{"id":"https://openalex.org/W2989894248","doi":"https://doi.org/10.1561/2200000057","title":"Learning on Matrices and Tensors","display_name":"Learning on Matrices and Tensors","publication_year":2019,"publication_date":"2019-11-28","ids":{"openalex":"https://openalex.org/W2989894248","doi":"https://doi.org/10.1561/2200000057","mag":"2989894248"},"language":"en","primary_location":{"id":"doi:10.1561/2200000057","is_oa":false,"landing_page_url":"https://doi.org/10.1561/2200000057","pdf_url":null,"source":{"id":"https://openalex.org/S4210188176","display_name":"Foundations and Trends\u00ae in Machine Learning","issn_l":"1935-8237","issn":["1935-8237","1935-8245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318575","host_organization_name":"Now Publishers","host_organization_lineage":["https://openalex.org/P4310318575"],"host_organization_lineage_names":["Now Publishers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations and Trends\u00ae in Machine Learning","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2004.07984","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053327055","display_name":"Majid Janzamin","orcid":null},"institutions":[{"id":"https://openalex.org/I113979032","display_name":"Twitter (United States)","ror":"https://ror.org/04wt43v05","country_code":"US","type":"company","lineage":["https://openalex.org/I113979032"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Majid Janzamin","raw_affiliation_strings":["Twitter, USA"],"affiliations":[{"raw_affiliation_string":"Twitter, USA","institution_ids":["https://openalex.org/I113979032"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035001911","display_name":"Rong Ge","orcid":"https://orcid.org/0000-0002-2218-3675"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rong Ge","raw_affiliation_strings":["Duke University, USA"],"affiliations":[{"raw_affiliation_string":"Duke University, USA","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006048318","display_name":"Jean Kossaifi","orcid":"https://orcid.org/0000-0002-4445-3429"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jean Kossaifi","raw_affiliation_strings":["Imperial College London, UK"],"affiliations":[{"raw_affiliation_string":"Imperial College London, UK","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014498545","display_name":"Anima Anandkumar","orcid":"https://orcid.org/0000-0002-6974-6797"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]},{"id":"https://openalex.org/I4210127875","display_name":"Nvidia (United States)","ror":"https://ror.org/03jdj4y14","country_code":"US","type":"company","lineage":["https://openalex.org/I4210127875"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anima Anandkumar","raw_affiliation_strings":["NVIDIA and California Institute of Technology, USA"],"affiliations":[{"raw_affiliation_string":"NVIDIA and California Institute of Technology, USA","institution_ids":["https://openalex.org/I4210127875","https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5053327055"],"corresponding_institution_ids":["https://openalex.org/I113979032"],"apc_list":null,"apc_paid":null,"fwci":1.7606,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.8368356,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"12","issue":"5-6","first_page":"393","last_page":"536"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.953000009059906,"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":0.9225999712944031,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/principal-component-analysis","display_name":"Principal component analysis","score":0.5923778414726257},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5757203102111816},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.5707626938819885},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5512984395027161},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.4767887592315674},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.46994760632514954},{"id":"https://openalex.org/keywords/latent-variable","display_name":"Latent variable","score":0.4449462890625},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.44295793771743774},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.4394083321094513},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42224639654159546},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42147672176361084},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4209003746509552},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.4173215627670288},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.4150291979312897},{"id":"https://openalex.org/keywords/eigendecomposition-of-a-matrix","display_name":"Eigendecomposition of a matrix","score":0.4130842685699463}],"concepts":[{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.5923778414726257},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5757203102111816},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.5707626938819885},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5512984395027161},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.4767887592315674},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.46994760632514954},{"id":"https://openalex.org/C51167844","wikidata":"https://www.wikidata.org/wiki/Q4422623","display_name":"Latent