{"id":"https://openalex.org/W4385278446","doi":"https://doi.org/10.1007/s00354-023-00226-1","title":"Structured Matrices and Their Application in Neural Networks: A Survey","display_name":"Structured Matrices and Their Application in Neural Networks: A Survey","publication_year":2023,"publication_date":"2023-07-26","ids":{"openalex":"https://openalex.org/W4385278446","doi":"https://doi.org/10.1007/s00354-023-00226-1"},"language":"en","primary_location":{"id":"doi:10.1007/s00354-023-00226-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00354-023-00226-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00354-023-00226-1.pdf","source":{"id":"https://openalex.org/S165364243","display_name":"New Generation Computing","issn_l":"0288-3635","issn":["0288-3635","1882-7055"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"New Generation Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00354-023-00226-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033656694","display_name":"Matthias Kissel","orcid":"https://orcid.org/0000-0003-4089-3934"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Matthias Kissel","raw_affiliation_strings":["TUM School of Computation, Information and Technology, Technical University of Munich, Arcisstr. 21, 80333, Munich, Bavaria, Germany"],"raw_orcid":"https://orcid.org/0000-0003-4089-3934","affiliations":[{"raw_affiliation_string":"TUM School of Computation, Information and Technology, Technical University of Munich, Arcisstr. 21, 80333, Munich, Bavaria, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074346065","display_name":"Klaus Diepold","orcid":"https://orcid.org/0000-0003-0439-7511"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Klaus Diepold","raw_affiliation_strings":["TUM School of Computation, Information and Technology, Technical University of Munich, Arcisstr. 21, 80333, Munich, Bavaria, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TUM School of Computation, Information and Technology, Technical University of Munich, Arcisstr. 21, 80333, Munich, Bavaria, Germany","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5033656694"],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":{"value":3090,"currency":"USD","value_usd":3090},"fwci":1.2683,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.8234793,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"41","issue":"3","first_page":"697","last_page":"722"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9994000196456909,"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":0.9994000196456909,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.7593925595283508},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.6897212862968445},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6502538919448853},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5920118689537048},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.5565662384033203},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.54609215259552},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4727139174938202},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.43792960047721863},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.431179016828537},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.42484748363494873},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34698113799095154},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.34171828627586365},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.13739630579948425}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7593925595283508},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6897212862968445},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6502538919448853},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5920118689537048},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5565662384033203},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.54609215259552},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4727139174938202},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.43792960047721863},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.431179016828537},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.42484748363494873},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34698113799095154},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.34171828627586365},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.13739630579948425},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00354-023-00226-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00354-023-00226-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00354-023-00226-1.pdf","source":{"id":"https://openalex.org/S165364243","display_name":"New Generation Computing","issn_l":"0288-3635","issn":["0288-3635","1882-7055"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"New Generation Computing","raw_type":"journal-article"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1763561","is_oa":true,"landing_page_url":"https://mediatum.ub.tum.de/1763561","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s00354-023-00226-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00354-023-00226-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00354-023-00226-1.pdf","source":{"id":"https://openalex.org/S165364243","display_name":"New Generation