{"id":"https://openalex.org/W7225655361","doi":"https://doi.org/10.5281/zenodo.24069894","title":"Heavy-ball momentum and batch size in streaming least squares: matching bounds on the tuned speedup over SGD","display_name":"Heavy-ball momentum and batch size in streaming least squares: matching bounds on the tuned speedup over SGD","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225655361","doi":"https://doi.org/10.5281/zenodo.24069894"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24069894","doi":"https://doi.org/10.5281/zenodo.24069894","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24069894","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24069894","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041315596","display_name":"Yitzchak Shmalo","orcid":"https://orcid.org/0000-0002-2886-3049","observed_orcids":["https://orcid.org/0000-0002-2886-3049"]},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Shmalo, Yitzchak","raw_affiliation_strings":["Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5041315596"],"corresponding_institution_ids":["https://openalex.org/I197251160"],"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":0.9980000257492065,"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":0.9980000257492065,"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":0.0003000000142492354,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/heavy-ball-momentum","display_name":"heavy-ball momentum","score":0.8370000123977661},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"stochastic gradient descent","score":0.8820000290870667},{"id":"https://openalex.org/keywords/mini-batch-size","display_name":"mini-batch size","score":0.9350000023841858},{"id":"https://openalex.org/keywords/spectral-radius","display_name":"spectral radius","score":0.5519999861717224},{"id":"https://openalex.org/keywords/condition-number","display_name":"condition number","score":0.6050000190734863},{"id":"https://openalex.org/keywords/critical-damping","display_name":"critical damping","score":0.7960000038146973},{"id":"https://openalex.org/keywords/mean-square-stability","display_name":"mean square stability","score":0.753000020980835},{"id":"https://openalex.org/keywords/renewal-equation","display_name":"renewal equation","score":0.8820000290870667}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7182999849319458},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7009000182151794},{"id":"https://openalex.org/C60718061","wikidata":"https://www.wikidata.org/wiki/Q1414747","display_name":"Momentum (technical analysis)","level":2,"score":0.6919999718666077},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.6087999939918518},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5778999924659729},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5342000126838684},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5335000157356262},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5318999886512756},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.504800021648407},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4311999976634979},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.4140999913215637},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.4133000075817108},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41100001335144043},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.31690001487731934},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3021000027656555},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.29919999837875366},{"id":"https://openalex.org/C187166803","wikidata":"https://www.wikidata.org/wiki/Q2835831","display_name":"Streaming algorithm","level":3,"score":0.296099990606308},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.295199990272522},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.27480000257492065},{"id":"https://openalex.org/C109663097","wikidata":"https://www.wikidata.org/wiki/Q182453","display_name":"Adiabatic process","level":2,"score":0.2703999876976013},{"id":"https://openalex.org/C157524613","wikidata":"https://www.wikidata.org/wiki/Q2828883","display_name":"Fine-tuning","level":2,"score":0.26030001044273376},{"id":"https://openalex.org/C2777894999","wikidata":"https://www.wikidata.org/wiki/Q4781758","display_name":"Approx","level":2,"score":0.2590999901294708},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.25540000200271606},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2515000104904175}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24069894","doi":"https://doi.org/10.5281/zenodo.24069894","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24069894","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.24069895","doi":"https://doi.org/10.5281/zenodo.24069895","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24069895","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"doi:10.5281/zenodo.24069894","doi":"https://doi.org/10.5281/zenodo.24069894","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24069894","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7133190866","https://openalex.org/W4401445256","https://openalex.org/W7093641564","https://openalex.org/W7225290145","https://openalex.org/W3166400281","https://openalex.org/W4403963669","https://openalex.org/W7165203771","https://openalex.org/W4390898077","https://openalex.org/W7225640385","https://openalex.org/W2508844316"],"abstract_inverted_index":{"We":[0],"consider":[1],"realizable":[2],"streaming":[3],"least":[4],"squares":[5],"with":[6,21,27],"Gaussian":[7],"covariates":[8],"$x\\sim":[9],"N(0,H)$":[10],"and":[11,16,31,91,111,154],"mini-batches":[12],"of":[13,40,51,58,120],"size":[14,30],"$B$,":[15],"compare":[17],"stochastic":[18,23],"heavy-ball":[19],"momentum":[20,32],"plain":[22],"gradient":[24],"descent,":[25],"each":[26],"its":[28],"step":[29],"chosen":[33],"to":[34,85,107,132],"minimise":[35],"the":[36,41,48,56,59,88,93,113,125,144],"spectral":[37,61],"radius":[38],"$\\rho$":[39],"exact":[42,140],"second-moment":[43],"recursion.":[44],"Writing":[45],"$\\kappa=h_{\\max}/h_{\\min}$":[46],"for":[47,143,157],"condition":[49,156],"number":[50],"$H$,":[52],"we":[53],"prove":[54],"that":[55,128],"ratio":[57],"optimal":[60],"gaps":[62],"satisfies":[63],"\\[":[64],"\\max\\Bigl(1,\\tfrac1{16}\\,m\\Bigr)\\;\\le\\;\\frac{1-\\rho_{\\mathrm{HB}}^*}{1-\\rho_{\\mathrm{SGD}}^*}\\;\\le\\;\\frac{128}{3}\\,m,":[65],"\\qquad":[66],"m=\\min\\Bigl(\\max\\Bigl(1,\\frac{Bh_{\\max}}{\\operatorname{tr}":[67],"H}\\Bigr),\\sqrt\\kappa\\Bigr).":[68],"\\]":[69],"Momentum":[70],"therefore":[71],"gains":[72,81,92],"at":[73,124],"most":[74],"a":[75,82,133,151],"constant":[76],"factor":[77,83,95],"while":[78],"$B\\lesssim\\operatorname{tr}":[79],"H/h_{\\max}$,":[80],"proportional":[84],"$B$":[86],"in":[87],"intermediate":[89],"range,":[90],"full":[94],"$\\sqrt\\kappa$":[96],"once":[97],"$B\\gtrsim\\sqrt\\kappa\\,\\operatorname{tr}":[98],"H/h_{\\max}$.":[99],"The":[100],"upper":[101],"bound":[102],"$1-\\rho_{\\mathrm{HB}}^*\\le8\\min(Bh_{\\min}/\\operatorname{tr}":[103],"H,1/\\sqrt\\kappa)$":[104],"is":[105,116],"due":[106],"Morwani,":[108],"Meterez,":[109],"Nair":[110],"Kakade;":[112],"new":[114],"ingredient":[115],"an":[117,139],"explicit":[118],"choice":[119],"parameters,":[121],"critical":[122],"damping":[123],"smallest":[126],"eigenvalue,":[127],"attains":[129],"it":[130],"up":[131],"constant.":[134],"Both":[135],"directions":[136],"rest":[137],"on":[138],"renewal":[141],"equation":[142],"diagonal":[145],"second":[146],"moments,":[147],"which":[148],"also":[149],"gives":[150],"closed-form":[152],"necessary":[153],"sufficient":[155],"mean-square":[158],"stability.":[159]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}
