{"id":"https://openalex.org/W7165358966","doi":"https://doi.org/10.48550/arxiv.2606.19876","title":"Global Convergence of Gradient Descent for Score Matching in Gaussian Mixtures via Reverse Fisher Divergence","display_name":"Global Convergence of Gradient Descent for Score Matching in Gaussian Mixtures via Reverse Fisher Divergence","publication_year":2026,"publication_date":"2026-06-18","ids":{"openalex":"https://openalex.org/W7165358966","doi":"https://doi.org/10.48550/arxiv.2606.19876"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.19876","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.19876","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.19876","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135847823","display_name":"Alexander Tyurin","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tyurin, Alexander","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5135847823"],"corresponding_institution_ids":[],"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":0.7021999955177307,"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":0.7021999955177307,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.08129999786615372,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.0414000004529953,"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/gaussian","display_name":"Gaussian","score":0.6553000211715698},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.5485000014305115},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5320000052452087},{"id":"https://openalex.org/keywords/mixture-model","display_name":"Mixture model","score":0.5178999900817871},{"id":"https://openalex.org/keywords/fisher-information","display_name":"Fisher information","score":0.5160999894142151},{"id":"https://openalex.org/keywords/initialization","display_name":"Initialization","score":0.5023000240325928},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4837000072002411},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4106999933719635},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.3919999897480011},{"id":"https://openalex.org/keywords/students-t-distribution","display_name":"Student's t-distribution","score":0.3808000087738037}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7233999967575073},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6553000211715698},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.5485000014305115},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5378000140190125},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5320000052452087},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.5178999900817871},{"id":"https://openalex.org/C29406490","wikidata":"https://www.wikidata.org/wiki/Q1420659","display_name":"Fisher information","level":2,"score":0.5160999894142151},{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.5023000240325928},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4837000072002411},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4106999933719635},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3919999897480011},{"id":"https://openalex.org/C49232408","wikidata":"https://www.wikidata.org/wiki/Q576072","display_name":"Student's t-distribution","level":4,"score":0.3808000087738037},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37229999899864197},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36329999566078186},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.3547999858856201},{"id":"https://openalex.org/C93959086","wikidata":"https://www.wikidata.org/wiki/Q6888345","display_name":"Model selection","level":2,"score":0.34459999203681946},{"id":"https://openalex.org/C51267290","wikidata":"https://www.wikidata.org/wiki/Q5527848","display_name":"Gaussian random field","level":4,"score":0.33880001306533813},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.32839998602867126},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.32339999079704285},{"id":"https://openalex.org/C83282275","wikidata":"https://www.wikidata.org/wiki/Q7435350","display_name":"Scoring algorithm","level":2,"score":0.3181000053882599},{"id":"https://openalex.org/C132878287","wikidata":"https://www.wikidata.org/wiki/Q1671727","display_name":"Inverse Gaussian distribution","level":3,"score":0.3151000142097473},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.30300000309944153},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.2980000078678131},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.29649999737739563},{"id":"https://openalex.org/C202021718","wikidata":"https://www.wikidata.org/wiki/Q7051759","display_name":"Normal-inverse Gaussian distribution","level":5,"score":0.2946000099182129},{"id":"https://openalex.org/C177384507","wikidata":"https://www.wikidata.org/wiki/Q1149000","display_name":"Multivariate normal distribution","level":3,"score":0.2912999987602234},{"id":"https://openalex.org/C102094743","wikidata":"https://www.wikidata.org/wiki/Q133871","display_name":"Normal distribution","level":2,"score":0.27619999647140503},{"id":"https://openalex.org/C164752517","wikidata":"https://www.wikidata.org/wiki/Q5570875","display_name":"Global optimization","level":2,"score":0.274399995803833},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.2651999890804291},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.2621999979019165},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.25850000977516174},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.2565999925136566},{"id":"https://openalex.org/C51432778","wikidata":"https://www.wikidata.org/wiki/Q1259145","display_name":"Independent component analysis","level":2,"score":0.2538999915122986},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.25220000743865967}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.19876","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.19876","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.19876","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.19876","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.47968047857284546,"display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"score":[1],"matching":[2],"problem":[3],"is":[4,25,35,80,117,124,156],"a":[5,118,125,158,168,174,213,229],"central":[6],"training":[7],"objective":[8,56,105],"in":[9,49,103,205],"modern":[10],"generative":[11],"modeling,":[12],"diffusion":[13],"models,":[14,18],"fitting":[15,94],"unnormalized":[16],"statistical":[17],"and":[19,61,98,121,132,162,173,195],"inverse":[20],"problems.":[21],"A":[22],"standard":[23],"approach":[24],"to":[26,39,59,84,107,150],"minimize":[27],"the":[28,33,40,73,78,85,104,114,122,137,148,151,154,178,201,218,224,236],"forward":[29,237],"Fisher":[30,75,226,238],"divergence,":[31,76],"where":[32,77,153],"expectation":[34,79],"taken":[36,81],"with":[37,82,129,183],"respect":[38,83],"teacher":[41,115,155,193],"distribution.":[42,87],"However,":[43],"recent":[44],"results":[45],"show":[46,99],"that":[47,100,223],"even":[48],"simple":[50],"Gaussian":[51,95,120,126,159],"mixture":[52,96,127,160],"model":[53,128,161],"settings,":[54],"this":[55,66,101],"can":[57],"lead":[58],"undesirable":[60],"initialization-dependent":[62],"convergence":[63,139,165],"behavior.":[64],"In":[65,181],"paper,":[67],"we":[68,135,146,196],"study":[69],"an":[70],"alternative":[71],"objective:":[72],"reverse":[74,225],"student":[86,123,187,202],"We":[88],"analyze":[89],"gradient":[90,219],"descent":[91,220],"(GD)":[92],"for":[93],"models":[97],"change":[102],"leads":[106],"significantly":[108],"better":[109],"optimization":[110,233],"properties.":[111],"First,":[112],"when":[113],"distribution":[116,203],"single":[119],"fixed":[130],"weights":[131],"identity":[133],"covariances,":[134],"prove":[136,163],"global":[138,164,169],"of":[140,217],"GD":[141],"from":[142],"arbitrary":[143],"initializations.":[144],"Second,":[145],"extend":[147],"analysis":[149,216],"case":[152],"also":[157],"guarantees":[166],"under":[167,199],"random":[170],"initialization":[171],"scheme":[172],"$\\widetilde\u03a9(1)$-separation":[175],"assumption":[176],"on":[177,212],"target":[179],"means.":[180],"particular,":[182],"high":[184],"probability,":[185],"each":[186],"component":[188],"converges":[189,204],"near":[190],"its":[191],"closest":[192],"component,":[194],"provide":[197],"conditions":[198],"which":[200],"total":[206],"variation":[207],"distance.":[208],"Our":[209],"proofs":[210],"rely":[211],"new":[214],"Lyapunov-based":[215],"dynamics,":[221],"showing":[222],"divergence":[227],"has":[228],"much":[230],"more":[231],"favorable":[232],"landscape":[234],"than":[235],"divergence.":[239]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-20T00:00:00"}