{"id":"https://openalex.org/W7203663719","doi":"https://doi.org/10.5281/zenodo.21843787","title":"Normalized Spatial Synchronization Analysis of Weight Corrections during Adam Optimization of Neural Networks","display_name":"Normalized Spatial Synchronization Analysis of Weight Corrections during Adam Optimization of Neural Networks","publication_year":2026,"publication_date":"2026-08-07","ids":{"openalex":"https://openalex.org/W7203663719","doi":"https://doi.org/10.5281/zenodo.21843787"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.21843787","doi":"https://doi.org/10.5281/zenodo.21843787","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.21843787","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Dataset"},"parent_works":[],"lineage":["https://openalex.org/W7203663719"],"child_works_count":0,"type":"dataset","is_traditional":false,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.21843787","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108297879","display_name":"Serhiy Sveleba","orcid":"https://orcid.org/0000-0002-0823-910X","observed_orcids":["https://orcid.org/0000-0002-0823-910X"]},"institutions":[{"id":"https://openalex.org/I200280692","display_name":"Lviv University","ror":"https://ror.org/01s7y5e82","country_code":"UA","type":"education","lineage":["https://openalex.org/I200280692"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Sveleba, Sergey","raw_affiliation_strings":["Ivan Franko National University of Lviv, Lviv, Ukraine"],"raw_orcid":"https://orcid.org/0000-0002-0823-910X","affiliations":[{"raw_affiliation_string":"Ivan Franko National University of Lviv, Lviv, Ukraine","institution_ids":["https://openalex.org/I200280692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009109156","display_name":"Ivan Katerynchuk","orcid":"https://orcid.org/0000-0001-8877-8324","observed_orcids":["https://orcid.org/0000-0001-8877-8324"]},"institutions":[{"id":"https://openalex.org/I200280692","display_name":"Lviv University","ror":"https://ror.org/01s7y5e82","country_code":"UA","type":"education","lineage":["https://openalex.org/I200280692"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Katerynchuk, Ivan","raw_affiliation_strings":["Ivan Franko National University of Lviv, Lviv, Ukraine"],"raw_orcid":"https://orcid.org/0000-0001-8877-8324","affiliations":[{"raw_affiliation_string":"Ivan Franko National University of Lviv, Lviv, Ukraine","institution_ids":["https://openalex.org/I200280692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079092972","display_name":"Ivan Kuno","orcid":"https://orcid.org/0000-0001-6092-7949","observed_orcids":["https://orcid.org/0000-0001-6092-7949"]},"institutions":[{"id":"https://openalex.org/I200280692","display_name":"Lviv University","ror":"https://ror.org/01s7y5e82","country_code":"UA","type":"education","lineage":["https://openalex.org/I200280692"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Kuno, Ivan","raw_affiliation_strings":["Ivan Franko National University of Lviv, Lviv, Ukraine"],"raw_orcid":"https://orcid.org/0000-0001-6092-7949","affiliations":[{"raw_affiliation_string":"Ivan Franko National University of Lviv, Lviv, Ukraine","institution_ids":["https://openalex.org/I200280692"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017786142","display_name":"Nazar Sveleba","orcid":"https://orcid.org/0009-0002-5573-1380","observed_orcids":["https://orcid.org/0009-0002-5573-1380"]},"institutions":[{"id":"https://openalex.org/I4210133108","display_name":"European University","ror":"https://ror.org/032s10s29","country_code":"UA","type":"education","lineage":["https://openalex.org/I4210133108"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Sveleba, Nazar","raw_affiliation_strings":["European University, Kyiv, Ukraine"],"raw_orcid":"https://orcid.org/0009-0002-5573-1380","affiliations":[{"raw_affiliation_string":"European University, Kyiv, Ukraine","institution_ids":["https://openalex.org/I4210133108"]}]}],"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":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.8432999849319458,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.8432999849319458,"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/T10320","display_name":"Neural Networks and Applications","score":0.12999999523162842,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.004999999888241291,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/adam-optimizer","display_name":"Adam