{"id":"https://openalex.org/W7128675794","doi":"https://doi.org/10.48550/arxiv.2602.10680","title":"A solvable high-dimensional model where nonlinear autoencoders learn structure invisible to PCA while test loss misaligns with generalization","display_name":"A solvable high-dimensional model where nonlinear autoencoders learn structure invisible to PCA while test loss misaligns with generalization","publication_year":2026,"publication_date":"2026-02-11","ids":{"openalex":"https://openalex.org/W7128675794","doi":"https://doi.org/10.48550/arxiv.2602.10680"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.10680","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5125733063","display_name":"Vicente Conde Mendes","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mendes, Vicente Conde","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125769034","display_name":"Lorenzo Bardone","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bardone, Lorenzo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5099040346","display_name":"C\u00e9dric Koller","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Koller, C\u00e9dric","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125706408","display_name":"Jorge Medina Moreira","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Moreira, Jorge Medina","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062834828","display_name":"Vittorio Erba","orcid":"https://orcid.org/0000-0001-8017-928X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Erba, Vittorio","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044679630","display_name":"Emanuele Troiani","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Troiani, Emanuele","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5125717212","display_name":"Lenka Zdeborov\u00e1","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zdeborov\u00e1, Lenka","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16707781,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.3846000134944916,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.3846000134944916,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.08780000358819962,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.08290000259876251,"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/autoencoder","display_name":"Autoencoder","score":0.8284000158309937},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.7534000277519226},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6460999846458435},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5856000185012817},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.5159000158309937},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4977000057697296},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.46880000829696655},{"id":"https://openalex.org/keywords/linear-model","display_name":"Linear model","score":0.4348999857902527}],"concepts":[{"id":"https://openalex.org/C101738243","wikidata":"https://www.wikidata.org/wiki/Q786435","display_name":"Autoencoder","level":3,"score":0.8284000158309937},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7534000277519226},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6460999846458435},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6366999745368958},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5856000185012817},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5410000085830688},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.5159000158309937},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4977000057697296},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.46880000829696655},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.4348999857902527},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.43149998784065247},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.4235999882221222},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3873000144958496},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.3490999937057495},{"id":"https://openalex.org/C51167844","wikidata":"https://www.wikidata.org/wiki/Q4422623","display_name":"Latent variable","level":2,"score":0.34769999980926514},{"id":"https://openalex.org/C16910744","wikidata":"https://www.wikidata.org/wiki/Q7705759","display_name":"Test data","level":2,"score":0.3467000126838684},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34380000829696655},{"id":"https://openalex.org/C65965080","wikidata":"https://www.wikidata.org/wiki/Q1806885","display_name":"Latent variable model","level":3,"score":0.3382999897003174},{"id":"https://openalex.org/C8038995","wikidata":"https://www.wikidata.org/wiki/Q1152135","display_name":"Unsupervised learning","level":2,"score":0.3163999915122986},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.298799991607666},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.2775999903678894},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.2678999900817871},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.2603999972343445},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.2572999894618988}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.10680","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.10680","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.10680","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.10680","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Many":[0],"real-world":[1],"datasets":[2],"contain":[3],"hidden":[4,51],"structure":[5,52,151],"that":[6,152],"cannot":[7],"be":[8,68],"detected":[9],"by":[10],"simple":[11],"linear":[12,105,153],"correlations":[13],"between":[14],"input":[15],"features.":[16],"For":[17],"example,":[18],"latent":[19,86,150],"factors":[20],"may":[21],"influence":[22],"the":[23,110,123],"data":[24],"in":[25,48,53,100],"a":[26,60,79,113,134],"coordinated":[27],"way,":[28],"even":[29,156],"though":[30,157],"their":[31,158],"effect":[32],"is":[33,141,161],"invisible":[34],"to":[35,90,108],"covariance-based":[36],"methods":[37,154],"such":[38,50],"as":[39],"PCA.":[40],"In":[41],"practice,":[42],"nonlinear":[43,115,147],"neural":[44],"networks":[45],"often":[46],"succeed":[47],"extracting":[49],"unsupervised":[54],"and":[55,92,104,126],"self-supervised":[56,138],"learning.":[57],"However,":[58],"constructing":[59],"minimal":[61,114],"high-dimensional":[62,81],"model":[63,83,131],"where":[64,137],"this":[65],"advantage":[66],"can":[67],"rigorously":[69],"analyzed":[70],"has":[71],"remained":[72],"an":[73],"open":[74],"theoretical":[75],"challenge.":[76],"We":[77,120],"introduce":[78],"tractable":[80,135],"spiked":[82],"with":[84,144],"two":[85],"factors:":[87],"one":[88,93],"visible":[89],"covariance,":[91],"statistically":[94],"dependent":[95],"yet":[96],"uncorrelated,":[97],"appearing":[98],"only":[99],"higher-order":[101],"moments.":[102],"PCA":[103],"autoencoders":[106,148],"fail":[107],"recover":[109,149],"latter,":[111],"while":[112],"autoencoder":[116],"provably":[117],"extracts":[118],"both.":[119],"analyze":[121],"both":[122],"population":[124],"risk,":[125],"empirical":[127],"risk":[128],"minimization.":[129],"Our":[130],"also":[132],"provides":[133],"example":[136],"test":[139],"loss":[140,160],"poorly":[142],"aligned":[143],"representation":[145],"quality:":[146],"miss,":[155],"reconstruction":[159],"higher.":[162]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-02-13T00:00:00"}
