{"id":"https://openalex.org/W7165619297","doi":"https://doi.org/10.48550/arxiv.2606.23477","title":"Sublinearly Structured Deep Neural Networks Achieve Feature Learning Consistency for Compositional Functions","display_name":"Sublinearly Structured Deep Neural Networks Achieve Feature Learning Consistency for Compositional Functions","publication_year":2026,"publication_date":"2026-06-22","ids":{"openalex":"https://openalex.org/W7165619297","doi":"https://doi.org/10.48550/arxiv.2606.23477"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.23477","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.23477","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":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.2606.23477","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139137387","display_name":"Sehwan Kim","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kim, Sehwan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139129274","display_name":"Yan Sun","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sun, Yan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5085287370","display_name":"Faming Liang","orcid":"https://orcid.org/0000-0002-1177-5501"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liang, Faming","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/T10036","display_name":"Advanced Neural Network Applications","score":0.33309999108314514,"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"}},"topics":[{"id":"https://openalex.org/T10036","display_name":"Advanced Neural Network Applications","score":0.33309999108314514,"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"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.12150000035762787,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.1193000003695488,"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/consistency","display_name":"Consistency (knowledge bases)","score":0.6707000136375427},{"id":"https://openalex.org/keywords/convolutional-neural-network","display_name":"Convolutional neural network","score":0.5077000260353088},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.49239999055862427},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.47690001130104065},{"id":"https://openalex.org/keywords/statistical-learning","display_name":"Statistical learning","score":0.4715000092983246},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.37450000643730164},{"id":"https://openalex.org/keywords/statistical-model","display_name":"Statistical model","score":0.33550000190734863},{"id":"https://openalex.org/keywords/data-consistency","display_name":"Data consistency","score":0.3165000081062317}],"concepts":[{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.6707000136375427},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5946999788284302},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5558000206947327},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.5077000260353088},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.49239999055862427},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.47690001130104065},{"id":"https://openalex.org/C2982736386","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Statistical learning","level":2,"score":0.4715000092983246},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.37450000643730164},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.33550000190734863},{"id":"https://openalex.org/C93361087","wikidata":"https://www.wikidata.org/wiki/Q4426698","display_name":"Data consistency","level":2,"score":0.3165000081062317},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.31439998745918274},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.31369999051094055},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.3124000132083893},{"id":"https://openalex.org/C2781147490","wikidata":"https://www.wikidata.org/wiki/Q5156808","display_name":"Compositional data","level":2,"score":0.3082999885082245},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.30489999055862427},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.3046000003814697},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.2799000144004822},{"id":"https://openalex.org/C31388003","wikidata":"https://www.wikidata.org/wiki/Q7624548","display_name":"Strong consistency","level":3,"score":0.27709999680519104},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.2766999900341034},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.27549999952316284},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.2603999972343445}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.23477","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.23477","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":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.2606.23477","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.23477","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":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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Over":[0],"the":[1,17,80,95,100,106,151,163],"past":[2],"decade,":[3],"deep":[4,186],"neural":[5,131],"networks":[6,132],"(DNNs)":[7],"have":[8],"achieved":[9],"remarkable":[10],"success":[11],"on":[12,142,193],"complex":[13],"machine-learning":[14],"tasks,":[15],"yet":[16],"theoretical":[18],"foundations":[19],"of":[20,43,74,103,108],"their":[21,143],"performance":[22],"remain":[23],"incomplete.":[24],"From":[25],"a":[26,29,47,57,180],"statistical":[27,181],"viewpoint,":[28],"natural":[30],"question":[31],"is:":[32],"can":[33],"DNNs":[34,114,119,154],"attain":[35],"feature-learning":[36,62],"and":[37,72],"prediction":[38],"consistency":[39,63,90],"comparable":[40],"to":[41],"that":[42,127,150],"classical":[44],"models?":[45],"While":[46],"full":[48],"characterization":[49],"is":[50],"open,":[51],"we":[52],"provide":[53],"positive":[54],"results":[55,177],"for":[56,65,158],"broad":[58],"subclass.":[59],"We":[60,147],"establish":[61],"guarantees":[64],"sublinearly":[66,78,112,140,152],"structured":[67,113,141,153],"DNNs-architectures":[68],"whose":[69],"input/output":[70],"dimensions":[71],"number":[73,102,107],"hidden":[75],"neurons":[76],"grow":[77],"with":[79],"sample":[81],"size-when":[82],"learning":[83,187],"hierarchically":[84,159],"compositional":[85,160,172],"target":[86],"functions.":[87],"Importantly,":[88],"this":[89],"still":[91],"holds":[92],"even":[93],"in":[94,120,162],"conventional":[96],"\"over-parameterized\"":[97],"regime":[98],"where":[99],"total":[101],"parameters":[104],"exceeds":[105],"training":[109,192],"samples.":[110],"Empirically,":[111],"match":[115],"or":[116],"surpass":[117],"wide":[118],"prediction.":[121],"A":[122],"structural":[123],"audit":[124],"further":[125,148],"indicates":[126],"widely":[128],"used":[129],"convolutional":[130],"(CNNs),":[133],"including":[134],"AlexNet,":[135],"VGGNet,":[136],"ResNet,":[137],"GoogLeNet,":[138],"are":[139],"image":[144,195],"classification":[145],"benchmarks.":[146],"prove":[149],"achieve":[155],"universal":[156],"approximation":[157],"functions":[161],"large-sample":[164],"limit.":[165],"Moreover,":[166],"images":[167],"exhibit":[168],"an":[169],"inherent":[170],"hierarchical,":[171],"structure.":[173],"Taken":[174],"together,":[175],"these":[176],"explain,":[178],"through":[179],"lens,":[182],"why":[183],"many":[184],"large-scale":[185],"models":[188],"succeed":[189],"after":[190],"adequate":[191],"massive":[194],"datasets.":[196]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-24T00:00:00"}