variable","level":2,"score":0.4449462890625},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.44295793771743774},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.4394083321094513},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42224639654159546},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42147672176361084},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4209003746509552},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4173215627670288},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.4150291979312897},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.4130842685699463},{"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/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1561/2200000057","is_oa":false,"landing_page_url":"https://doi.org/10.1561/2200000057","pdf_url":null,"source":{"id":"https://openalex.org/S4210188176","display_name":"Foundations and Trends\u00ae in Machine Learning","issn_l":"1935-8237","issn":["1935-8237","1935-8245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318575","host_organization_name":"Now Publishers","host_organization_lineage":["https://openalex.org/P4310318575"],"host_organization_lineage_names":["Now Publishers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations and Trends\u00ae in Machine Learning","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2004.07984","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2004.07984","pdf_url":"https://arxiv.org/pdf/2004.07984","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"},{"id":"pmh:oai:authors.library.caltech.edu:103456","is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20200526-130837701","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:aleph.bib-bvb.de:BVB01-033293317","is_oa":false,"landing_page_url":"https://www.nowpublishers.com/article/Details/MAL-057","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"software, multimedia"},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/79271","is_oa":false,"landing_page_url":"http://hdl.handle.net/10044/1/79271","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"536","raw_type":"Journal Article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2004.07984","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2004.07984","pdf_url":"https://arxiv.org/pdf/2004.07984","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":[{"id":"https://metadata.un.org/sdg/14","display_name":"Life below water","score":0.7300000190734863}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":140,"referenced_works":["https://openalex.org/W632330365","https://openalex.org/W658559791","https://openalex.org/W1505878979","https://openalex.org/W1581152950","https://openalex.org/W1583477766","https://openalex.org/W1612003148","https://openalex.org/W1697075315","https://openalex.org/W1755563775","https://openalex.org/W1798945469","https://openalex.org/W1811734137","https://openalex.org/W1839868949","https://openalex.org/W1870083876","https://openalex.org/W1880262756","https://openalex.org/W1885038349","https://openalex.org/W1939652453","https://openalex.org/W1964724001","https://openalex.org/W1970136394","https://openalex.org/W1970377488","https://openalex.org/W1974403130","https://openalex.org/W1974511160","https://openalex.org/W1978632288","https://openalex.org/W1981651876","https://openalex.org/W1988738948","https://openalex.org/W2000134594","https://openalex.org/W2000215628","https://openalex.org/W2002598080","https://openalex.org/W2004026774","https://openalex.org/W2007321142","https://openalex.org/W2011301426","https://openalex.org/W2014565165","https://openalex.org/W2022749269","https://openalex.org/W2022852240","https://openalex.org/W2024165284","https://openalex.org/W2025341678","https://openalex.org/W2030699645","https://openalex.org/W2031213242","https://openalex.org/W2033154334","https://openalex.org/W2046164006","https://openalex.org/W2047064469","https://openalex.org/W2050616618","https://openalex.org/W2057214765","https://openalex.org/W2057503509","https://openalex.org/W2057853309","https://openalex.org/W2063392856","https://openalex.org/W2071128523","https://openalex.org/W2072802070","https://openalex.org/W2073414385","https://openalex.org/W2079231426","https://openalex.org/W2079705627","https://openalex.org/W2090208105","https://openalex.org/W2096295738","https://openalex.org/W2099741732","https://openalex.org/W2101234009","https://openalex.org/W2101641981","https://openalex.org/W2106100072","https://openalex.org/W2107052785","https://openalex.org/W2107438106","https://openalex.org/W2111448058","https://openalex.org/W2113722075","https://openalex.org/W2116658704","https://openalex.org/W2120340025","https://openalex.org/W2121739212","https://openalex.org/W2123649031","https://openalex.org/W2127218421","https://openalex.org/W2133487567","https://openalex.org/W2137837859","https://openalex.org/W2142496058","https://openalex.org/W2146292423","https://openalex.org/W2146777332","https://openalex.org/W2149655761","https://openalex.org/W2150059498","https://openalex.org/W2162636131","https://openalex.org/W2163246442","https://openalex.org/W2167026441","https://openalex.org/W2191540403","https://openalex.org/W2258054274","https://openalex.org/W2294384375","https://openalex.org/W2304387544","https://openalex.org/W2340369089","https://openalex.org/W2469230926","https://openalex.org/W2528907418","https://openalex.org/W2544822491","https://openalex.org/W2565444551","https://openalex.org/W2580834719","https://openalex.org/W2594905747","https://openalex.org/W2610857016","https://openalex.org/W2614634292","https://openalex.org/W2621097878","https://openalex.org/W2738900641","https://openalex.org/W2773126525","https://openalex.org/W2798909945","https://openalex.org/W2899771611","https://openalex.org/W2916976785","https://openalex.org/W2950275553","https://openalex.org/W2951439068","https://openalex.org/W2952594493","https://openalex.org/W2953337630","https://openalex.org/W2962785660","https://openalex.org/W2962790067","https://openalex.org