{"id":"https://openalex.org/W3171780980","doi":"https://doi.org/10.48550/arxiv.2106.07683","title":"Extracting Global Dynamics of Loss Landscape in Deep Learning Models","display_name":"Extracting Global Dynamics of Loss Landscape in Deep Learning Models","publication_year":2021,"publication_date":"2021-06-14","ids":{"openalex":"https://openalex.org/W3171780980","doi":"https://doi.org/10.48550/arxiv.2106.07683","mag":"3171780980"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2106.07683","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.07683","pdf_url":"https://arxiv.org/pdf/2106.07683","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2106.07683","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036081460","display_name":"Mohammed Eslami","orcid":"https://orcid.org/0000-0001-5488-1542","observed_orcids":["https://orcid.org/0000-0001-5488-1542"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eslami, Mohammed","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010119669","display_name":"Hamed Eramian","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eramian, Hamed","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051475216","display_name":"Marcio Gameiro","orcid":"https://orcid.org/0000-0003-2168-0757","observed_orcids":["https://orcid.org/0000-0003-2168-0757"]},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gameiro, Marcio","raw_affiliation_strings":["Rutgers University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rutgers University","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004040775","display_name":"William D. Kalies","orcid":"https://orcid.org/0000-0002-8228-3598","observed_orcids":["https://orcid.org/0000-0002-8228-3598"]},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]},{"id":"https://openalex.org/I63772739","display_name":"Florida Atlantic University","ror":"https://ror.org/05p8w6387","country_code":"US","type":"education","lineage":["https://openalex.org/I63772739"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kalies, William","raw_affiliation_strings":["Florida Atlantic University","Rutgers University *"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Florida Atlantic University","institution_ids":["https://openalex.org/I63772739"]},{"raw_affiliation_string":"Rutgers University *","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049298090","display_name":"Konstantin Mischaikow","orcid":"https://orcid.org/0000-0003-2876-4558","observed_orcids":["https://orcid.org/0000-0003-2876-4558"]},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]},{"id":"https://openalex.org/I63772739","display_name":"Florida Atlantic University","ror":"https://ror.org/05p8w6387","country_code":"US","type":"education","lineage":["https://openalex.org/I63772739"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mischaikow, Konstantin","raw_affiliation_strings":["Rutgers University","Florida Atlantic University#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rutgers University","institution_ids":["https://openalex.org/I102322142"]},{"raw_affiliation_string":"Florida Atlantic University#TAB#","institution_ids":["https://openalex.org/I63772739"]}]}],"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":true,"cited_by_count":1,"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":0.8115000128746033,"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":0.8115000128746033,"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":0.1597999930381775,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.00989999994635582,"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/loss-landscape","display_name":"loss landscape","score":0.9350000023841858},{"id":"https://openalex.org/keywords/training-dynamics","display_name":"training dynamics","score":0.6869999766349792},{"id":"https://openalex.org/keywords/dynamical-systems","display_name":"dynamical systems","score":0.7599999904632568},{"id":"https://openalex.org/keywords/global-dynamics","display_name":"global dynamics","score":0.38499999046325684},{"id":"https://openalex.org/keywords/interpretability","display_name":"interpretability","score":0.5989999771118164},{"id":"https://openalex.org/keywords/training-instability","display_name":"training