{"id":"https://openalex.org/W4289598249","doi":"https://doi.org/10.48550/arxiv.2208.01003","title":"What Can Be Learnt With Wide Convolutional Neural Networks?","display_name":"What Can Be Learnt With Wide Convolutional Neural Networks?","publication_year":2022,"publication_date":"2022-08-01","ids":{"openalex":"https://openalex.org/W4289598249","doi":"https://doi.org/10.48550/arxiv.2208.01003"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2208.01003","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2208.01003","pdf_url":"https://arxiv.org/pdf/2208.01003","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2208.01003","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000481488","display_name":"Francesco Cagnetta","orcid":"https://orcid.org/0000-0002-8302-431X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Cagnetta, Francesco","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113591724","display_name":"Alessandro Favero","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Favero, Alessandro","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5019813807","display_name":"Matthieu Wyart","orcid":"https://orcid.org/0000-0003-0644-0990"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wyart, Matthieu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5000481488"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":4,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9983999729156494,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9983999729156494,"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/T12676","display_name":"Machine Learning and ELM","score":0.9962999820709229,"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/T10036","display_name":"Advanced Neural Network Applications","score":0.995199978351593,"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/convolutional-neural-network","display_name":"Convolutional neural network","score":0.7248900532722473},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.6828011870384216},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6329709887504578},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6047028303146362},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5975005626678467},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5536907911300659},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.5197291374206543},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5075415372848511},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45212674140930176},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4480826258659363},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.42994681000709534},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.4125877022743225},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.286265105009079},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.09023332595825195}],"concepts":[{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.7248900532722473},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.6828011870384216},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6329709887504578},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6047028303146362},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5975005626678467},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5536907911300659},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.5197291374206543},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5075415372848511},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45212674140930176},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4480826258659363},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.42994681000709534},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4125877022743225},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.286265105009079},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.09023332595825195},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2208.01003","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2208.01003","pdf_url":"https://arxiv.org/pdf/2208.01003","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.2208.01003","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2208.01003","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2208.01003","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2208.01003","pdf_url":"https://arxiv.org/pdf/2208.01003","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4296209631","https://openalex.org/W4226493464","https://openalex.org/W4312417841","https://openalex.org/W3193565141","https://openalex.org/W3133861977","https://openalex.org/W2951211570","https://openalex.org/W3167935049","https://openalex.org/W3103566983","https://openalex.org/W408992594","https://openalex.org/W3029198973"],"abstract_inverted_index":{"Understanding":[0],"how":[1,41],"convolutional":[2],"neural":[3],"networks":[4],"(CNNs)":[5],"can":[6],"efficiently":[7,215],"learn":[8],"high-dimensional":[9],"functions":[10,204],"remains":[11],"a":[12,37,181],"fundamental":[13],"challenge.":[14],"A":[15],"popular":[16],"belief":[17],"is":[18,141,167],"that":[19,76,106,122],"these":[20,148],"models":[21],"harness":[22],"the":[23,47,52,56,70,77,80,84,88,111,115,124,136,139,144,152,157,164,170,177,186,203],"local":[24],"and":[25,90],"hierarchical":[26,85,201],"structure":[27,43,86],"of":[28,40,49,51,58,79,87,114,131,138,147,160,180,188],"natural":[29],"data":[30],"such":[31,42],"as":[32],"images.":[33],"Yet,":[34],"we":[35,64,74,91,96,120,196],"lack":[36],"quantitative":[38],"understanding":[39],"affects":[44],"performance,":[45],"e.g.,":[46],"rate":[48],"decay":[50,137,166],"generalisation":[53,102,178],"error":[54,140,165,179],"with":[55,101,192],"number":[57],"training":[59],"samples.":[60],"In":[61,118],"this":[62,98],"paper,":[63],"study":[65],"infinitely-wide":[66,207],"deep":[67,107,182,190,208],"CNNs":[68,108,209],"in":[69,217],"kernel":[71,82],"regime.":[72],"First,":[73],"show":[75],"spectrum":[78],"corresponding":[81],"inherits":[83],"network,":[89],"characterise":[92],"its":[93],"asymptotics.":[94],"Then,":[95],"use":[97],"result":[99],"together":[100],"bounds":[103],"to":[104,110,213],"prove":[105],"adapt":[109],"spatial":[112],"scale":[113],"target":[116,125,153],"function.":[117],"particular,":[119],"find":[121,197],"if":[123,151],"function":[126,154],"depends":[127,155],"on":[128,156,185],"low-dimensional":[129],"subsets":[130],"adjacent":[132],"input":[133,161,171],"variables,":[134,162],"then":[135,163],"controlled":[142,168],"by":[143,169,175,206],"effective":[145],"dimensionality":[146],"subsets.":[149],"Conversely,":[150],"full":[158],"set":[159],"dimension.":[172,219],"We":[173],"conclude":[174],"computing":[176],"CNN":[183,191],"trained":[184],"output":[187],"another":[189],"randomly-initialised":[193],"parameters.":[194],"Interestingly,":[195],"that,":[198],"despite":[199],"their":[200],"structure,":[202],"generated":[205],"are":[210],"too":[211],"rich":[212],"be":[214],"learnable":[216],"high":[218]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
