{"id":"https://openalex.org/W3080273719","doi":"https://doi.org/10.1145/3394486.3403203","title":"Measuring Model Complexity of Neural Networks with Curve Activation Functions","display_name":"Measuring Model Complexity of Neural Networks with Curve Activation Functions","publication_year":2020,"publication_date":"2020-08-20","ids":{"openalex":"https://openalex.org/W3080273719","doi":"https://doi.org/10.1145/3394486.3403203","mag":"3080273719"},"language":"en","primary_location":{"id":"doi:10.1145/3394486.3403203","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3394486.3403203","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery &amp; Data Mining","raw_type":"proceedings-article"},"type":"article","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/A5068477431","display_name":"Xia Hu","orcid":"https://orcid.org/0000-0003-2234-3226"},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Xia Hu","raw_affiliation_strings":["Simon Fraser University, Burnaby, BC, Canada"],"affiliations":[{"raw_affiliation_string":"Simon Fraser University, Burnaby, BC, Canada","institution_ids":["https://openalex.org/I18014758"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101522967","display_name":"Weiqing Liu","orcid":"https://orcid.org/0000-0003-1951-2594"},"institutions":[{"id":"https://openalex.org/I4210113369","display_name":"Microsoft Research Asia (China)","ror":"https://ror.org/0300m5276","country_code":"CN","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210113369"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weiqing Liu","raw_affiliation_strings":["Microsoft Research, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Microsoft Research, Beijing, China","institution_ids":["https://openalex.org/I4210113369"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101544241","display_name":"Jiang Bian","orcid":"https://orcid.org/0000-0002-9472-600X"},"institutions":[{"id":"https://openalex.org/I4210113369","display_name":"Microsoft Research Asia (China)","ror":"https://ror.org/0300m5276","country_code":"CN","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210113369"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiang Bian","raw_affiliation_strings":["Microsoft Research, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Microsoft Research, Beijing, China","institution_ids":["https://openalex.org/I4210113369"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062247330","display_name":"Jian Pei","orcid":"https://orcid.org/0000-0002-2200-8711"},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Jian Pei","raw_affiliation_strings":["Simon Fraser University, Burnaby, BC, Canada"],"affiliations":[{"raw_affiliation_string":"Simon Fraser University, Burnaby, BC, Canada","institution_ids":["https://openalex.org/I18014758"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5068477431"],"corresponding_institution_ids":["https://openalex.org/I18014758"],"apc_list":null,"apc_paid":null,"fwci":1.3717,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.85395852,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"1521","last_page":"1531"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9983000159263611,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9983000159263611,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9980999827384949,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.9980000257492065,"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/overfitting","display_name":"Overfitting","score":0.9601564407348633},{"id":"https://openalex.org/keywords/pruning","display_name":"Pruning","score":0.6676616668701172},{"id":"https://openalex.org/keywords/activation-function","display_name":"Activation function","score":0.6674686670303345},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6106407642364502},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5946928262710571},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5858498811721802},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5752986073493958},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5456583499908447},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.47504356503486633},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.47194069623947144},{"id":"https://openalex.org/keywords/linear-model","display_name":"Linear model","score":0.46150022745132446},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40580832958221436},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3776912987232208},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36949703097343445},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3054555058479309},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.13522037863731384}],"concepts":[{"id":"https://openalex.org/C22019652","wikidata":"https://www.wikidata.org/wiki/Q331309","display_name":"Overfitting","level":3,"score":0.9601564407348633},{"id":"https://openalex.org/C108010975","wikidata":"https://www.wikidata.org/wiki/Q500094","display_name":"Pruning","level":2,"score":0.6676616668701172},{"id":"https://openalex.org/C38365724","wikidata":"https://www.wikidata.org/wiki/Q4677469","display_name":"Activation