{"id":"https://openalex.org/W2971683405","doi":"https://doi.org/10.1109/allerton.2019.8919900","title":"Learning and Recovery in the ReLU Model","display_name":"Learning and Recovery in the ReLU Model","publication_year":2019,"publication_date":"2019-09-01","ids":{"openalex":"https://openalex.org/W2971683405","doi":"https://doi.org/10.1109/allerton.2019.8919900","mag":"2971683405"},"language":"en","primary_location":{"id":"doi:10.1109/allerton.2019.8919900","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2019.8919900","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051046818","display_name":"Arya Mazumdar","orcid":"https://orcid.org/0000-0003-4605-7996"},"institutions":[{"id":"https://openalex.org/I177605424","display_name":"Amherst College","ror":"https://ror.org/028vqfs63","country_code":"US","type":"education","lineage":["https://openalex.org/I177605424"]},{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Arya Mazumdar","raw_affiliation_strings":["University of Massachusetts Amherst,College of Information and Computer Sciences,Amherst,MA,USA,01003","College of Information and Computer Sciences, University of Massachusetts Amherst, Amherst, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Massachusetts Amherst,College of Information and Computer Sciences,Amherst,MA,USA,01003","institution_ids":["https://openalex.org/I177605424","https://openalex.org/I24603500"]},{"raw_affiliation_string":"College of Information and Computer Sciences, University of Massachusetts Amherst, Amherst, MA, USA","institution_ids":["https://openalex.org/I177605424","https://openalex.org/I24603500"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079621556","display_name":"Ankit Singh Rawat","orcid":"https://orcid.org/0000-0001-9790-6500"},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ankit Singh Rawat","raw_affiliation_strings":["Google Research,New York,NY,USA,10011","Google Research, New York, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Google Research,New York,NY,USA,10011","institution_ids":["https://openalex.org/I1291425158"]},{"raw_affiliation_string":"Google Research, New York, NY, USA","institution_ids":["https://openalex.org/I1291425158"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8747,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.80228989,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"108","last_page":"115"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9915000200271606,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9915000200271606,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9269999861717224,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9204999804496765,"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/computer-science","display_name":"Computer science","score":0.5905712246894836},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.35256677865982056}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5905712246894836},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.35256677865982056}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/allerton.2019.8919900","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2019.8919900","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W616376197","https://openalex.org/W1546851689","https://openalex.org/W1564947197","https://openalex.org/W1839868949","https://openalex.org/W1959608418","https://openalex.org/W1996023858","https://openalex.org/W2000157792","https://openalex.org/W2005876975","https://openalex.org/W2057690238","https://openalex.org/W2069588275","https://openalex.org/W2088911135","https://openalex.org/W2099471712","https://openalex.org/W2100495367","https://openalex.org/W2115324389","https://openalex.org/W2121716262","https://openalex.org/W2122536596","https://openalex.org/W2128084896","https://openalex.org/W2129131372","https://openalex.org/W2144730813","https://openalex.org/W2156387975","https://openalex.org/W2558384550","https://openalex.org/W2595294663","https://openalex.org/W2611328865","https://openalex.org/W2751645773","https://openalex.org/W2787248994","https://openalex.org/W2790769103","https://openalex.org/W2962921634","https://openalex.org/W2963827833","https://openalex.org/W2964200481","https://openalex.org/W3101788906","https://openalex.org/W3104030484","https://openalex.org/W4250954493","https://openalex.org/W4300945894","https://openalex.org/W4301028776","https://openalex.org/W4302027967","https://openalex.org/W4320013936","https://openalex.org/W6619198760","https://openalex.org/W6638665692","https://openalex.org/W6640963894","https://openalex.org/W6678283600","https://openalex.org/W6682889407","https://openalex.org/W6730349232","https://openalex.org/W6735307612","https://openalex.org/W6737871451","https://openalex.org/W6743806199","https://openalex.org/W6749479796"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W4391913857","https://openalex.org/W2350741829","https://openalex.org/W2530322880"],"abstract_inverted_index":{"Rectified":[0],"linear":[1],"units,":[2],"or":[3],"ReLUs,":[4],"have":[5],"become":[6],"a":[7,30,35,49,63,104,224],"preferred":[8],"activation":[9],"function":[10],"for":[11],"artificial":[12],"neural":[13],"networks.":[14],"In":[15,155],"this":[16,156],"paper":[17],"we":[18,44,79,140,158],"consider":[19,141],"two":[20],"basic":[21],"learning":[22,48],"problems":[23],"assuming":[24],"that":[25,110,143,204],"the":[26,53,59,83,87,94,116,133,148,151,163,173,187,197,205],"underlying":[27],"data":[28],"follow":[29],"generative":[31,50],"model":[32,51,95],"based":[33],"on":[34,132],"simple":[36],"network":[37,84],"with":[38,189],"ReLU":[39,60,97],"activations.":[40],"The":[41,137],"first":[42],"problem":[43,139],"study":[45],"corresponds":[46],"to":[47,81,114],"in":[52,150,161],"presence":[54,152],"of":[55,65,119,124,135,144,147,153,172,215],"nonlinearity":[56],"(modeled":[57],"by":[58],"functions).":[61],"Given":[62],"set":[64],"signal":[66,149],"vectors":[67],"yi\u2208":[68],"Rd,":[69],"i":[70],"=":[71,176],"1,":[72],"2,":[73],".":[74,75,76],",":[77],"n,":[78],"aim":[80],"learn":[82],"parameters,":[85],"i.e.,":[86],"d":[88],"\u00d7":[89],"k":[90],"matrix":[91],"A,":[92],"under":[93,129],"yi=":[96],"(Aci+":[98],"b),":[99],"where":[100,182],"b":[101],"\u2208":[102],"Rdis":[103],"random":[105,225],"bias":[106],"vector.":[107],"We":[108,202],"show":[109,203],"it":[111],"is":[112,142,223],"possible":[113],"recover":[115],"column":[117],"space":[118],"A":[120,222],"within":[121,212],"an":[122,213],"error":[123],"O(d)":[125],"(in":[126],"Frobenius":[127],"norm)":[128],"certain":[130],"conditions":[131],"distribution":[134],"b.":[136],"second":[138],"robust":[145],"recovery":[146],"outliers.":[154],"setting,":[157],"are":[159],"interested":[160],"recovering":[162],"latent":[164],"vector":[165],"c":[166,209],"from":[167],"its":[168],"noisy":[169],"nonlinear":[170],"images":[171],"form":[174],"v":[175],"ReLU(Ac)":[177],"+":[178,180,217],"e":[179,183],"w,":[181],"E":[184,194,210],"Rd":[185,195],"denotes":[186],"outliers":[188],"sparsity":[190],"s":[191],"and":[192],"w":[193],"denote":[196],"dense":[198],"but":[199],"small":[200],"noise.":[201],"LASSO":[206],"algorithm":[207],"recovers":[208],"Rk":[211],"\u21132-error":[214],"O(\u221a((k":[216],"s)":[218],"log":[219],"d)/d)":[220],"when":[221],"Gaussian":[226],"matrix.":[227]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}