/W2962804816","https://openalex.org/W2962907923","https://openalex.org/W2962988160","https://openalex.org/W2963048316","https://openalex.org/W2963055343","https://openalex.org/W2963058819","https://openalex.org/W2963225922","https://openalex.org/W2963250364","https://openalex.org/W2963396025","https://openalex.org/W2963553534","https://openalex.org/W2963595633","https://openalex.org/W2963811132","https://openalex.org/W2963993553","https://openalex.org/W2964015691","https://openalex.org/W2964106499","https://openalex.org/W2965132998","https://openalex.org/W3004970274","https://openalex.org/W3005347330","https://openalex.org/W3029645440","https://openalex.org/W3081927587","https://openalex.org/W3098015574","https://openalex.org/W3098045837","https://openalex.org/W3103788012","https://openalex.org/W3104815482","https://openalex.org/W3141898517","https://openalex.org/W3213228770","https://openalex.org/W4210358174","https://openalex.org/W4220801984","https://openalex.org/W4229972328","https://openalex.org/W4231510805","https://openalex.org/W4238805501","https://openalex.org/W4249925659","https://openalex.org/W4249992252","https://openalex.org/W4253115531","https://openalex.org/W4293052541","https://openalex.org/W4293775970","https://openalex.org/W4294326629","https://openalex.org/W4297573986","https://openalex.org/W4297755884","https://openalex.org/W4300001159","https://openalex.org/W4302036486"],"related_works":["https://openalex.org/W4294224199","https://openalex.org/W2156897583","https://openalex.org/W2289858865","https://openalex.org/W2150953077","https://openalex.org/W2112519774","https://openalex.org/W2110126483","https://openalex.org/W2548342391","https://openalex.org/W4287208482","https://openalex.org/W3155045649","https://openalex.org/W2148026948"],"abstract_inverted_index":{"Spectral":[0],"methods":[1,162],"have":[2,98],"been":[3],"the":[4,39,49,56,60,64,115,159,169,247],"mainstay":[5],"in":[6,85,131,147],"several":[7,99],"domains":[8],"such":[9],"as":[10,73],"machine":[11],"learning,":[12],"applied":[13,95],"mathematics":[14],"and":[15,91,188,260,309,320,323],"scientific":[16],"computing.":[17],"They":[18,256],"involve":[19],"finding":[20],"a":[21,111,148,155,173,237,291,301],"certain":[22],"kind":[23],"of":[24,63,75,154,176,236,240],"spectral":[25,46,93,160],"decomposition":[26,161,203,218,254],"to":[27,68,96,103,128,163,171,229,250,263,283,316],"obtain":[28],"basis":[29],"functions":[30],"that":[31,140,209],"can":[32,183,191,204,219,324],"capture":[33],"important":[34],"structures":[35],"or":[36,59,151],"directions":[37],"for":[38,232,295],"problem":[40],"at":[41],"hand.":[42],"The":[43],"most":[44],"common":[45],"method":[47],"is":[48,82],"principal":[50,57],"component":[51],"analysis":[52],"(PCA).":[53],"It":[54,299],"utilizes":[55],"components":[58],"top":[61],"eigenvectors":[62],"data":[65,79,122,134,265],"covariance":[66],"matrix":[67,213],"carry":[69,317],"out":[70,228,318],"dimensionality":[71],"reduction":[72],"one":[74],"its":[76],"applications.":[77],"This":[78,313],"pre-processing":[80],"step":[81],"often":[83],"effective":[84],"separating":[86],"signal":[87],"from":[88],"noise.":[89],"PCA":[90],"other":[92],"techniques":[94,249],"matrices":[97],"limitations.":[100],"By":[101,157],"limiting":[102],"only":[104],"pairwise":[105,197],"moments,":[106,166],"they":[107,119,190],"are":[108,137,210,257,280],"effectively":[109],"making":[110],"Gaussian":[112],"approximation":[113],"on":[114,121],"underlying":[116,152],"data.":[117],"Hence,":[118],"fail":[120],"with":[123,329],"hidden":[124],"variables":[125],"which":[126,289],"lead":[127],"non-Gaussianity.":[129],"However,":[130],"almost":[132],"any":[133],"set,":[135],"there":[136,268],"latent":[138,177,207,241],"effects":[139,208],"cannot":[141],"be":[142,184,230,284,326],"directly":[143],"observed,":[144],"e.g.,":[145],"topics":[146],"document":[149],"corpus,":[150],"causes":[153],"disease.":[156],"extending":[158],"higher":[164],"order":[165],"we":[167],"demonstrate":[168],"ability":[170],"learn":[172],"wide":[174,238],"range":[175,239],"variable":[178,242],"models":[179],"efficiently.":[180],"Higher-order":[181],"moments":[182],"represented":[185],"by":[186,212],"tensors,":[187],"intuitively,":[189],"encode":[192],"more":[193],"information":[194],"than":[195],"just":[196],"moment":[198],"matrices.":[199],"More":[200],"crucially,":[201],"tensor":[202,217,253,277,297],"pick":[205],"up":[206],"missed":[211],"methods.":[214,255],"For":[215],"instance,":[216],"uniquely":[220],"identify":[221],"non-orthogonal":[222],"components.":[223],"Exploiting":[224],"these":[225],"aspects":[226],"turns":[227],"fruitful":[231],"provable":[233],"unsupervised":[234],"learning":[235],"models.":[243],"We":[244,286],"also":[245,281,325],"outline":[246],"computational":[248],"design":[251],"efficient":[252,276],"embarrassingly":[258],"parallel":[259],"thus":[261],"scalable":[262],"large":[264],"sets.":[266],"Whilst":[267],"exist":[269],"many":[270],"optimized":[271],"linear":[272],"algebra":[273,278],"software":[274],"packages,":[275],"packages":[279],"beginning":[282],"developed.":[285],"introduce":[287],"Tensorly,":[288],"has":[290,300],"simple":[292],"python":[293],"interface":[294],"expressing":[296],"operations.":[298],"flexible":[302],"back-end":[303],"system":[304],"supporting":[305],"NumPy,":[306],"PyTorch,":[307],"TensorFlow":[308],"MXNet":[310],"amongst":[311],"others.":[312],"allows":[314],"it":[315],"multi-GPU":[319],"CPU":[321],"operations,":[322],"seamlessly":[327],"integrated":[328],"deep-learning":[330],"functionalities.":[331]},"counts_by_year":[{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
