{"id":"https://openalex.org/W2859678021","doi":"https://doi.org/10.1109/hpec.2018.8547742","title":"Sparse Deep Neural Network Exact Solutions","display_name":"Sparse Deep Neural Network Exact Solutions","publication_year":2018,"publication_date":"2018-09-01","ids":{"openalex":"https://openalex.org/W2859678021","doi":"https://doi.org/10.1109/hpec.2018.8547742","mag":"2859678021"},"language":"en","primary_location":{"id":"doi:10.1109/hpec.2018.8547742","is_oa":false,"landing_page_url":"https://doi.org/10.1109/hpec.2018.8547742","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE High Performance extreme Computing Conference (HPEC)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1807.03165","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072108599","display_name":"Jeremy Kepner","orcid":"https://orcid.org/0000-0001-9668-2613"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jeremy Kepner","raw_affiliation_strings":["Massachusetts Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106926627","display_name":"Vikalo Gadepally","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vikalo Gadepally","raw_affiliation_strings":["Massachusetts Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070814106","display_name":"Hayden Jananthan","orcid":"https://orcid.org/0000-0001-6877-0923"},"institutions":[{"id":"https://openalex.org/I200719446","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34","country_code":"US","type":"education","lineage":["https://openalex.org/I200719446"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hayden Jananthan","raw_affiliation_strings":["Vanderbilt University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Vanderbilt University","institution_ids":["https://openalex.org/I200719446"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055866024","display_name":"Lauren Milechin","orcid":"https://orcid.org/0000-0002-0554-3624"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lauren Milechin","raw_affiliation_strings":["Massachusetts Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086076221","display_name":"Sid Samsi","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sid Samsi","raw_affiliation_strings":["Massachusetts Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9976999759674072,"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/T13650","display_name":"Computational Physics and Python Applications","score":0.9901999831199646,"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":0.6626905202865601},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.6620696783065796},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5924481153488159},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.5226028561592102},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5174030065536499},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4697188436985016},{"id":"https://openalex.org/keywords/deep-neural-networks","display_name":"Deep neural networks","score":0.46696996688842773},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.44303297996520996},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.4185869097709656},{"id":"https://openalex.org/keywords/content-addressable-memory","display_name":"Content-addressable memory","score":0.41376256942749023},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.39780476689338684},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.36972880363464355},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3645161986351013},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3519485592842102},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20946228504180908}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6626905202865601},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.6620696783065796},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5924481153488159},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.5226028561592102},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5174030065536499},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4697188436985016},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.46696996688842773},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.44303297996520996},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.4185869097709656},{"id":"https://openalex.org/C53442348","wikidata":"https://www.wikidata.org/wiki/Q745101","display_name":"Content-addressable memory","level":3,"score":0.41376256942749023},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.39780476689338684},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.36972880363464355},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3645161986351013},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3519485592842102},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20946228504180908},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/hpec.2018.8547742","is_oa":false,"landing_page_url":"https://doi.org/10.1109/hpec.2018.8547742","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE High