{"id":"https://openalex.org/W2862832041","doi":"https://doi.org/10.1609/aaai.v33i01.33013574","title":"The Goldilocks Zone: Towards Better Understanding of Neural Network Loss Landscapes","display_name":"The Goldilocks Zone: Towards Better Understanding of Neural Network Loss Landscapes","publication_year":2019,"publication_date":"2019-07-17","ids":{"openalex":"https://openalex.org/W2862832041","doi":"https://doi.org/10.1609/aaai.v33i01.33013574","mag":"2862832041"},"language":"en","primary_location":{"id":"doi:10.1609/aaai.v33i01.33013574","is_oa":true,"landing_page_url":"https://doi.org/10.1609/aaai.v33i01.33013574","pdf_url":"https://ojs.aaai.org/index.php/AAAI/article/download/4237/4115","source":{"id":"https://openalex.org/S4210191458","display_name":"Proceedings of the AAAI Conference on Artificial Intelligence","issn_l":"2159-5399","issn":["2159-5399","2374-3468"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320058","host_organization_name":"Association for the Advancement of Artificial Intelligence","host_organization_lineage":["https://openalex.org/P4310320058"],"host_organization_lineage_names":["Association for the Advancement of Artificial Intelligence"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the AAAI Conference on Artificial Intelligence","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://ojs.aaai.org/index.php/AAAI/article/download/4237/4115","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082696325","display_name":"Stanislav Fort","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Stanislav Fort","raw_affiliation_strings":["Stanford University","Stanford University ()"],"affiliations":[{"raw_affiliation_string":"Stanford University","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Stanford University ()","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050585164","display_name":"Adam Scherlis","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Adam Scherlis","raw_affiliation_strings":["Stanford University","Stanford University ()"],"affiliations":[{"raw_affiliation_string":"Stanford University","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Stanford University ()","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082696325"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00139373,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"33","issue":"01","first_page":"3574","last_page":"3581"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10036","display_name":"Advanced Neural Network Applications","score":0.9962999820709229,"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"}},"topics":[{"id":"https://openalex.org/T10036","display_name":"Advanced Neural Network Applications","score":0.9962999820709229,"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"}},{"id":"https://openalex.org/T14510","display_name":"Medical Imaging and Analysis","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9779000282287598,"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/goldilocks-principle","display_name":"Goldilocks principle","score":0.918255090713501},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.7983546257019043},{"id":"https://openalex.org/keywords/initialization","display_name":"Initialization","score":0.7355951070785522},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.6542066335678101},{"id":"https://openalex.org/keywords/mnist-database","display_name":"MNIST database","score":0.6411839127540588},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.5615971088409424},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5271334648132324},{"id":"https://openalex.org/keywords/hypersurface","display_name":"Hypersurface","score":0.49677401781082153},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4931756854057312},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.47390806674957275},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44053342938423157},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41356712579727173},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33545970916748047},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.28516626358032227},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2850952744483948},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2747664153575897},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.2700074017047882},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.25129565596580505}],"concepts":[{"id":"https://openalex.org/C177321328","wikidata":"https://www.wikidata.org/wiki/Q13580479","display_name":"Goldilocks principle","level":2,"score":0.918255090713501},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.7983546257019043},{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.7355951070785522},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.6542066335678101},{"id":"https://openalex.org/C190502265","wikidata":"https://www.wikidata.org/wiki/Q17069496","display_name":"MNIST database","level":3,"score":0.6411839127540588},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5615971088409424},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5271334648132324},{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.49677401781082153},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4931756854057312},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.47390806674957275},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44053342938423157},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41356712579727173},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33545970916748047},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.28516626358032227},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2850952744483948},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2747664153575897},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2700074017047882},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25129565596580505},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C87355193","wikidata":"https://www.wikidata.org/wiki/Q411","display_name":"Astrobiology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1609/aaai.v33i01.33013574","is_oa":true,"landing_page_url":"https://doi.org/10.1609/aaai.v33i01.33013574","pdf_url":"https://ojs.aaai.org/index.php/AAAI/article/download/4237/4115","source":{"id":"https://openalex.org/S4210191458","display_name":"Proceedings