{"id":"https://openalex.org/W3180526619","doi":"https://doi.org/10.1109/tnnls.2023.3241100","title":"Neural Network Layer Algebra: A Framework to Measure Capacity and Compression in Deep Learning","display_name":"Neural Network Layer Algebra: A Framework to Measure Capacity and Compression in Deep Learning","publication_year":2023,"publication_date":"2023-02-16","ids":{"openalex":"https://openalex.org/W3180526619","doi":"https://doi.org/10.1109/tnnls.2023.3241100","mag":"3180526619","pmid":"https://pubmed.ncbi.nlm.nih.gov/37027551"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2023.3241100","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2023.3241100","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5062200261","display_name":"Alberto Bad\u00edas","orcid":"https://orcid.org/0000-0001-7639-6767"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alberto Bad\u00edas","raw_affiliation_strings":["Department of Mechanical Engineering, University of Washington, Seattle, WA, USA"],"raw_orcid":"https://orcid.org/0000-0001-7639-6767","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of Washington, Seattle, WA, USA","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001953637","display_name":"Ashis G. Banerjee","orcid":"https://orcid.org/0000-0001-5898-7563"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ashis G. Banerjee","raw_affiliation_strings":["Department of Industrial and Systems Engineering and the Department of Mechanical Engineering, University of Washington, Seattle, WA, USA"],"raw_orcid":"https://orcid.org/0000-0001-5898-7563","affiliations":[{"raw_affiliation_string":"Department of Industrial and Systems Engineering and the Department of Mechanical Engineering, University of Washington, Seattle, WA, USA","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I201448701"],"apc_list":null,"apc_paid":null,"fwci":0.8065,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.76598286,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"35","issue":"8","first_page":"10380","last_page":"10393"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9994999766349792,"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":0.9994999766349792,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.9970999956130981,"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":0.9961000084877014,"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/computer-science","display_name":"Computer science","score":0.6655769348144531},{"id":"https://openalex.org/keywords/network-architecture","display_name":"Network architecture","score":0.6341210007667542},{"id":"https://openalex.org/keywords/learnability","display_name":"Learnability","score":0.6277058720588684},{"id":"https://openalex.org/keywords/layer","display_name":"Layer (electronics)","score":0.5468640923500061},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5440430641174316},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5229709148406982},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.49700382351875305},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4938817620277405},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.47667741775512695},{"id":"https://openalex.org/keywords/convolutional-neural-network","display_name":"Convolutional neural network","score":0.4721928834915161},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.469350665807724},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4170222282409668},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.32747653126716614},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2318301796913147},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.2062288224697113}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6655769348144531},{"id":"https://openalex.org/C193415008","wikidata":"https://www.wikidata.org/wiki/Q639681","display_name":"Network architecture","level":2,"score":0.6341210007667542},{"id":"https://openalex.org/C2777723229","wikidata":"https://www.wikidata.org/wiki/Q4367921","display_name":"Learnability","level":2,"score":0.6277058720588684},{"id":"https://openalex.org/C2779227376","wikidata":"https://www.wikidata.org/wiki/Q6505497","display_name":"Layer (electronics)","level":2,"score":0.5468640923500061},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5440430641174316},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5229709148406982},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.49700382351875305},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4938817620277405},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.47667741775512695},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.4721928834915161},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.469350665807724},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4170222282409668},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.32747653126716614},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2318301796913147},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.2062288224697113},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","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},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2023.3241100","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2023.3241100","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:37027551","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37027551","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":93,"referenced_works":["https://openalex.org/W1533861849","https://openalex.org/W1594730842","https://openalex.org/W1677182931","https://openalex.org/W1836465849","https://openalex.org/W1836632961","https