{"id":"https://openalex.org/W4412462829","doi":"https://doi.org/10.1088/2632-2153/adf02e","title":"Architecture-aware minimization (A<sup>2</sup>M): how to find flat minima in neural architecture search","display_name":"Architecture-aware minimization (A<sup>2</sup>M): how to find flat minima in neural architecture search","publication_year":2025,"publication_date":"2025-07-15","ids":{"openalex":"https://openalex.org/W4412462829","doi":"https://doi.org/10.1088/2632-2153/adf02e"},"language":"en","primary_location":{"id":"doi:10.1088/2632-2153/adf02e","is_oa":true,"landing_page_url":"https://doi.org/10.1088/2632-2153/adf02e","pdf_url":null,"source":{"id":"https://openalex.org/S4210200687","display_name":"Machine Learning Science and Technology","issn_l":"2632-2153","issn":["2632-2153"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning: Science and Technology","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1088/2632-2153/adf02e","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008809497","display_name":"Matteo Gambella","orcid":"https://orcid.org/0000-0001-9734-670X"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Matteo Gambella","raw_affiliation_strings":["Department of Electronics, Information and Bioengineering, Politecnico di Milano, Via Ponzio 34/5, 20133 Milano, Italy"],"raw_orcid":"https://orcid.org/0000-0001-9734-670X","affiliations":[{"raw_affiliation_string":"Department of Electronics, Information and Bioengineering, Politecnico di Milano, Via Ponzio 34/5, 20133 Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035460406","display_name":"Fabrizio Pittorino","orcid":"https://orcid.org/0000-0002-1919-6141"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Fabrizio Pittorino","raw_affiliation_strings":["Department of Electronics, Information and Bioengineering, Politecnico di Milano, Via Ponzio 34/5, 20133 Milano, Italy"],"raw_orcid":"https://orcid.org/0000-0002-1919-6141","affiliations":[{"raw_affiliation_string":"Department of Electronics, Information and Bioengineering, Politecnico di Milano, Via Ponzio 34/5, 20133 Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035547226","display_name":"Manuel Roveri","orcid":"https://orcid.org/0000-0001-7828-7687"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Manuel Roveri","raw_affiliation_strings":["Department of Electronics, Information and Bioengineering, Politecnico di Milano, Via Ponzio 34/5, 20133 Milano, Italy"],"raw_orcid":"https://orcid.org/0000-0001-7828-7687","affiliations":[{"raw_affiliation_string":"Department of Electronics, Information and Bioengineering, Politecnico di Milano, Via Ponzio 34/5, 20133 Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5008809497","https://openalex.org/A5035460406","https://openalex.org/A5035547226"],"corresponding_institution_ids":["https://openalex.org/I93860229"],"apc_list":{"value":1600,"currency":"GBP","value_usd":1962},"apc_paid":{"value":1600,"currency":"GBP","value_usd":1962},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06604063,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"6","issue":"3","first_page":"035016","last_page":"035016"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.8525999784469604,"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/T10320","display_name":"Neural Networks and Applications","score":0.8525999784469604,"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/maxima-and-minima","display_name":"Maxima and minima","score":0.8808062672615051},{"id":"https://openalex.org/keywords/architecture","display_name":"Architecture","score":0.7149294018745422},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.7146254777908325},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48736029863357544},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.47151386737823486},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.36963343620300293},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32982751727104187},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.302610844373703},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.26064223051071167},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.17033013701438904},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12232285737991333}],"concepts":[{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.8808062672615051},{"id":"https://openalex.org/C123657996","wikidata":"https://www.wikidata.org/wiki/Q12271","display_name":"Architecture","level":2,"score":0.7149294018745422},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.7146254777908325},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48736029863357544},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.47151386737823486},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.36963343620300293},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32982751727104187},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.302610844373703},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.26064223051071167},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.17033013701438904},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12232285737991333},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1088/2632-2153/adf02e","is_oa":true,"landing_page_url":"https://doi.org/10.1088/2632-2153/adf02e","pdf_url":null,"source":{"id":"https://openalex.org/S4210200687","display_name":"Machine Learning Science and Technology","issn_l":"2632-2153","issn":["2632-2153"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning: Science and Technology","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2503.10404","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2503.10404","pdf_url":"https://arxiv.org/pdf/2503.10404","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:6b995b4d4b4544db9238634adf6653df","is_oa":true,"landing_page_url":"https://doaj.org/article/6b995b4d4b4544db9238634adf6653df","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Machine