function","level":3,"score":0.6674686670303345},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6106407642364502},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5946928262710571},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5858498811721802},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5752986073493958},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5456583499908447},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.47504356503486633},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.47194069623947144},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.46150022745132446},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40580832958221436},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3776912987232208},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36949703097343445},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3054555058479309},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.13522037863731384},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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":1,"locations":[{"id":"doi:10.1145/3394486.3403203","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3394486.3403203","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery &amp; Data Mining","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":18,"referenced_works":["https://openalex.org/W116068320","https://openalex.org/W192659748","https://openalex.org/W2010629420","https://openalex.org/W2022428385","https://openalex.org/W2112796928","https://openalex.org/W2141473882","https://openalex.org/W2161388792","https://openalex.org/W2166116275","https://openalex.org/W2213612645","https://openalex.org/W2402758762","https://openalex.org/W2752387826","https://openalex.org/W2962824709","https://openalex.org/W2962836461","https://openalex.org/W2963639956","https://openalex.org/W2964088238","https://openalex.org/W2964313743","https://openalex.org/W4205241946","https://openalex.org/W4240981432"],"related_works":["https://openalex.org/W1574414179","https://openalex.org/W1585770001","https://openalex.org/W2075873371","https://openalex.org/W4245210885","https://openalex.org/W84383711","https://openalex.org/W4242351093","https://openalex.org/W3214206881","https://openalex.org/W2893539081","https://openalex.org/W4224215271","https://openalex.org/W1827695239"],"abstract_inverted_index":{"It":[0],"is":[1,172],"fundamental":[2],"to":[3,18,83,113,202],"measure":[4,15,138],"model":[5,13,27,36,88,179,195,208],"complexity":[6,14,37,49,137,150,180],"of":[7,50,103,110,125,128,148,158,170,178,194],"deep":[8,87],"neural":[9,41,51,74,159],"networks.":[10],"A":[11],"good":[12],"can":[16],"help":[17],"tackle":[19,63],"many":[20],"challenging":[21],"problems,":[22],"such":[23],"as":[24],"overfitting":[25,171,204],"detection,":[26],"selection,":[28],"and":[29,106,134,161,188,213],"performance":[30],"improvement.":[31],"The":[32],"existing":[33],"literature":[34],"on":[35,40,140],"mainly":[38],"focuses":[39],"networks":[42,52,160],"with":[43,53,89,175],"piecewise":[44,80,96],"linear":[45,72,81,97,111,129],"activation":[46,56,91,101],"functions.":[47],"Model":[48],"general":[54],"curve":[55,90],"functions":[57],"remains":[58],"an":[59],"open":[60],"problem.":[61],"To":[62,144],"the":[64,100,108,122,126,136,141,146,149,155,168,176,186,192],"challenge,":[65],"in":[66],"this":[67],"paper,":[68],"we":[69,120,152,198],"first":[70],"propose":[71,199],"approximation":[73,98,117],"network":[75],"(LANN":[76],"for":[77,99],"short),":[78],"a":[79,85,115],"framework":[82],"approximate":[84],"given":[86],"function.":[92],"LANN":[93],"constructs":[94],"individual":[95],"function":[102],"each":[104],"neuron,":[105],"minimizes":[107],"number":[109,127],"regions":[112,130],"satisfy":[114],"required":[116],"degree.":[118],"Then,":[119],"analyze":[121],"upper":[123,142],"bound":[124],"formed":[131],"by":[132,205],"LANNs,":[133],"derive":[135],"based":[139],"bound.":[143],"examine":[145],"usefulness":[147],"measure,":[151],"experimentally":[153],"explore":[154],"training":[156],"process":[157],"detect":[162],"overfitting.":[163],"Our":[164],"results":[165],"demonstrate":[166],"that":[167,185],"occurrence":[169],"positively":[173],"correlated":[174],"increase":[177,193],"during":[181],"training.":[182],"We":[183],"find":[184],"L1":[187,215],"L2":[189],"regularizations":[190],"suppress":[191],"complexity.":[196],"Finally,":[197],"two":[200],"approaches":[201],"prevent":[203],"directly":[206],"constraining":[207],"complexity,":[209],"namely":[210],"neuron":[211],"pruning":[212],"customized":[214],"regularization.":[216]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3}],"updated_date":"2026-03-13T16:22:10.518609","created_date":"2025-10-10T00:00:00"}
