],"iteration":[53],"complexity":[54],"deterministic":[57],"method,":[59],"while":[60],"using":[61],"only":[62],"single":[64],"sampled":[65],"(or":[67],"minibatch)":[69],"each":[71],"iteration.":[72],"contrast,":[74],"all":[75],"existing":[76],"guarantees":[77],"require":[78],"take":[84],"small":[85],"steps,":[86],"thereby":[87],"resulting":[88],"slower":[92],"linear":[93,113],"rate":[94],"convergence.":[96],"Finally,":[97],"demonstrate":[99],"that":[100],"our":[101],"holds":[103],"when":[104],"training":[105],"sufficiently":[106],"wide":[107],"feedforward":[108],"neural":[109],"networks":[110],"output":[114],"layer.":[115]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-10-15T10:00:46.086208","created_date":"2026-03-03T00:00:00"}