Learning: Science and Technology, Vol 6, Iss 3, p 035016 (2025)","raw_type":"article"},{"id":"pmh:oai:re.public.polimi.it:11311/1295436","is_oa":true,"landing_page_url":"https://iopscience.iop.org/article/10.1088/2632-2153/adf02e","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1088/2632-2153/adf02e","is_oa":true,"landing_page_url":"https://doi.org/10.1088/2632-2153/adf02e","pdf_url":null,"source":{"id":"https://openalex.org/S4210200687","display_name":"Machine Learning Science and Technology","issn_l":"2632-2153","issn":["2632-2153"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning: Science and Technology","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W2998438489","https://openalex.org/W3035620341","https://openalex.org/W3208681360","https://openalex.org/W4205795626","https://openalex.org/W4214717370","https://openalex.org/W4309374366","https://openalex.org/W4309880056","https://openalex.org/W4385572933","https://openalex.org/W4386573694","https://openalex.org/W4387910965","https://openalex.org/W4388116480","https://openalex.org/W4389130403","https://openalex.org/W4393153991","https://openalex.org/W4396926906","https://openalex.org/W4411244509","https://openalex.org/W6698540200","https://openalex.org/W6741978826","https://openalex.org/W6752515464","https://openalex.org/W6767064347","https://openalex.org/W6767953722","https://openalex.org/W6767994309","https://openalex.org/W6769344749","https://openalex.org/W6770070843","https://openalex.org/W6770866462","https://openalex.org/W6771233102","https://openalex.org/W6771784742","https://openalex.org/W6771859737","https://openalex.org/W6773935006","https://openalex.org/W6782312781","https://openalex.org/W6783600611","https://openalex.org/W6787972765","https://openalex.org/W6788673338","https://openalex.org/W6790545018","https://openalex.org/W6799334665","https://openalex.org/W6811049417","https://openalex.org/W6849166581","https://openalex.org/W6849777495","https://openalex.org/W6850020804","https://openalex.org/W6852441456","https://openalex.org/W6853924433","https://openalex.org/W6862821429","https://openalex.org/W6871198612"],"related_works":["https://openalex.org/W2375684291","https://openalex.org/W2354676191","https://openalex.org/W3188646203","https://openalex.org/W2909957174","https://openalex.org/W4246278799","https://openalex.org/W4210838092","https://openalex.org/W2121922170","https://openalex.org/W2127982566","https://openalex.org/W2153731865","https://openalex.org/W2471196694"],"abstract_inverted_index":{"Abstract":[0],"Neural":[1],"architecture":[2,27,39,48,87,155],"search":[3,40,88,181],"(NAS)":[4],"has":[5],"become":[6],"an":[7],"essential":[8],"tool":[9,235],"for":[10,141,236],"designing":[11],"effective":[12],"and":[13,37,53,61,174,179,208,239],"efficient":[14],"neural":[15,26,70],"networks.":[16],"In":[17,77],"this":[18],"paper,":[19],"we":[20,58,79,125],"investigate":[21],"the":[22,66,81,86,92,119,142,145,191],"geometric":[23],"properties":[24,68],"of":[25,45,69,85,94,118,147],"spaces":[28],"commonly":[29],"used":[30],"in":[31,47,74,106,154,241],"differentiable":[32,38,148,198,229],"NAS":[33,149,199,230],"methods,":[34,200],"specifically":[35],"NAS-Bench-201":[36,178],"(DARTS).":[41],"By":[42],"introducing":[43],"notions":[44],"flatness":[46,62],"space":[49,156],"such":[50],"as":[51],"neighborhoods":[52],"accuracy":[54,218],"barriers":[55,95],"along":[56],"paths,":[57],"reveal":[59],"locality":[60],"characteristics":[63],"analogous":[64],"to":[65,189],"well-known":[67],"network":[71],"loss":[72],"landscapes":[73],"weight":[75],"space.":[76],"particular,":[78],"unveil":[80],"detailed":[82],"geometrical":[83],"structure":[84],"landscape":[89],"by":[90,201],"uncovering":[91],"absence":[93],"between":[96],"well-performing":[97],"architectures,":[98],"finding":[99,214],"that":[100,138],"highly":[101],"accurate":[102],"architectures":[103,111,215],"cluster":[104],"together":[105],"flat":[107,152],"regions,":[108],"while":[109,213],"suboptimal":[110],"instead":[112],"remain":[113],"isolated,":[114],"showing":[115],"higher":[116],"values":[117],"barriers.":[120,219],"Building":[121],"on":[122,168,194,203,206,210],"these":[123],"insights,":[124],"propose":[126],"architecture-aware":[127],"minimization":[128],"(A":[129],"2":[130,159,185,221],"M),":[131],"a":[132,233],"novel":[133],"analytically":[134],"derived":[135],"algorithmic":[136],"framework":[137],"explicitly":[139],"biases,":[140],"first":[143],"time,":[144],"gradient":[146],"methods":[150],"towards":[151],"minima":[153],".":[157,252],"A":[158,184,220],"M":[160,186,222],"consistently":[161],"improves":[162],"generalization":[163],"over":[164],"state-of-the-art":[165],"DARTS-based":[166],"algorithms":[167],"benchmark":[169],"datasets":[170],"including":[171],"CIFAR-10,":[172,204],"CIFAR-100,":[173,207],"ImageNet-16-120,":[175],"across":[176,196],"both":[177],"DARTS":[180],"spaces.":[182],"Notably,":[183],"is":[187],"able":[188],"increase":[190],"test":[192],"accuracy,":[193],"average":[195],"different":[197],"+3.60%":[202],"+4.60%":[205],"+3.64%":[209],"ImageNet-16-120":[211],"-":[212],"with":[216],"low":[217],"can":[223],"be":[224],"easily":[225],"integrated":[226],"into":[227],"existing":[228],"frameworks,":[231],"offering":[232],"versatile":[234],"future":[237],"research":[238],"applications":[240],"automated":[242],"machine":[243],"learning.":[244],"We":[245],"will":[246],"open-source":[247],"our":[248],"code":[249],"at":[250],"https://github.com/AI-Tech-Research-Lab/AsquaredM":[251]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}