optimizer","score":0.953000009059906},{"id":"https://openalex.org/keywords/neural-network-training-dynamics","display_name":"neural network training dynamics","score":0.7329999804496765},{"id":"https://openalex.org/keywords/weight-correction","display_name":"weight correction","score":0.6710000038146973},{"id":"https://openalex.org/keywords/spatial-synchrony","display_name":"spatial synchrony","score":0.9639999866485596},{"id":"https://openalex.org/keywords/desynchronization","display_name":"desynchronization","score":0.5849999785423279},{"id":"https://openalex.org/keywords/multilayer-perceptron","display_name":"multilayer perceptron","score":0.7129999995231628},{"id":"https://openalex.org/keywords/cifar-10","display_name":"CIFAR-10","score":0.925000011920929},{"id":"https://openalex.org/keywords/momentum-parameter","display_name":"momentum parameter","score":0.574999988079071},{"id":"https://openalex.org/keywords/learning-rate","display_name":"learning rate","score":0.7239999771118164},{"id":"https://openalex.org/keywords/nonlinear-dynamical-systems","display_name":"nonlinear dynamical systems","score":0.7350000143051147},{"id":"https://openalex.org/keywords/adaptive-optimization","display_name":"adaptive optimization","score":0.6299999952316284},{"id":"https://openalex.org/keywords/high-dimensional-optimization","display_name":"high-dimensional optimization","score":0.4519999921321869}],"concepts":[{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.6590999960899353},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6563000082969666},{"id":"https://openalex.org/C60908668","wikidata":"https://www.wikidata.org/wiki/Q690207","display_name":"Perceptron","level":3,"score":0.5288000106811523},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48339998722076416},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.45879998803138733},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.447299987077713},{"id":"https://openalex.org/C60718061","wikidata":"https://www.wikidata.org/wiki/Q1414747","display_name":"Momentum (technical analysis)","level":2,"score":0.4341999888420105},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.41019999980926514},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4090999960899353},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3961000144481659},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.3465000092983246},{"id":"https://openalex.org/C159620131","wikidata":"https://www.wikidata.org/wiki/Q1938983","display_name":"Spatial analysis","level":2,"score":0.3325999975204468},{"id":"https://openalex.org/C179717631","wikidata":"https://www.wikidata.org/wiki/Q2991667","display_name":"Multilayer perceptron","level":3,"score":0.32919999957084656},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.321399986743927},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.31290000677108765},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.27970001101493835},{"id":"https://openalex.org/C205372480","wikidata":"https://www.wikidata.org/wiki/Q210521","display_name":"Image resolution","level":2,"score":0.26420000195503235},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.2533999979496002}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.21843787","doi":"https://doi.org/10.5281/zenodo.21843787","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.21843787","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Dataset"},{"id":"doi:10.5281/zenodo.21843788","doi":"https://doi.org/10.5281/zenodo.21843788","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.21843788","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Dataset"}],"best_oa_location":{"id":"doi:10.5281/zenodo.21843787","doi":"https://doi.org/10.5281/zenodo.21843787","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.21843787","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Dataset"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7204775134","https://openalex.org/W7203935391","https://openalex.org/W7160868503","https://openalex.org/W7151025598","https://openalex.org/W4413215864","https://openalex.org/W2997791832","https://openalex.org/W4404390276","https://openalex.org/W7127983712","https://openalex.org/W4312051919","https://openalex.org/W7167623173"],"abstract_inverted_index":{"This":[0,347],"dataset":[1,