://openalex.org/W1981530182","https://openalex.org/W2089947415","https://openalex.org/W2095705004","https://openalex.org/W2108598243","https://openalex.org/W2117130368","https://openalex.org/W2146337213","https://openalex.org/W2156387975","https://openalex.org/W2161388792","https://openalex.org/W2163605009","https://openalex.org/W2194775991","https://openalex.org/W2302255633","https://openalex.org/W2402144811","https://openalex.org/W2410678056","https://openalex.org/W2419597278","https://openalex.org/W2496126447","https://openalex.org/W2558008572","https://openalex.org/W2558967331","https://openalex.org/W2579923771","https://openalex.org/W2606101940","https://openalex.org/W2743909828","https://openalex.org/W2767286248","https://openalex.org/W2772552125","https://openalex.org/W2786622092","https://openalex.org/W2800415562","https://openalex.org/W2811004130","https://openalex.org/W2889756710","https://openalex.org/W2891495000","https://openalex.org/W2901024736","https://openalex.org/W2902305746","https://openalex.org/W2912117543","https://openalex.org/W2941045521","https://openalex.org/W2955425717","https://openalex.org/W2962845550","https://openalex.org/W2963097630","https://openalex.org/W2963131860","https://openalex.org/W2963399222","https://openalex.org/W2963421552","https://openalex.org/W2963982496","https://openalex.org/W2964031514","https://openalex.org/W2970971581","https://openalex.org/W2992043355","https://openalex.org/W3099132019","https://openalex.org/W3099937123","https://openalex.org/W3103322710","https://openalex.org/W3105416979","https://openalex.org/W3118608800","https://openalex.org/W3128308947","https://openalex.org/W4289220573","https://openalex.org/W4289287927","https://openalex.org/W4297813707","https://openalex.org/W4299436927","https://openalex.org/W4320930577","https://openalex.org/W6631943919","https://openalex.org/W6638868411","https://openalex.org/W6638899659","https://openalex.org/W6645550903","https://openalex.org/W6674330103","https://openalex.org/W6681686951","https://openalex.org/W6682889407","https://openalex.org/W6684191040","https://openalex.org/W6695477072","https://openalex.org/W6713134421","https://openalex.org/W6714763347","https://openalex.org/W6717177883","https://openalex.org/W6718212895","https://openalex.org/W6723731493","https://openalex.org/W6730657577","https://openalex.org/W6732517885","https://openalex.org/W6736534893","https://openalex.org/W6737988291","https://openalex.org/W6741253635","https://openalex.org/W6743923790","https://openalex.org/W6746668429","https://openalex.org/W6748230616","https://openalex.org/W6751002639","https://openalex.org/W6754189474","https://openalex.org/W6754715197","https://openalex.org/W6755310813","https://openalex.org/W6756221064","https://openalex.org/W6756584662","https://openalex.org/W6757782233","https://openalex.org/W6758779330","https://openalex.org/W6761636357","https://openalex.org/W6762718338","https://openalex.org/W6766978945","https://openalex.org/W6771233102","https://openalex.org/W6787972765","https://openalex.org/W6790606811"],"related_works":["https://openalex.org/W4302791369","https://openalex.org/W2951285859","https://openalex.org/W2766040214","https://openalex.org/W72092541","https://openalex.org/W37360785","https://openalex.org/W1973394166","https://openalex.org/W180475243","https://openalex.org/W1482441085","https://openalex.org/W2966858528","https://openalex.org/W2151687600"],"abstract_inverted_index":{"We":[0,160,181],"present":[1],"a":[2,153],"new":[3],"framework":[4,21],"to":[5,25,41,48,197],"measure":[6],"the":[7,56,63,73,80,88,101,108,125,128,133,137,157,175,184,195],"intrinsic":[8,93],"properties":[9,52,130,185,196],"of":[10,62,83,110,140,156,186],"(deep)":[11],"neural":[12,142],"networks.":[13],"While":[14],"we":[15,31,69],"focus":[16],"on":[17,55,107,124,132,201],"convolutional":[18],"networks,":[19],"our":[20,163,191],"can":[22,144,167],"be":[23,145,168],"extrapolated":[24],"any":[26,84,141],"network":[27,34,57,64,85,134,143],"architecture.":[28],"In":[29],"particular,":[30],"evaluate":[32],"two":[33,71],"properties,":[35],"namely,":[36],"capacity,":[37],"which":[38,45,113],"is":[39,46,114,122],"related":[40,47],"expressivity,":[42],"and":[43,59,136,170,193],"compression,":[44],"learnability.":[49],"Both":[50],"these":[51],"depend":[53,131],"only":[54],"structure":[58],"are":[60,98,105],"independent":[61],"parameters.":[65],"To":[66],"this":[67,118],"end,":[68],"propose":[70],"metrics:":[72],"first":[74],"one,":[75,90],"called":[76,91],"layer":[77,92,111],"complexity,":[78],"captures":[79],"architectural":[81],"complexity":[82,165],"layer;":[86],"and,":[87],"second":[89],"power,":[94],"encodes":[95],"how":[96],"data":[97],"compressed":[99],"along":[100],"network.":[102],"The":[103],"metrics":[104,192],"based":[106,123],"concept":[109,121],"algebra,":[112],"also":[115,182],"introduced":[116],"in":[117],"article.":[119],"This":[120],"idea":[126],"that":[127,162],"global":[129,158,164],"topology,":[135],"leaf":[138],"nodes":[139],"approximated":[146],"using":[147,190],"local":[148],"transfer":[149],"functions,":[150],"thereby":[151],"allowing":[152],"simple":[154],"computation":[155],"metrics.":[159],"show":[161],"metric":[166],"calculated":[169],"represented":[171],"more":[172],"conveniently":[173],"than":[174],"widely":[176],"used":[177],"Vapnik-Chervonenkis":[178],"(VC)":[179],"dimension.":[180],"compare":[183],"various":[187],"state-of-the-art":[188],"architectures":[189],"use":[194],"analyze":[198],"their":[199],"accuracy":[200],"benchmark":[202],"image":[203],"classification":[204],"datasets.":[205]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}