{"id":"https://openalex.org/W4412969780","doi":"https://doi.org/10.1090/mcom/4124","title":"Truncated kernel stochastic gradient descent on spheres","display_name":"Truncated kernel stochastic gradient descent on spheres","publication_year":2025,"publication_date":"2025-07-18","ids":{"openalex":"https://openalex.org/W4412969780","doi":"https://doi.org/10.1090/mcom/4124"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/4124","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4124","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","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/A5060022875","display_name":"Jiaming Bai","orcid":"https://orcid.org/0000-0003-0293-3237"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jinhui Bai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101499716","display_name":"Lei Shi","orcid":"https://orcid.org/0009-0004-0649-5443"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lei Shi","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":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17677183,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"95","issue":"361","first_page":"2409","last_page":"2480"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9952999949455261,"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"}},"topics":[{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9952999949455261,"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"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9951000213623047,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9947999715805054,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.7250098586082458},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6259089708328247},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5648728609085083},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4991884231567383},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.4367119073867798},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3874243497848511},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3664918839931488},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.24479982256889343},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14723923802375793}],"concepts":[{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.7250098586082458},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6259089708328247},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5648728609085083},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4991884231567383},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.4367119073867798},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3874243497848511},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3664918839931488},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.24479982256889343},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14723923802375793},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/4124","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4124","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W33346649","https://openalex.org/W333643410","https://openalex.org/W567568486","https://openalex.org/W1149783239","https://openalex.org/W1837874438","https://openalex.org/W1847890728","https://openalex.org/W1994616650","https://openalex.org/W1996652862","https://openalex.org/W2012501405","https://openalex.org/W2025343193","https://openalex.org/W2034978228","https://openalex.org/W2040314635","https://openalex.org/W2042354455","https://openalex.org/W2047278710","https://openalex.org/W2052920194","https://openalex.org/W2059571389","https://openalex.org/W2087789467","https://openalex.org/W2095800081","https://openalex.org/W2102201073","https://openalex.org/W2150621701","https://openalex.org/W2158781299","https://openalex.org/W2509171749","https://openalex.org/W2568875900","https://openalex.org/W2745428954","https://openalex.org/W2799404641","https://openalex.org/W2884695109","https://openalex.org/W2950055521","https://openalex.org/W2950678188","https://openalex.org/W2955094427","https://openalex.org/W2962942717","https://openalex.org/W2964017994","https://openalex.org/W2964033869","https://openalex.org/W2964198904","https://openalex.org/W2968350215","https://openalex.org/W3037531075","https://openalex.org/W3043072433","https://openalex.org/W3081731186","https://openalex.org/W3122053438","https://openalex.org/W3140364814","https://openalex.org/W3166324261","https://openalex.org/W3168833755","https://openalex.org/W3183420805","https://openalex.org/W4211030719","https://openalex.org/W4292023735","https://openalex.org/W4292058084","https://openalex.org/W4388321579","https://openalex.org/W4391225489","https://openalex.org/W4393093174","https://openalex.org/W4396661659","https://openalex.org/W4415799054"],"related_works":["https://openalex.org/W2089892314","https://openalex.org/W1603091392","https://openalex.org/W4386075310","https://openalex.