26,115,235,348],"contains":[2,116],"experimental":[3],"results":[4,117],"from":[5,140],"a":[6,32,362],"normalized":[7,136,248],"spatial":[8,48,137,162,207,228,249,265,277,302],"synchronization":[9,208,309],"analysis":[10,133],"of":[11,17,54,85,94,164,206,230,247,279,304,319,325,367],"weight":[12,39,87,143,191,232,307],"correction":[13,56,146,165,216],"dynamics":[14,84],"during":[15],"training":[16,30],"neural":[18,28,66,212,305,352],"networks":[19,67,353],"optimized":[20],"with":[21],"the":[22,70,83,160,203,210,241,256,264,269],"Adam":[23,43,86,142,261,320],"algorithm.":[24],"The":[25,58,114,132,234,293,330],"investigates":[27],"network":[29,306],"as":[31,355],"high-dimensional":[33],"nonlinear":[34,322],"dynamical":[35,323,358],"process,":[36],"where":[37,255],"adaptive":[38,231,299,357],"updates":[40],"generated":[41,337],"by":[42,274],"optimization":[44,300,328,368],"are":[45,295],"analyzed":[46,211],"through":[47],"organization,":[49],"synchronization,":[50],"and":[51,82,260,282,286,310,339,344,360],"temporal":[52],"evolution":[53],"neuron-wise":[55,141,215],"patterns.":[57],"experiments":[59],"were":[60,76,89],"performed":[61],"using":[62],"multilayer":[63],"perceptron":[64],"(MLP)":[65],"trained":[68],"on":[69,135,351],"CIFAR-10":[71,80],"dataset.":[72],"Binary":[73],"classification":[74],"tasks":[75],"constructed":[77],"for":[78,119,226,289,297,342,364],"individual":[79],"classes,":[81],"corrections":[88],"studied":[90],"under":[91],"different":[92,120],"combinations":[93],"optimizer":[95],"parameters:":[96],"learning":[97,314,327],"rate:":[98],"\u03b1":[99],"=":[100,124,127,130,149,174,199,219],"0.01;":[101],"first":[102],"momentum":[103,109],"parameter:":[104,110],"\u03b2\u2081":[105],"\u2208":[106,112],"[0,1);":[107],"second":[108],"\u03b2\u2082":[111],"[0,1).":[113],"obtained":[118],"input":[121],"dimensionalities:":[122],"d":[123,126,129],"32;":[125],"256;":[128],"2048.":[131],"focuses":[134],"observables":[138],"derived":[139],"corrections:":[144],"Normalized":[145,214],"amplitude":[147],"A_i(t)":[148],"(x_i(t)^2":[150],"+":[151,155,180,182,223],"x_{i+1}(t)^2)":[152],"/":[153,178,221],"(2\u00b7mean(x(t)^2)":[154],"\u03b5),":[156,224],"which":[157,184,201],"x_i(t)":[158,181,220],"characterizes":[159],"local":[161,187],"distribution":[163],"amplitudes":[166],"between":[167,189],"neighboring":[168,190],"neurons.":[169],"Local":[170],"synchronization-loss":[171],"coefficient":[172],"S_i(t)":[173,185],"|x_{i+1}(t)":[175],"\u2212":[176],"x_i(t)|":[177],"(x_{i+1}(t)":[179],"\u03b5)":[183],"quantifies":[186],"desynchronization":[188,311],"corrections.":[192],"Global":[193],"Spatial":[194],"Synchronization":[195],"Coefficient":[196],"(SSC)":[197],"S(t)":[198],"sqrt(mean(S_i(t)^2)),":[200],"describes":[202],"overall":[204],"level":[205],"within":[209],"layer.":[213],"profile":[217],"X_norm_i(t)":[218],"(sqrt(mean(x_j(t)^2))":[222],"used":[225],"studying":[227],"organization":[229,303],"updates.":[233],"includes:":[236],"dynamic":[237],"regime":[238,317],"maps":[239],"in":[240,313],"(\u03b21,\u03b22)":[242],"parameter":[243,266],"space;":[244],"three-dimensional":[245],"surfaces":[246],"observables;":[250],"full":[251],"four-dimensional":[252],"fields:":[253],"F(i,\u03b21,\u03b22),":[254],"neuron-pair":[257],"index":[258],"iii":[259],"parameters":[262],"define":[263],"domain,":[267],"while":[268],"field":[270],"value":[271],"is":[272],"represented":[273],"color":[275],"intensity;":[276],"profiles":[278],"Ai,":[280],"Si,":[281],"Xinorm;":[283],"numerical":[284,335],"matrices":[285],"CSV":[287],"summaries":[288],"further":[290,345],"statistical":[291],"analysis.":[292,346],"data":[294],"intended":[296],"studying:":[298],"dynamics;":[301],"corrections;":[308],"phenomena":[312],"processes;":[315],"parameter-dependent":[316],"transitions":[318],"optimization;":[321],"interpretation":[324],"deep":[326],"algorithms.":[329],"accompanying":[331],"files":[332],"provide":[333],"raw":[334],"results,":[336],"figures,":[338],"metadata":[340],"required":[341],"reproduction":[343],"supports":[349],"research":[350],"considered":[354],"complex":[356],"systems":[359],"provides":[361],"basis":[363],"quantitative":[365],"comparison":[366],"regimes":[369],"beyond":[370],"conventional":[371],"accuracy-based":[372],"evaluation.":[373]},"counts_by_year":[],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2026-08-19T00:00:00"}