{"id":"https://openalex.org/W4298185481","doi":"https://doi.org/10.48550/arxiv.2209.14778","title":"Batch Normalization Explained","display_name":"Batch Normalization Explained","publication_year":2022,"publication_date":"2022-09-29","ids":{"openalex":"https://openalex.org/W4298185481","doi":"https://doi.org/10.48550/arxiv.2209.14778"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2209.14778","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2209.14778","pdf_url":"https://arxiv.org/pdf/2209.14778","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,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2209.14778","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047293370","display_name":"Randall Balestriero","orcid":"https://orcid.org/0000-0002-5692-4187","observed_orcids":["https://orcid.org/0000-0002-5692-4187"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Balestriero, Randall","raw_affiliation_strings":["Meta AI , FAIR New York , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Meta AI , FAIR New York , USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072713767","display_name":"Richard G. Baraniuk","orcid":"https://orcid.org/0000-0002-0721-8999","observed_orcids":["https://orcid.org/0000-0002-0721-8999"]},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Baraniuk, Richard G.","raw_affiliation_strings":["ECE Department , Rice University Texas , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ECE Department , Rice University Texas , USA","institution_ids":["https://openalex.org/I74775410"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":38,"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/T10320","display_name":"Neural Networks and Applications","score":0.6708999872207642,"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":0.6708999872207642,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.16329999268054962,"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":0.09059999883174896,"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/batch-normalization","display_name":"batch normalization","score":1.0},{"id":"https://openalex.org/keywords/deep-neural-network","display_name":"deep neural network","score":0.7390000224113464},{"id":"https://openalex.org/keywords/function-approximation","display_name":"function approximation","score":0.7680000066757202},{"id":"https://openalex.org/keywords/linear-region","display_name":"linear region","score":0.9649999737739563},{"id":"https://openalex.org/keywords/unsupervised-learning","display_name":"unsupervised learning","score":0.8029999732971191},{"id":"https://openalex.org/keywords/initialization","display_name":"initialization","score":0.4830000102519989},{"id":"https://openalex.org/keywords/dropout","display_name":"dropout","score":0.5210000276565552},{"id":"https://openalex.org/keywords/decision-boundaries","display_name":"decision boundaries","score":0.8149999976158142},{"id":"https://openalex.org/keywords/overfitting","display_name":"overfitting","score":0.8029999732971191},{"id":"https://openalex.org/keywords/generalization","display_name":"generalization","score":0.7620000243186951},{"id":"https://openalex.org/keywords/margins","display_name":"margins","score":0.8980000019073486}],"concepts":[{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.561978816986084},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5020191669464111},{"id":"https://openalex.org/C42023084","wikidata":"https://www.wikidata.org/wiki/Q5249231","display_name":"Decision boundary","level":3,"score":0.4831797182559967},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4776833653450012},{"id":"https://openalex.org/C22019652","wikidata":"https://www.wikidata.org/wiki/Q331309","display_name":"Overfitting","level":3,"score":0.44181787967681885},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.4391213059425354},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.43353524804115295},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3920328915119171},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3894987106323242},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3406985402107239},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.28124985098838806},{"id":"https://openalex.org/C95623464","wikidata":"https://www.wikidata.org/wiki/Q1096149","display_name":"Classifier (UML)","level":2,"score":0.27023622393608093},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11124968528747559},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2209.14778","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2209.14778","pdf_url":"https://arxiv.org/pdf/2209.14778","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,"listed_in":[],"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":"doi:10.48550/arxiv.2209.14778","doi":"https://doi.org/10.48550/arxiv.2209.14778","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2209.14778","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,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2209.14778","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2209.14778","pdf_url":"https://arxiv.org/pdf/2209.14778","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,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4298185481.pdf","grobid_xml":"https://content.openalex.org/works/W4298185481.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1836465849","https://openalex.org/W2009385843","https://openalex.org/W2125930537","https://openalex.org/W2178237821","https://openalex.org/W2582745083","https://openalex.org/W2884447957","https://openalex.org/W2945177846","https://openalex.org/W2962933129","https://openalex.org/W2964121744","https://openalex.org/W3038013616","https://openalex.org/W3126536942","https://openalex.org/W4221162276"],"related_works":["https://openalex.org/W7160500506","https://openalex.org/W2964068654","https://openalex.org/W2898988784","https://openalex.org/W6885045674","https://openalex.org/W6982273903","https://openalex.org/W6903806691","https://openalex.org/W3125907025","https://openalex.org/W3037353226","https://openalex.org/W6960096091","https://openalex.org/W6902624915"],"abstract_inverted_index":{"A":[0],"critically":[1],"important,":[2],"ubiquitous,":[3],"and":[4,20,39,190,204,215],"yet":[5],"poorly":[6],"understood":[7],"ingredient":[8],"in":[9],"modern":[10],"deep":[11],"networks":[12],"(DNs)":[13],"is":[14,112],"batch":[15],"normalization":[16],"(BN),":[17],"which":[18],"centers":[19],"normalizes":[21],"the":[22,63,70,89,100,121,129,138,147,168,174,187,192,209,212,216],"feature":[23],"maps.":[24],"To":[25],"date,":[26],"only":[27],"limited":[28],"progress":[29],"has":[30,43],"been":[31],"made":[32],"understanding":[33],"why":[34],"BN":[35,49,60,111,140,177],"boosts":[36,146],"DN":[37,150,157],"learning":[38,115,126],"inference":[40],"performance;":[41],"work":[42],"focused":[44],"exclusively":[45],"on":[46],"showing":[47],"that":[48,72,84,110,117,145,173],"smooths":[50],"a":[51,86,97,132,142,156,182],"DN's":[52,122,133],"loss":[53],"landscape.":[54],"In":[55],"this":[56],"paper,":[57],"we":[58,68],"study":[59],"theoretically":[61],"from":[62],"perspective":[64],"of":[65,74,99,120,131,149,176],"function":[66],"approximation;":[67],"exploit":[69],"fact":[71],"most":[73],"today's":[75],"state-of-the-art":[76],"DNs":[77],"are":[78],"continuous":[79],"piecewise":[80],"affine":[81,93],"(CPA)":[82],"splines":[83],"fit":[85],"predictor":[87],"to":[88,136,162,186],"training":[90,213],"data":[91],"via":[92],"mappings":[94],"defined":[95],"over":[96],"partition":[98,135,166,188],"input":[101],"space":[102],"(the":[103],"so-called":[104],"\"linear":[105],"regions\").":[106],"{\\em":[107],"We":[108,170],"demonstrate":[109],"an":[113],"unsupervised":[114],"technique":[116],"--":[118,127],"independent":[119],"weights":[123,161],"or":[124],"gradient-based":[125],"adapts":[128,154],"geometry":[130],"spline":[134,165],"match":[137],"data.}":[139],"provides":[141],"\"smart":[143],"initialization\"":[144],"performance":[148],"learning,":[151],"because":[152],"it":[153],"even":[155],"initialized":[158],"with":[159,167],"random":[160,184],"align":[163],"its":[164],"data.":[169],"also":[171],"show":[172],"variation":[175],"statistics":[178],"between":[179,211],"mini-batches":[180],"introduces":[181],"dropout-like":[183],"perturbation":[185,201],"boundaries":[189],"hence":[191],"decision":[193,217],"boundary":[194],"for":[195],"classification":[196],"problems.":[197],"This":[198],"per":[199],"mini-batch":[200],"reduces":[202],"overfitting":[203],"improves":[205],"generalization":[206],"by":[207],"increasing":[208],"margin":[210],"samples":[214],"boundary.":[218]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":15},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":8}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2022-10-01T00:00:00"}