{"id":"https://openalex.org/W7128798348","doi":"https://doi.org/10.48550/arxiv.2602.12257","title":"On the implicit regularization of Langevin dynamics with projected noise","display_name":"On the implicit regularization of Langevin dynamics with projected noise","publication_year":2026,"publication_date":"2026-02-12","ids":{"openalex":"https://openalex.org/W7128798348","doi":"https://doi.org/10.48550/arxiv.2602.12257"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.12257","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065480740","display_name":"Govind Menon","orcid":"https://orcid.org/0000-0002-9953-1615"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Menon, Govind","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047757466","display_name":"Austin J. Stromme","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stromme, Austin J.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5005013356","display_name":"Adrien Vacher","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vacher, Adrien","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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.682699978351593,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.682699978351593,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.05820000171661377,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.04149999842047691,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/langevin-dynamics","display_name":"Langevin dynamics","score":0.7666000127792358},{"id":"https://openalex.org/keywords/langevin-equation","display_name":"Langevin equation","score":0.5719000101089478},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.5335000157356262},{"id":"https://openalex.org/keywords/brownian-dynamics","display_name":"Brownian dynamics","score":0.5281999707221985},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.513700008392334},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5029000043869019},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5016999840736389},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.4514000117778778},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.4327000081539154}],"concepts":[{"id":"https://openalex.org/C2780004032","wikidata":"https://www.wikidata.org/wiki/Q6485978","display_name":"Langevin dynamics","level":2,"score":0.7666000127792358},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5845000147819519},{"id":"https://openalex.org/C2777577648","wikidata":"https://www.wikidata.org/wiki/Q584537","display_name":"Langevin equation","level":2,"score":0.5719000101089478},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5335000157356262},{"id":"https://openalex.org/C130603088","wikidata":"https://www.wikidata.org/wiki/Q4976526","display_name":"Brownian dynamics","level":3,"score":0.5281999707221985},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.513700008392334},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5029000043869019},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5016999840736389},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47769999504089355},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.4514000117778778},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.43689998984336853},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.4327000081539154},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4099000096321106},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.3790999948978424},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.3702000081539154},{"id":"https://openalex.org/C5297727","wikidata":"https://www.wikidata.org/wiki/Q786970","display_name":"Autocorrelation","level":2,"score":0.3682999908924103},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.3447999954223633},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.3287000060081482},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.3183000087738037},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.3034999966621399},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.3012999892234802},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.30000001192092896},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.295199990272522},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2782000005245209},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C123954133","wikidata":"https://www.wikidata.org/wiki/Q7595775","display_name":"Stable process","level":3,"score":0.258899986743927},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.25769999623298645},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.25760000944137573},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.25049999356269836}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.12257","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.12257","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.12257","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.12257","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"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":[0,91],"study":[1],"Langevin":[2,60,70],"dynamics":[3,61,71],"with":[4,62,72,76],"noise":[5,64],"projected":[6,63],"onto":[7],"the":[8,26,48,57,83,88,100,108,113,117,121],"directions":[9],"orthogonal":[10],"to":[11,21,69,82],"an":[12,77],"isometric":[13],"group":[14,58,89,109],"action.":[15],"This":[16],"mathematical":[17],"model":[18],"is":[19,65],"introduced":[20],"shed":[22],"new":[23],"light":[24],"on":[25,30,107],"effects":[27],"of":[28,44,87,99,120],"symmetry":[29],"stochastic":[31],"gradient":[32],"descent":[33],"for":[34],"over-parametrized":[35],"models.":[36],"Our":[37],"main":[38],"result":[39,94],"identifies":[40],"a":[41,97,104],"novel":[42],"form":[43],"implicit":[45],"regularization:":[46],"when":[47],"initial":[49],"and":[50,111],"target":[51],"density":[52],"are":[53],"both":[54],"invariant":[55],"under":[56],"action,":[59],"equivalent":[66],"in":[67],"law":[68],"isotropic":[73],"diffusion":[74],"but":[75],"additional":[78,114],"drift":[79,115],"term":[80],"proportional":[81],"negative":[84],"log":[85],"volume":[86],"orbit.":[90],"prove":[92],"this":[93],"by":[95],"constructing":[96],"coupling":[98],"two":[101],"processes":[102],"via":[103],"third":[105],"process":[106],"itself,":[110],"identify":[112],"as":[116],"mean":[118],"curvature":[119],"orbits.":[122]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-02-14T00:00:00"}