Performance extreme Computing Conference (HPEC)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1807.03165","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1807.03165","pdf_url":"https://arxiv.org/pdf/1807.03165","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":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1807.03165","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1807.03165","pdf_url":"https://arxiv.org/pdf/1807.03165","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W180578187","https://openalex.org/W1870868768","https://openalex.org/W1935978687","https://openalex.org/W1968774621","https://openalex.org/W1978460546","https://openalex.org/W2037531197","https://openalex.org/W2041823554","https://openalex.org/W2042264548","https://openalex.org/W2045031658","https://openalex.org/W2062231579","https://openalex.org/W2073869024","https://openalex.org/W2101927907","https://openalex.org/W2108598243","https://openalex.org/W2108665656","https://openalex.org/W2112984492","https://openalex.org/W2125930537","https://openalex.org/W2127265337","https://openalex.org/W2130325614","https://openalex.org/W2133257461","https://openalex.org/W2146320039","https://openalex.org/W2147270524","https://openalex.org/W2156387975","https://openalex.org/W2163605009","https://openalex.org/W2172654076","https://openalex.org/W2185907055","https://openalex.org/W2279098554","https://openalex.org/W2601424732","https://openalex.org/W2603221039","https://openalex.org/W2606722458","https://openalex.org/W2607538525","https://openalex.org/W2735575534","https://openalex.org/W2743799610","https://openalex.org/W2775406941","https://openalex.org/W2780896127","https://openalex.org/W2911296969","https://openalex.org/W2919115771","https://openalex.org/W2953212265","https://openalex.org/W3099786550","https://openalex.org/W3122020404","https://openalex.org/W3198350258","https://openalex.org/W3210129736","https://openalex.org/W4298852295","https://openalex.org/W4389158502","https://openalex.org/W6640289440","https://openalex.org/W6676231525","https://openalex.org/W6678803612","https://openalex.org/W6679718588","https://openalex.org/W6682889407","https://openalex.org/W6684191040","https://openalex.org/W6735901087","https://openalex.org/W6741094427"],"related_works":["https://openalex.org/W1492794944","https://openalex.org/W169603398","https://openalex.org/W2049033869","https://openalex.org/W279701215","https://openalex.org/W2107697999","https://openalex.org/W1902246517","https://openalex.org/W3145837419","https://openalex.org/W4381050447","https://openalex.org/W1835670156","https://openalex.org/W4296405127"],"abstract_inverted_index":{"Deep":[0],"neural":[1],"networks":[2],"(DNNs)":[3],"have":[4],"emerged":[5],"as":[6],"key":[7],"enablers":[8],"of":[9,62,80,86,92,135,194,204],"machine":[10],"learning.":[11],"Applying":[12,127],"larger":[13],"DNNs":[14,43,66,131,141,152],"to":[15,58,111,130,153,161,173],"more":[16,45,48],"diverse":[17],"applications":[18],"is":[19,75],"an":[20],"important":[21],"challenge.":[22],"The":[23],"computations":[24],"performed":[25],"during":[26],"DNN":[27,136,167,179,190,195],"training":[28],"and":[29,47,82,94,113,117,138,157,197],"inference":[30,93],"are":[31,67,142],"dominated":[32],"by":[33,106],"operations":[34],"on":[35],"the":[36,40,72,77,90,107,133,162,202],"weight":[37,53],"matrices":[38,54],"describing":[39],"DNN.":[41],"As":[42],"incorporate":[44],"layers":[46],"neurons":[49],"per":[50],"layers,":[51],"these":[52],"may":[55],"be":[56,59,171,187],"required":[57],"sparse":[60,124,178,205],"because":[61],"memory":[63],"limitations.":[64],"Sparse":[65],"one":[68],"possible":[69],"approach,":[70],"but":[71],"underlying":[73],"theory":[74],"in":[76,122],"early":[78],"stages":[79],"development":[81],"presents":[83],"a":[84,198],"number":[85],"challenges,":[87],"including":[88],"determining":[89],"accuracy":[91],"selecting":[95],"nonzero":[96],"weights":[97],"for":[98,120,177,189,201],"training.":[99,206],"Associative":[100],"array":[101,151],"algebra":[102],"has":[103],"been":[104],"developed":[105],"big":[108],"data":[109,125],"community":[110],"combine":[112],"extend":[114],"database,":[115],"matrix,":[116],"graph/network":[118],"concepts":[119],"use":[121],"large,":[123],"problems.":[126],"this":[128],"mathematics":[129,137],"simplifies":[132],"formulation":[134],"reveals":[139],"that":[140,169],"linear":[143,164],"over":[144,181],"oscillating":[145],"semirings.":[146],"This":[147],"work":[148],"uses":[149],"associative":[150],"construct":[154,174],"exact":[155],"solutions":[156,185],"corresponding":[158],"perturbation":[159],"models":[160],"rectified":[163],"unit":[165],"(ReLU)":[166],"equations":[168],"can":[170,186],"used":[172,188],"test":[175],"vectors":[176],"implementations":[180],"various":[182],"precisions.":[183],"These":[184],"verification,":[191],"theoretical":[192],"explorations":[193],"properties,":[196],"starting":[199],"point":[200],"challenge":[203]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
