{"id":"https://openalex.org/W7160896462","doi":"https://doi.org/10.48550/arxiv.2605.09991","title":"Optimizer-Induced Mode Connectivity: From AdamW to Muon","display_name":"Optimizer-Induced Mode Connectivity: From AdamW to Muon","publication_year":2026,"publication_date":"2026-05-11","ids":{"openalex":"https://openalex.org/W7160896462","doi":"https://doi.org/10.48550/arxiv.2605.09991"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.09991","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.09991","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":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.2605.09991","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135954036","display_name":"Fangzhao Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Fangzhao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135953108","display_name":"Sungyoon Kim","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kim, Sungyoon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135945456","display_name":"Erica Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Erica","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135974545","display_name":"Yiqi Jiang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiang, Yiqi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5001436196","display_name":"Mert Pilanc\u0131","orcid":"https://orcid.org/0000-0002-0870-9992"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pilanci, Mert","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/T11804","display_name":"Quantum many-body systems","score":0.09449999779462814,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.09449999779462814,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.06710000336170197,"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/T10425","display_name":"Cold Atom Physics and Bose-Einstein Condensates","score":0.0649000033736229,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/disjoint-sets","display_name":"Disjoint sets","score":0.699999988079071},{"id":"https://openalex.org/keywords/traverse","display_name":"Traverse","score":0.6992999911308289},{"id":"https://openalex.org/keywords/mode","display_name":"Mode (computer interface)","score":0.635699987411499},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5058000087738037},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.5001000165939331},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.49720001220703125}],"concepts":[{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.699999988079071},{"id":"https://openalex.org/C176809094","wikidata":"https://www.wikidata.org/wiki/Q15401496","display_name":"Traverse","level":2,"score":0.6992999911308289},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.635699987411499},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.569599986076355},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5058000087738037},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.5001000165939331},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.49720001220703125},{"id":"https://openalex.org/C205334942","wikidata":"https://www.wikidata.org/wiki/Q3151","display_name":"Muon","level":2,"score":0.478300005197525},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.47589999437332153},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3822000026702881},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3785000145435333},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3677999973297119},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3328000009059906},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32109999656677246},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31679999828338623}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.09991","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.09991","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":"doi:10.48550/arxiv.2605.09991","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.09991","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":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":{"Mode":[0],"connectivity":[1,23,138],"has":[2],"been":[3],"widely":[4],"studied,":[5],"yet":[6],"the":[7,10,52],"role":[8],"of":[9],"optimizer":[11,45],"remains":[12],"underexplored.":[13],"We":[14,71],"revisit":[15],"it":[16],"through":[17],"optimizer-induced":[18,75],"implicit":[19],"regularization,":[20,91],"asking":[21],"how":[22,74],"behaves":[24],"when":[25],"restricted":[26],"to":[27,101],"solutions":[28,41],"constrained":[29],"by":[30,68,106],"a":[31,43,57,64,107,127],"given":[32],"optimizer.":[33],"For":[34],"two-layer":[35],"ReLU":[36],"networks,":[37],"we":[38,115],"show":[39],"that":[40],"from":[42],"single":[44],"--":[46,55],"AdamW,":[47],"Muon,":[48],"or":[49,87],"others":[50],"in":[51,93,112],"Lion-$\\mathcal{K}$":[53],"family":[54],"form":[56],"connected":[58],"set":[59],"at":[60,78],"sufficiently":[61],"large":[62,79],"width,":[63],"result":[65],"not":[66],"implied":[67],"prior":[69],"work.":[70],"then":[72],"characterize":[73],"regions":[76,83],"interact:":[77],"width":[80],"two":[81],"different":[82],"can":[84],"be":[85],"disjoint":[86],"overlap":[88],"depending":[89],"on":[90],"while":[92,123],"our":[94],"small-width":[95],"example":[96],"AdamW":[97],"and":[98],"Muon":[99],"converge":[100],"disconnected":[102],"zero-loss":[103],"components":[104],"separated":[105],"provable":[108],"loss":[109],"barrier.":[110],"Empirically,":[111],"GPT-2":[113],"pretraining,":[114],"observe":[116],"same-optimizer":[117],"paths":[118,125],"preserve":[119],"each":[120],"model's":[121],"spectrum":[122],"cross-optimizer":[124],"traverse":[126],"smooth":[128],"transition.":[129],"Our":[130],"results":[131],"reveal":[132],"optimizer-dependent":[133],"structure":[134],"beyond":[135],"classical":[136],"mode":[137],"literature.":[139]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-13T00:00:00"}
