{"id":"https://openalex.org/W7162326533","doi":"https://doi.org/10.48550/arxiv.2605.23871","title":"Move on Muon : A Hamiltonian probability gradient flow perspective of Muon optimizer","display_name":"Move on Muon : A Hamiltonian probability gradient flow perspective of Muon optimizer","publication_year":2026,"publication_date":"2026-05-22","ids":{"openalex":"https://openalex.org/W7162326533","doi":"https://doi.org/10.48550/arxiv.2605.23871"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.23871","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.23871","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.2605.23871","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136972644","display_name":"Aratrika Mustafi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mustafi, Aratrika","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136940750","display_name":"Soumya Mukherjee","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mukherjee, Soumya","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109582233","display_name":"Bharath K. Sriperumbudur","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sriperumbudur, Bharath K.","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":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/T12579","display_name":"Muon and positron interactions and applications","score":0.48980000615119934,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12579","display_name":"Muon and positron interactions and applications","score":0.48980000615119934,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10921","display_name":"Neutrino Physics Research","score":0.06809999793767929,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy 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/T10093","display_name":"Nuclear physics research studies","score":0.0560000017285347,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5454000234603882},{"id":"https://openalex.org/keywords/balanced-flow","display_name":"Balanced flow","score":0.5284000039100647},{"id":"https://openalex.org/keywords/muon","display_name":"Muon","score":0.4564000070095062},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.4101000130176544},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.36800000071525574},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.3433000147342682},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.32440000772476196}],"concepts":[{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5454000234603882},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.5284000039100647},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49380001425743103},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4779999852180481},{"id":"https://openalex.org/C205334942","wikidata":"https://www.wikidata.org/wiki/Q3151","display_name":"Muon","level":2,"score":0.4564000070095062},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.4101000130176544},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.36800000071525574},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35089999437332153},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3433000147342682},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.32989999651908875},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.32440000772476196},{"id":"https://openalex.org/C173386949","wikidata":"https://www.wikidata.org/wiki/Q192735","display_name":"Inertial frame of reference","level":2,"score":0.30230000615119934},{"id":"https://openalex.org/C40375134","wikidata":"https://www.wikidata.org/wiki/Q1303846","display_name":"Eikonal equation","level":2,"score":0.289000004529953},{"id":"https://openalex.org/C152991086","wikidata":"https://www.wikidata.org/wiki/Q1225362","display_name":"Position and momentum space","level":2,"score":0.28189998865127563},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.273499995470047},{"id":"https://openalex.org/C136864674","wikidata":"https://www.wikidata.org/wiki/Q477921","display_name":"Hamiltonian mechanics","level":3,"score":0.26899999380111694},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.26460000872612},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.2628999948501587},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2526000142097473},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.2515999972820282}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.23871","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.23871","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.2605.23871","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.23871","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,70,164,211],"develop":[1],"a":[2,41,56,78,93,130,148,246],"gradient":[3,39],"flow":[4,142,250],"on":[5,12,137,241],"the":[6,24,33,38,46,51,60,67,87,104,113,118,159,173,179,188,208,214,217,228,235],"space":[7],"of":[8,23,40,45,86,99,121,216,224],"probability":[9,84,135,151,249],"measures":[10],"defined":[11],"matrix-valued":[13],"parameters":[14],"induced":[15,157],"by":[16,96,158],"regularized":[17,34,160],"Muon,":[18],"an":[19,166],"analytically":[20],"smoothed":[21],"version":[22],"idealized":[25],"Muon":[26,53,76,161,190,248],"optimizer.":[27],"The":[28,140],"key":[29],"observation":[30],"is":[31,37,156],"that":[32,172],"orthogonalization":[35],"map":[36],"smooth":[42,253],"Fenchel-dual":[43],"smoothing":[44],"nuclear":[47],"norm.":[48],"This":[49],"identifies":[50],"(regularized)":[52],"update":[54,61],"as":[55,66],"mirror/prox":[57],"step":[58,122],"in":[59],"variable,":[62],"with":[63],"momentum":[64],"acting":[65],"dual":[68],"coordinate.":[69],"use":[71],"this":[72,109],"structure":[73],"to":[74,82,129,146,237,252],"lift":[75],"from":[77],"single":[79],"matrix":[80,243],"parameter":[81],"finite-particle":[83,114],"objectives":[85],"form":[88],"$J(\u03c1)=R\\left(\\int":[89],"F":[90],"d":[91],"\u03c1\\right)$,":[92],"setting":[94],"motivated":[95],"mean-field":[97,132,218],"descriptions":[98],"neural-network":[100],"training,":[101],"and":[102,124,126,196,202,221],"derive":[103,112],"inertial":[105,119,189],"continuous-time":[106,115],"limit.":[107],"Using":[108],"structure,":[110],"we":[111,199,233],"limit":[116,219],"under":[117,192],"scaling":[120],"size":[123],"momentum,":[125],"then":[127],"pass":[128],"phase-space":[131],"equation":[133,220],"over":[134],"laws":[136],"parameter-momentum":[138],"pairs.":[139],"resulting":[141],"can":[143],"be":[144,147,185],"shown":[145],"damped":[149],"Hamiltonian":[150,168,174],"dynamics":[152],"whose":[153],"kinetic":[154],"energy":[155,175],"mirror":[162],"potential.":[163],"prove":[165],"exact":[167],"dissipation":[169],"identity,":[170],"showing":[171],"decreases":[176],"monotonically.":[177],"While":[178],"target":[180],"objective":[181,209],"itself":[182],"need":[183],"not":[184],"monotone":[186],"along":[187],"dynamics,":[191],"additional":[193],"gradient-dominance,":[194],"bounded-momentum,":[195],"curvature/alignment":[197],"assumptions,":[198],"obtain":[200],"continuous":[201],"discrete-time":[203],"exponential":[204],"convergence":[205],"rates":[206],"for":[207,227],"gap.":[210],"also":[212],"study":[213],"well-posedness":[215],"establish":[222],"propagation":[223],"chaos":[225],"guarantees":[226],"interacting":[229],"particle":[230],"system.":[231],"Finally,":[232],"extend":[234],"formulation":[236],"Hilbert-valued":[238],"feature":[239],"maps":[240],"product":[242],"spaces,":[244],"yielding":[245],"blockwise":[247],"applicable":[251],"transformer":[254],"mixture-of-experts":[255],"models.":[256]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-26T00:00:00"}