of the AAAI Conference on Artificial Intelligence","issn_l":"2159-5399","issn":["2159-5399","2374-3468"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320058","host_organization_name":"Association for the Advancement of Artificial Intelligence","host_organization_lineage":["https://openalex.org/P4310320058"],"host_organization_lineage_names":["Association for the Advancement of Artificial Intelligence"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the AAAI Conference on Artificial Intelligence","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1807.02581","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1807.02581","pdf_url":"https://arxiv.org/pdf/1807.02581","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":"mag:2862832041","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1807.02581.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1807.02581","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1807.02581","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1609/aaai.v33i01.33013574","is_oa":true,"landing_page_url":"https://doi.org/10.1609/aaai.v33i01.33013574","pdf_url":"https://ojs.aaai.org/index.php/AAAI/article/download/4237/4115","source":{"id":"https://openalex.org/S4210191458","display_name":"Proceedings of the AAAI Conference on Artificial Intelligence","issn_l":"2159-5399","issn":["2159-5399","2374-3468"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320058","host_organization_name":"Association for the Advancement of Artificial Intelligence","host_organization_lineage":["https://openalex.org/P4310320058"],"host_organization_lineage_names":["Association for the Advancement of Artificial Intelligence"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the AAAI Conference on Artificial Intelligence","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2862832041.pdf","grobid_xml":"https://content.openalex.org/works/W2862832041.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1533861849","https://openalex.org/W1677182931","https://openalex.org/W1850240193","https://openalex.org/W1998623809","https://openalex.org/W2523060838","https://openalex.org/W2751811815","https://openalex.org/W2785533664","https://openalex.org/W2963959597","https://openalex.org/W3118608800","https://openalex.org/W3207342693","https://openalex.org/W6654536944","https://openalex.org/W6743701321"],"related_works":["https://openalex.org/W2962733100","https://openalex.org/W2949807021","https://openalex.org/W2949261895","https://openalex.org/W3158495019","https://openalex.org/W3108510223","https://openalex.org/W2892675615","https://openalex.org/W3011817850","https://openalex.org/W2950183359","https://openalex.org/W3092788404","https://openalex.org/W2962804662","https://openalex.org/W1960772788","https://openalex.org/W3105287053","https://openalex.org/W2143527551","https://openalex.org/W2726109130","https://openalex.org/W2270734194","https://openalex.org/W3043374753","https://openalex.org/W2203233923","https://openalex.org/W1961558643","https://openalex.org/W2953111892","https://openalex.org/W2281204610"],"abstract_inverted_index":{"We":[0,72,132,173],"explore":[1],"the":[2,18,22,35,69,94,115,126,135,151,154,157,166,250],"loss":[3,23],"landscape":[4],"of":[5,21,34,37,40,47,54,83,119,122,128,168,186,190,212,219,226,229,258],"fully-connected":[6,77],"and":[7,15,42,86,90,96,99,125,137,156,160,193,214],"convolutional":[8,104],"neural":[9,78,180,207],"networks":[10,79,181],"using":[11],"random,":[12,144],"low-dimensional":[13,145],"hyperplanes":[14],"hyperspheres.":[16],"Evaluating":[17],"Hessian,":[19],"H,":[20,41,230],"function":[24],"on":[25,88,143,241,244],"these":[26],"hypersurfaces,":[27],"we":[28,65,109,202,247],"observe":[29,73],"1)":[30],"an":[31,254],"unusual":[32],"excess":[33],"number":[36,211,225],"positive":[38,123,191,227],"eigenvalues":[39,228],"2)":[43],"a":[44,50,60,81,100,111,129,162,195,206,210],"large":[45],"value":[46],"Tr(H)/||H||":[48],"at":[49,209],"well":[51],"defined":[52],"range":[53,82],"configuration":[55],"space":[56],"radii,":[57],"corresponding":[58],"to":[59,67,150,236],"thick,":[61],"hollow,":[62],"spherical":[63],"shell":[64],"refer":[66],"as":[68,161,223],"Goldilocks":[70,116,158,251],"zone.":[71],"this":[74,183],"effect":[75,102],"for":[76,103,198,216],"over":[80],"network":[84,130,208],"widths":[85],"depths":[87],"MNIST":[89],"CIFAR-10":[91],"datasets":[92],"with":[93],"ReLU":[95],"tanh":[97],"non-linearities,":[98],"similar":[101],"networks.":[105],"Using":[106],"our":[107,245],"observations,":[108,246],"demonstrate":[110,164,203],"close":[112],"connection":[113],"between":[114,153],"zone,":[117,159],"measures":[118,218],"local":[120,220],"convexity/prevalence":[121,189],"curvature,":[124,192],"suitability":[127],"initialization.":[131],"show":[133],"that":[134,165,175,204,249],"high":[136,188,217,256],"stable":[138],"accuracy":[139],"reached":[140],"when":[141],"optimizing":[142],"hypersurfaces":[146],"is":[147,171],"directly":[148],"related":[149],"overlap":[152],"hypersurface":[155],"corollary":[163],"notion":[167],"intrinsic":[169],"dimension":[170],"initialization-dependent.":[172],"note":[174],"common":[176],"initialization":[177,260],"techniques":[178],"initialize":[179],"in":[182],"particular":[184],"region":[185],"unusually":[187,255],"offer":[194],"geometric":[196],"intuition":[197],"their":[199],"success.":[200],"Furthermore,":[201],"initializing":[205],"points":[213],"selecting":[215],"convexity":[221],"such":[222],"Tr(H)/||H||,":[224],"or":[231],"low":[232],"initial":[233],"loss,":[234],"leads":[235],"statistically":[237],"significantly":[238],"faster":[239],"training":[240],"MNIST.":[242],"Based":[243],"hypothesize":[248],"zone":[252],"contains":[253],"density":[257],"suitable":[259],"configurations.":[261]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}