instability","score":0.47600001096725464}],"concepts":[{"id":"https://openalex.org/C177774035","wikidata":"https://www.wikidata.org/wiki/Q1246948","display_name":"Granularity","level":2,"score":0.7383414506912231},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6254367232322693},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6092004179954529},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.5785651206970215},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.5679160356521606},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.5645127892494202},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5560019612312317},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.5209633111953735},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.45680469274520874},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.45359063148498535},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4508058428764343},{"id":"https://openalex.org/C151876577","wikidata":"https://www.wikidata.org/wiki/Q7049464","display_name":"Nonlinear dimensionality reduction","level":3,"score":0.4109612703323364},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.35309267044067383},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21798419952392578},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.12478992342948914},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08961322903633118},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2106.07683","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.07683","pdf_url":"https://arxiv.org/pdf/2106.07683","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"mag:3171780980","doi":null,"is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2106.07683","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2106.07683","doi":"https://doi.org/10.48550/arxiv.2106.07683","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2106.07683","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2106.07683","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.07683","pdf_url":"https://arxiv.org/pdf/2106.07683","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1850240193","https://openalex.org/W1866328638","https://openalex.org/W2314752401","https://openalex.org/W2805288495","https://openalex.org/W2896374939","https://openalex.org/W2896542238","https://openalex.org/W2952606356","https://openalex.org/W2962933129","https://openalex.org/W2963384892","https://openalex.org/W2970249264","https://openalex.org/W2970865211","https://openalex.org/W2997733093","https://openalex.org/W3021772978","https://openalex.org/W3100511085"],"related_works":["https://openalex.org/W4403571182","https://openalex.org/W6958345160","https://openalex.org/W7125506360","https://openalex.org/W4404569135","https://openalex.org/W3101581426","https://openalex.org/W4317435191","https://openalex.org/W3126672113","https://openalex.org/W4387839287","https://openalex.org/W3185178836","https://openalex.org/W7133184177"],"abstract_inverted_index":{"Deep":[0,100],"learning":[1,119],"models":[2,67],"evolve":[3],"through":[4],"training":[5,109,178],"to":[6,15,26,44,47,140,146,162,171,175],"learn":[7],"the":[8,12,35,50,53,69,96,108,118,130,136,142,164,177],"manifold":[9],"in":[10,52,129],"which":[11,30],"data":[13,38],"exists":[14],"satisfy":[16],"an":[17,123,159],"objective.":[18],"It":[19],"is":[20,62,76],"well":[21],"known":[22],"that":[23,173],"evolution":[24],"leads":[25],"different":[27],"final":[28],"states":[29,149],"produce":[31],"inconsistent":[32],"predictions":[33],"of":[34,71,110,127,138,144,150,167,179],"same":[36],"test":[37],"points.":[39],"This":[40],"calls":[41],"for":[42,95],"techniques":[43],"be":[45],"able":[46],"empirically":[48],"quantify":[49],"difference":[51],"trajectories":[54,128],"and":[55,83,121,170],"highlight":[56],"problematic":[57],"regions.":[58],"While":[59],"much":[60],"focus":[61],"placed":[63],"on":[64],"discovering":[65],"what":[66],"learn,":[68],"question":[70],"how":[72],"a":[73,93,114,168],"model":[74,169],"learns":[75],"less":[77],"studied":[78],"beyond":[79],"theoretical":[80],"landscape":[81],"characterizations":[82],"local":[84],"geometric":[85],"approximations":[86],"near":[87],"optimal":[88],"conditions.":[89],"Here,":[90],"we":[91],"present":[92],"toolkit":[94],"Dynamical":[97],"Organization":[98],"Of":[99],"Learning":[101],"Loss":[102],"Landscapes,":[103],"or":[104,152],"DOODL3.":[105],"DOODL3":[106],"formulates":[107],"neural":[111,180],"networks":[112],"as":[113],"dynamical":[115],"system,":[116],"analyzes":[117],"process,":[120],"presents":[122,158],"interpretable":[124],"global":[125,165],"view":[126],"loss":[131],"landscape.":[132],"Our":[133],"approach":[134],"uses":[135],"coarseness":[137],"topology":[139],"capture":[141],"granularity":[143],"geometry":[145],"mitigate":[147],"against":[148],"instability":[151],"elongated":[153],"training.":[154],"Overall,":[155],"our":[156],"analysis":[157],"empirical":[160],"framework":[161],"extract":[163],"dynamics":[166],"use":[172],"information":[174],"guide":[176],"networks.":[181]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2021-06-22T00:00:00"}