{"id":"https://openalex.org/W7163543848","doi":"https://doi.org/10.48550/arxiv.2606.04754","title":"Beyond Structural Symmetries: Linear Mode Connectivity via Neuron Identifiability","display_name":"Beyond Structural Symmetries: Linear Mode Connectivity via Neuron Identifiability","publication_year":2026,"publication_date":"2026-06-03","ids":{"openalex":"https://openalex.org/W7163543848","doi":"https://doi.org/10.48550/arxiv.2606.04754"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.04754","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.04754","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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.2606.04754","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058018286","display_name":"Vincent B\u00fcrgin","orcid":"https://orcid.org/0000-0002-8563-4189"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"B\u00fcrgin, Vincent","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137875963","display_name":"Daniel Herbst","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Herbst, Daniel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056014171","display_name":"Ya-Wei Eileen Lin","orcid":"https://orcid.org/0000-0002-4592-0244"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lin, Ya-Wei Eileen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137830907","display_name":"Stefanie Jegelka","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jegelka, Stefanie","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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.6517999768257141,"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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.6517999768257141,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.059300001710653305,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.04580000042915344,"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/identifiability","display_name":"Identifiability","score":0.9271000027656555},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6100000143051147},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5231000185012817},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4681999981403351},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.43529999256134033},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.39750000834465027},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.38589999079704285}],"concepts":[{"id":"https://openalex.org/C122770356","wikidata":"https://www.wikidata.org/wiki/Q1656753","display_name":"Identifiability","level":2,"score":0.9271000027656555},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6100000143051147},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5231000185012817},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.492000013589859},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4681999981403351},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.43529999256134033},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4077000021934509},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.39750000834465027},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.38589999079704285},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.33809998631477356},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3206999897956848},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.30489999055862427},{"id":"https://openalex.org/C38365724","wikidata":"https://www.wikidata.org/wiki/Q4677469","display_name":"Activation function","level":3,"score":0.2985000014305115},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28110000491142273},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.27410000562667847},{"id":"https://openalex.org/C15312841","wikidata":"https://www.wikidata.org/wiki/Q1657198","display_name":"Set function","level":3,"score":0.2655999958515167},{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.2637999951839447},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2628999948501587},{"id":"https://openalex.org/C2778794669","wikidata":"https://www.wikidata.org/wiki/Q43054","display_name":"Neuron","level":2,"score":0.26080000400543213},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.25850000977516174},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.25200000405311584}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.04754","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.04754","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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.2606.04754","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.04754","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Many":[0],"striking":[1],"phenomena":[2],"in":[3,107,142],"deep":[4],"learning,":[5],"such":[6,126],"as":[7],"linear":[8,130],"mode":[9],"connectivity":[10],"and":[11,43,72,123],"the":[12,27,37,60,73,136,144],"structured":[13],"behavior":[14],"of":[15,55,62,76,102,138],"training":[16,90],"dynamics,":[17],"are":[18],"closely":[19],"tied":[20],"to":[21,34],"parameter":[22,35],"symmetries:":[23],"transformations":[24],"that":[25,95,114],"leave":[26],"realized":[28],"function":[29,57,140],"unchanged.":[30],"Despite":[31],"growing":[32],"attention":[33],"symmetries,":[36],"exact":[38],"interplay":[39],"between":[40],"parameters,":[41],"data,":[42],"representations":[44],"remains":[45],"underexplored.":[46],"To":[47],"investigate":[48],"this,":[49],"we":[50],"develop":[51],"a":[52,64,129],"theoretical":[53],"framework":[54],"effective":[56,82,139],"classes,":[58],"i.e.,":[59],"set":[61],"functions":[63],"neuron":[65,86,115],"can":[66,98],"realize":[67],"on":[68],"its":[69],"input":[70],"support,":[71],"norm":[74],"cost":[75],"realizing":[77],"them.":[78],"We":[79,111],"then":[80],"formalize":[81],"symmetry":[83],"breaking":[84],"via":[85],"identifiability":[87,116],"across":[88],"independent":[89],"runs.":[91],"Our":[92],"analysis":[93],"shows":[94],"neural":[96],"networks":[97],"admit":[99],"large":[100],"families":[101],"approximately":[103],"equivalent":[104],"solutions":[105],"even":[106],"structurally":[108],"asymmetric":[109],"models.":[110],"further":[112],"show":[113],"enables":[117],"representation":[118],"merging":[119,127],"without":[120],"prior":[121],"alignment,":[122],"characterize":[124],"when":[125],"admits":[128],"low-loss":[131],"path.":[132],"These":[133],"findings":[134],"highlight":[135],"role":[137],"classes":[141],"affecting":[143],"loss":[145],"landscape.":[146]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-05T00:00:00"}