{"id":"https://openalex.org/W2963012631","doi":"https://doi.org/10.1109/wacv.2016.7477624","title":"On the importance of normalisation layers in deep learning with piecewise linear activation units","display_name":"On the importance of normalisation layers in deep learning with piecewise linear activation units","publication_year":2016,"publication_date":"2016-03-01","ids":{"openalex":"https://openalex.org/W2963012631","doi":"https://doi.org/10.1109/wacv.2016.7477624","mag":"2963012631"},"language":"en","primary_location":{"id":"doi:10.1109/wacv.2016.7477624","is_oa":false,"landing_page_url":"https://doi.org/10.1109/wacv.2016.7477624","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE Winter Conference on Applications of Computer Vision (WACV)","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/A5103020604","display_name":"Zhibin Liao","orcid":"https://orcid.org/0000-0001-9965-4511"},"institutions":[{"id":"https://openalex.org/I4210127558","display_name":"Australian Centre for Robotic Vision","ror":"https://ror.org/02zv9xv82","country_code":"AU","type":"facility","lineage":["https://openalex.org/I4210127558"]},{"id":"https://openalex.org/I5681781","display_name":"The University of Adelaide","ror":"https://ror.org/00892tw58","country_code":"AU","type":"education","lineage":["https://openalex.org/I5681781"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Zhibin Liao","raw_affiliation_strings":["ARC Centre of Excellence for Robotic Vision, University of Adelaide, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ARC Centre of Excellence for Robotic Vision, University of Adelaide, Australia","institution_ids":["https://openalex.org/I4210127558","https://openalex.org/I5681781"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029215323","display_name":"Gustavo Carneiro","orcid":"https://orcid.org/0000-0002-5571-6220"},"institutions":[{"id":"https://openalex.org/I4210127558","display_name":"Australian Centre for Robotic Vision","ror":"https://ror.org/02zv9xv82","country_code":"AU","type":"facility","lineage":["https://openalex.org/I4210127558"]},{"id":"https://openalex.org/I5681781","display_name":"The University of Adelaide","ror":"https://ror.org/00892tw58","country_code":"AU","type":"education","lineage":["https://openalex.org/I5681781"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Gustavo Carneiro","raw_affiliation_strings":["ARC Centre of Excellence for Robotic Vision, University of Adelaide, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ARC Centre of Excellence for Robotic Vision, University of Adelaide, Australia","institution_ids":["https://openalex.org/I4210127558","https://openalex.org/I5681781"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.711,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.93599388,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10036","display_name":"Advanced Neural Network Applications","score":0.9995999932289124,"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":0.9995999932289124,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.9955999851226807,"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/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mnist-database","display_name":"MNIST database","score":0.8314751386642456},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6493947505950928},{"id":"https://openalex.org/keywords/activation-function","display_name":"Activation function","score":0.6447307467460632},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5846637487411499},{"id":"https://openalex.org/keywords/overfitting","display_name":"Overfitting","score":0.5722246766090393},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.558597207069397},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5418951511383057},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.5228619575500488},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5215689539909363},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.46609604358673096},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.435493528842926},{"id":"https://openalex.org/keywords/linear-model","display_name":"Linear model","score":0.43267005681991577},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.38384610414505005},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36201825737953186},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.27885860204696655}],"concepts":[{"id":"https://openalex.org/C190502265","wikidata":"https://www.wikidata.org/wiki/Q17069496","display_name":"MNIST database","level":3,"score":0.8314751386642456},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6493947505950928},{"id":"https://openalex.org/C38365724","wikidata":"https://www.wikidata.org/wiki/Q4677469","display_name":"Activation function","level":3,"score":0.6447307467460632},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5846637487411499},{"id":"https://openalex.org/C22019652","wikidata":"https://www.wikidata.org/wiki/Q331309","display_name":"Overfitting","level":3,"score":0.5722246766090393},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.558597207069397},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5418951511383057},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.5228619575500488},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5215689539909363},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.46609604358673096},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.435493528842926},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.43267005681991577},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.38384610414505005},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36201825737953186},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27885860204696655},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/wacv.2016.7477624","is_oa":false,"landing_page_url":"https://doi.org/10.1109/wacv.2016.7477624","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE Winter Conference on Applications of Computer Vision (WACV)","raw_type":"proceedings-article"},{"id":"pmh:oai:digital.library.adelaide.edu.au:2440/107549","is_oa":false,"landing_page_url":"http://hdl.handle.net/2440/107549","pdf_url":null,"source":{"id":"https://openalex.org/S4306401835","display_name":"Adelaide Research & Scholarship (AR&S) (University of Adelaide)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I5681781","host_organization_name":"The University of Adelaide","host_organization_lineage":["https://openalex.org/I5681781"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://dx.doi.org/10.1109/wacv.2016.7477624","raw_type":"Conference paper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309480","display_name":"Nvidia","ror":"https://ror.org/03jdj4y14"},{"id":"https://openalex.org/F4320331724","display_name":"Australian Centre for Robotic Vision","ror":"https://ror.org/02zv9xv82"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W4919037","https://openalex.org/W1498436455","https://openalex.org/W1665214252","https://openalex.org/W1677182931","https://openalex.org/W1836465849","https://openalex.org/W1934184906","https://openalex.org/W2095705004","https://openalex.org/W2099049980","https://openalex.org/W2107215754","https://openalex.org/W2112796928","https://openalex.org/W2161388792","https://openalex.org/W2163605009","https://openalex.org/W2168894214","https://openalex.org/W2294059674","https://openalex.org/W2335728318","https://openalex.org/W2951603627","https://openalex.org/W2953066166","https://openalex.org/W2963325419","https://openalex.org/W2963574257","https://openalex.org/W2963606038","https://openalex.org/W2963911037","https://openalex.org/W3118608800","https://openalex.org/W6600213771","https://openalex.org/W6607694896","https://openalex.org/W6629815555","https://openalex.org/W6637242042","https://openalex.org/W6638444622","https://openalex.org/W6638667902","https://openalex.org/W6639736908","https://openalex.org/W6674330103","https://openalex.org/W6676231585","https://openalex.org/W6684191040","https://openalex.org/W6684665197","https://openalex.org/W6703116779","https://openalex.org/W6787972765"],"related_works":["https://openalex.org/W2987302549","https://openalex.org/W3116943156","https://openalex.org/W4322631263","https://openalex.org/W3012219884","https://openalex.org/W4366999905","https://openalex.org/W2936783136","https://openalex.org/W3173926637","https://openalex.org/W3214206881","https://openalex.org/W2512630954","https://openalex.org/W4306639562"],"abstract_inverted_index":{"Deep":[0],"feedforward":[1,188],"neural":[2,189],"networks":[3,190],"with":[4,43,68,83,118,191,214],"piecewise":[5,31,125,136,192],"linear":[6,32,126,137,144,193],"activations":[7],"are":[8,259],"currently":[9],"producing":[10],"the":[11,37,44,54,61,75,100,121,124,135,163,174,180,209,227,245,265,269],"state-of-the-art":[12],"results":[13,250,257],"in":[14,53,150,247,251,271],"several":[15],"public":[16],"datasets":[17],"(e.g.,":[18],"CIFAR-10,":[19,272],"CIFAR-100,":[20,273],"MNIST,":[21,274],"and":[22,30,240,275],"SVHN).":[23],"The":[24],"combination":[25],"of":[26,39,46,50,56,102,115,123,154,165,182,201,208,219,229,268],"deep":[27,187,231],"learning":[28,232],"models":[29,109],"activation":[33,127,138,145,203,210],"functions":[34,42],"allows":[35],"for":[36],"estimation":[38],"exponentially":[40],"complex":[41,159],"use":[45,200],"a":[47,111,151,197,215,252],"large":[48,217],"number":[49,164],"subnetworks":[51,65],"specialized":[52],"classification":[55,256],"similar":[57],"input":[58],"examples.":[59],"During":[60],"training":[62,220],"process,":[63],"these":[64,108,202],"avoid":[66],"overfitting":[67],"an":[69,92],"implicit":[70],"regularization":[71],"scheme":[72],"based":[73],"on":[74],"fact":[76],"that":[77,95,107,130,236,254,258],"they":[78],"must":[79],"share":[80],"their":[81,155],"parameters":[82],"other":[84],"subnetworks.":[85],"Using":[86],"this":[87,169,223],"framework,":[88],"we":[89,178],"have":[90],"made":[91],"empirical":[93],"observation":[94],"can":[96,140,148],"improve":[97],"even":[98],"more":[99,198],"performance":[101],"such":[103],"models.":[104,233],"We":[105,234],"notice":[106],"assume":[110],"balanced":[112,199],"initial":[113,171],"distribution":[114,172],"data":[116],"points":[117],"respect":[119],"to":[120,157,244,264],"domain":[122],"function.":[128],"If":[129],"assumption":[131],"is":[132,212],"violated,":[133],"then":[134],"units":[139,185,243],"degenerate":[141],"into":[142,186],"purely":[143],"units,":[146,204],"which":[147,195],"result":[149],"significant":[152],"reduction":[153],"capacity":[156],"learn":[158],"functions.":[160],"Furthermore,":[161],"as":[162],"model":[166,175,249,253],"layers":[167],"increases,":[168],"unbalanced":[170],"makes":[173],"ill-conditioned.":[176],"Therefore,":[177],"propose":[179],"introduction":[181],"batch":[183,224,241],"normalisation":[184,225,242],"activations,":[194],"drives":[196],"where":[205],"each":[206],"region":[207],"function":[211],"trained":[213],"relatively":[216],"proportion":[218],"samples.":[221],"Also,":[222],"promotes":[226],"pre-conditioning":[228],"very":[230],"show":[235],"by":[237],"introducing":[238],"maxout":[239],"network":[246,248],"produces":[255],"better":[260],"than":[261],"or":[262],"comparable":[263],"current":[266],"state":[267],"art":[270],"SVHN":[276],"datasets.":[277]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}