org/W2095626363","https://openalex.org/W2169565408","https://openalex.org/W2127229869","https://openalex.org/W3123056048","https://openalex.org/W2129978300","https://openalex.org/W2150638158","https://openalex.org/W2121506664"],"abstract_inverted_index":{"Inspired":[0],"by":[1,34,62,73,332],"the":[2,9,42,45,58,76,86,105,110,120,279,318,322,333,337,341,345,348,353,360,363,376,386],"structure":[3,121],"of":[4,41,44,85,104,114,122,336,344,347,357,362,378],"spherical":[5,24,123],"harmonics,":[6],"we":[7,118],"propose":[8],"truncated":[10],"kernel":[11,56,115,139,354],"stochastic":[12,46],"gradient":[13,47],"descent":[14],"(T-kernel":[15],"SGD)":[16],"algorithm":[17,88],"with":[18,352],"a":[19,30,38,49,99],"least-square":[20],"loss":[21],"function":[22,339],"for":[23,278],"data":[25],"fitting.":[26],"T-kernel":[27,63,129,142,379],"SGD":[28,36,64,143],"introduces":[29],"novel":[31],"regularization":[32,59],"strategy":[33,60],"implementing":[35],"through":[37],"closed-form":[39],"solution":[40],"projection":[43],"in":[48,68,390],"low-dimensional":[50],"subspace.":[51],"In":[52],"contrast":[53],"to":[54,125,138,274],"traditional":[55],"SGD,":[57,130],"implemented":[61],"is":[65,89,330],"more":[66],"effective":[67],"balancing":[69],"bias":[70],"and":[71,134,212,340],"variance":[72],"dynamically":[74],"adjusting":[75],"hypothesis":[77],"space":[78,324],"during":[79],"iterations.":[80],"The":[81,381],"most":[82],"significant":[83],"advantage":[84],"proposed":[87],"that":[90],"it":[91],"can":[92,313],"achieve":[93,275],"theoretically":[94],"optimal":[95,276,319],"convergence":[96,377],"rates":[97,277],"using":[98],"constant":[100],"step":[101],"size":[102],"(independent":[103],"sample":[106],"size)":[107],"while":[108],"overcoming":[109],"inherent":[111],"saturation":[112],"problem":[113],"SGD.":[116,140,380],"Additionally,":[117],"leverage":[119],"polynomials":[124],"derive":[126],"an":[127],"equivalent":[128],"significantly":[131],"reducing":[132],"storage":[133,273],"computational":[135,210],"costs":[136],"compared":[137],"Typically,":[141],"requires":[144],"only":[145],"<inline-formula":[146,213,283],"content-type=\"math/mathml\">":[147,214,284],"<mml:math":[148,215,285],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[149,216,286],"alttext=\"script":[150,217],"upper":[151,218],"O":[152,219],"left-parenthesis":[153,220],"n":[154,221],"Superscript":[155,222],"1":[156,163,228],"plus":[157],"StartFraction":[158,223],"d":[159,161,224,226],"Over":[160,225],"minus":[162,227],"EndFraction":[164,229],"epsilon":[165,230,289],"Baseline":[166,231],"right-parenthesis\">":[167,232],"<mml:semantics>":[168,233,293],"<mml:mrow>":[169,186,234,249,294],"<mml:mrow":[170,180,235,245],"class=\"MJX-TeXAtom-ORD\">":[171,181,236,246],"<mml:mi":[172,237],"class=\"MJX-tex-caligraphic\"":[173,238],"mathvariant=\"script\">O</mml:mi>":[174,239],"</mml:mrow>":[175,192,197,201,240,255,260,264,305],"<mml:mo":[176,199,241,262],"stretchy=\"false\">(</mml:mo>":[177,242],"<mml:msup>":[178,243],"<mml:mi>n</mml:mi>":[179,244],"<mml:mn>1</mml:mn>":[182,191,254,302],"<mml:mo>+</mml:mo>":[183],"<mml:mfrac>":[184,247,301],"<mml:mi>d</mml:mi>":[185,187,248,250],"<mml:mo>":[188,251],"\u2212":[189,252],"</mml:mo>":[190,253],"</mml:mfrac>":[193,256,304],"<mml:mi>":[194,257,297],"\u03f5":[195,258,298],"</mml:mi>":[196,259,299],"</mml:msup>":[198,261],"stretchy=\"false\">)</mml:mo>":[200,263],"<mml:annotation":[202,265,306],"encoding=\"application/x-tex\">\\mathcal":[203,266],"{O}(n^{1+\\frac":[204],"{d}{d-1}\\epsilon":[205,268],"})</mml:annotation>":[206,269],"</mml:semantics>":[207,270,310],"</mml:math>":[208,271,311],"</inline-formula>":[209,272,312],"complexity":[211],"{O}(n^{\\frac":[267],"d-dimensional":[280],"sphere,":[281],"where":[282],"alttext=\"0":[287],"greater-than":[288,290],"one":[291],"half\">":[292],"<mml:mn>0</mml:mn>":[295],"<mml:mo>&gt;</mml:mo>":[296,300],"<mml:mn>2</mml:mn>":[303],"encoding=\"application/x-tex\">0&gt;\\epsilon":[307],"&gt;\\frac":[308],"{1}{2}</mml:annotation>":[309],"be":[314],"arbitrarily":[315],"small":[316],"if":[317],"fitting":[320],"or":[321],"underlying":[323],"possesses":[325],"sufficient":[326],"regularity.":[327],"This":[328],"regularity":[329],"determined":[331],"smoothness":[334],"parameter":[335],"objective":[338],"decaying":[342],"rate":[343],"eigenvalues":[346],"integral":[349],"operator":[350],"associated":[351],"function,":[355],"both":[356],"which":[358],"reflect":[359],"difficulty":[361],"estimation":[364],"problem.":[365],"Our":[366],"main":[367],"results":[368],"quantitatively":[369],"characterize":[370],"how":[371],"this":[372,391],"prior":[373],"information":[374],"influences":[375],"numerical":[382],"experiments":[383],"further":[384],"validate":[385],"theoretical":[387],"findings":[388],"presented":[389],"paper.":[392]},"counts_by_year":[],"updated_date":"2026-06-13T06:17:32.689207","created_date":"2025-08-05T00:00:00"}
