{"id":"https://openalex.org/W3166627127","doi":"https://doi.org/10.1007/s00332-023-09992-0","title":"Stochastic Gradient Descent with Noise of Machine Learning Type Part II: Continuous Time Analysis","display_name":"Stochastic Gradient Descent with Noise of Machine Learning Type Part II: Continuous Time Analysis","publication_year":2023,"publication_date":"2023-11-15","ids":{"openalex":"https://openalex.org/W3166627127","doi":"https://doi.org/10.1007/s00332-023-09992-0","mag":"3166627127"},"language":"en","primary_location":{"id":"doi:10.1007/s00332-023-09992-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00332-023-09992-0","pdf_url":null,"source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024215146","display_name":"Stephan Wojtowytsch","orcid":"https://orcid.org/0000-0003-3766-5332"},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Stephan Wojtowytsch","raw_affiliation_strings":["Department of Mathematics, University of Pittsburgh, Thackeray Hall, Pittsburgh, PA, 15213, USA"],"raw_orcid":"https://orcid.org/0000-0003-3766-5332","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Pittsburgh, Thackeray Hall, Pittsburgh, PA, 15213, USA","institution_ids":["https://openalex.org/I170201317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5024215146"],"corresponding_institution_ids":["https://openalex.org/I170201317"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.5337,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.85427784,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"34","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9987000226974487,"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/T10320","display_name":"Neural Networks and Applications","score":0.9987000226974487,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.8062487840652466},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.7660848498344421},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.6661984920501709},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.595305323600769},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4891276955604553},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.48580479621887207},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47843578457832336},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44564545154571533},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4234533905982971},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.4151313006877899},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36835265159606934},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.30566173791885376},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19789227843284607},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07903605699539185}],"concepts":[{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.8062487840652466},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.7660848498344421},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.6661984920501709},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.595305323600769},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4891276955604553},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.48580479621887207},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47843578457832336},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44564545154571533},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4234533905982971},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.4151313006877899},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36835265159606934},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.30566173791885376},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19789227843284607},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07903605699539185},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00332-023-09992-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00332-023-09992-0","pdf_url":null,"source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":68,"referenced_works":["https://openalex.org/W138734637","https://openalex.org/W171640559","https://openalex.org/W1580561995","https://openalex.org/W1866311589","https://openalex.org/W1974782455","https://openalex.org/W1983054352","https://openalex.org/W1994616650","https://openalex.org/W1995918022","https://openalex.org/W2071048859","https://openalex.org/W2110309295","https://openalex.org/W2137694675","https://openalex.org/W2167433878","https://openalex.org/W2173398862","https://openalex.org/W2245200779","https://openalex.org/W2263490141","https://openalex.org/W2550039210","https://openalex.org/W2617242334","https://openalex.org/W2768267830","https://openalex.org/W2770482887","https://openalex.org/W2790626470","https://openalex.org/W2801466482","https://openalex.org/W2804386825","https://openalex.org/W2804589149","https://openalex.org/W2889046694","https://openalex.org/W2910207440","https://openalex.org/W2912811302","https://openalex.org/W2946052306","https://openalex.org/W2962809143","https://openalex.org/W2962839956","https://openalex.org/W2963069632","https://openalex.org/W2963095610","https://openalex.org/W2963433607","https://openalex.org/W2963729625","https://openalex.org/W2963959597","https://openalex.org/W2964072432","https://openalex.org/W2964106499","https://openalex.org/W2964286272","https://openalex.org/W2995824857","https://openalex.org/W3006064982","https://openalex.org/W3010825589","https://openalex.org/W3016883099","https://openalex.org/W3021722416","https://openalex.org/W3032534482","https://openalex.org/W3033360065","https://openalex.org/W3088659931","https://openalex.org/W3091965439","https://openalex.org/W3104967301","https://openalex.org/W3111778284","https://openalex.org/W3112337968","https://openalex.org/W3118431319","https://openalex.org/W3119368353","https://openalex.org/W3123802267","https://openalex.org/W3130584495","https://openalex.org/W3158775690","https://openalex.org/W3160865277","https://openalex.org/W3166125248","https://openalex.org/W3168222560","https://openalex.org/W3170832232","https://openalex.org/W3186379569","https://openalex.org/W4206251610","https://openalex.org/W4210956211","https://openalex.org/W4242800525","https://openalex.org/W4285719527","https://openalex.org/W6600512042","https://openalex.org/W6600737549","https://openalex.org/W6600862597","https://openalex.org/W6601033504","https://openalex.org/W6763039812"],"related_works":["https://openalex.org/W2115886818","https://openalex.org/W3118431319","https://openalex.org/W3004700632","https://openalex.org/W2466106906","https://openalex.org/W3177888558","https://openalex.org/W2069187387","https://openalex.org/W3027810930","https://openalex.org/W2895097035","https://openalex.org/W4206903459","https://openalex.org/W2754816816"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}