Computing","issn_l":"0288-3635","issn":["0288-3635","1882-7055"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"New Generation Computing","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5799999833106995,"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320323383","display_name":"Technische Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/02kkvpp62"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4385278446.pdf"},"referenced_works_count":67,"referenced_works":["https://openalex.org/W21639112","https://openalex.org/W608773355","https://openalex.org/W1506342804","https://openalex.org/W1584657480","https://openalex.org/W1588915715","https://openalex.org/W1606733333","https://openalex.org/W1973786815","https://openalex.org/W1983452621","https://openalex.org/W1984439507","https://openalex.org/W1987393840","https://openalex.org/W1987724179","https://openalex.org/W2001626771","https://openalex.org/W2019166112","https://openalex.org/W2026651112","https://openalex.org/W2027828864","https://openalex.org/W2038198231","https://openalex.org/W2050746438","https://openalex.org/W2051395078","https://openalex.org/W2061171222","https://openalex.org/W2062240003","https://openalex.org/W2063961547","https://openalex.org/W2083206954","https://openalex.org/W2098602979","https://openalex.org/W2110404184","https://openalex.org/W2114977680","https://openalex.org/W2125389748","https://openalex.org/W2132820941","https://openalex.org/W2132984323","https://openalex.org/W2145140212","https://openalex.org/W2152332944","https://openalex.org/W2157164240","https://openalex.org/W2171506994","https://openalex.org/W2188296733","https://openalex.org/W2194775991","https://openalex.org/W2245896225","https://openalex.org/W2274086169","https://openalex.org/W2293747114","https://openalex.org/W2298381282","https://openalex.org/W2339536549","https://openalex.org/W2558026684","https://openalex.org/W2590462597","https://openalex.org/W2593110912","https://openalex.org/W2604319603","https://openalex.org/W2741427986","https://openalex.org/W2749641708","https://openalex.org/W2765315405","https://openalex.org/W2766447205","https://openalex.org/W2766697789","https://openalex.org/W2894977338","https://openalex.org/W2905100748","https://openalex.org/W2912029173","https://openalex.org/W2963230471","https://openalex.org/W2963585199","https://openalex.org/W2963809228","https://openalex.org/W2964156591","https://openalex.org/W2989600087","https://openalex.org/W3037399553","https://openalex.org/W3100023701","https://openalex.org/W3127887098","https://openalex.org/W3134229947","https://openalex.org/W3154671241","https://openalex.org/W4297811661","https://openalex.org/W4297811735","https://openalex.org/W4297838910","https://openalex.org/W4312396463","https://openalex.org/W6601144205","https://openalex.org/W6685298420"],"related_works":["https://openalex.org/W2378211422","https://openalex.org/W2745001401","https://openalex.org/W4321353415","https://openalex.org/W2130974462","https://openalex.org/W972276598","https://openalex.org/W2361403716","https://openalex.org/W2904061867","https://openalex.org/W4289115725","https://openalex.org/W3144644423","https://openalex.org/W2024384195"],"abstract_inverted_index":{"Abstract":[0],"Modern":[1],"neural":[2,127,153,187],"network":[3,47],"architectures":[4],"are":[5,62,121],"becoming":[6],"larger":[7],"and":[8,17,67,94,111,189],"deeper,":[9],"with":[10],"increasing":[11],"computational":[12,40],"resources":[13],"needed":[14],"for":[15,42,141],"training":[16],"inference.":[18],"One":[19],"approach":[20],"toward":[21],"handling":[22],"this":[23,71],"increased":[24],"resource":[25],"consumption":[26],"is":[27,56,164],"to":[28,114,180],"use":[29,182],"structured":[30,167,184],"weight":[31,37,158],"matrices.":[32,98,145,168],"By":[33],"exploiting":[34],"structures":[35,66,120],"in":[36,117,123,155,186],"matrices,":[38,86],"the":[39,46,53,78,101,119,124,134,139,149,157,161,171,181],"complexity":[41],"propagating":[43],"information":[44],"through":[45],"can":[48],"be":[49],"reduced.":[50],"However,":[51],"choosing":[52],"right":[54],"structure":[55,68,82,105,109],"not":[57],"trivial,":[58],"especially":[59],"since":[60],"there":[61],"many":[63],"different":[64,143],"matrix":[65,81,159],"classes.":[69,135],"In":[70],"paper,":[72],"we":[73,137,147,174],"give":[74],"an":[75],"overview":[76],"over":[77],"four":[79],"main":[80],"classes,":[83],"namely":[84],"semiseparable":[85],"matrices":[87,93,185],"of":[88,96,103,126,152,160,183],"low":[89],"displacement":[90],"rank,":[91],"hierarchical":[92],"products":[95],"sparse":[97],"We":[99,129],"recapitulate":[100],"definitions":[102],"each":[104],"class,":[106],"present":[107,130],"special":[108],"subclasses,":[110],"provide":[112],"references":[113],"research":[115,177,192],"papers":[116],"which":[118,156],"used":[122],"domain":[125],"networks.":[128],"two":[131],"benchmarks":[132],"comparing":[133],"First,":[136],"benchmark":[138,172],"error":[140],"approximating":[142],"test":[144],"Second,":[146],"compare":[148],"prediction":[150],"performance":[151],"networks":[154,188],"last":[162],"layer":[163],"replaced":[165],"by":[166],"After":[169],"presenting":[170],"results,":[173],"discuss":[175],"open":[176],"questions":[178],"related":[179],"highlight":[190],"future":[191],"directions.":[193]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
