{"id":"https://openalex.org/W2193298673","doi":null,"title":"Classification of Manifolds by Single-Layer Neural Networks.","display_name":"Classification of Manifolds by Single-Layer Neural Networks.","publication_year":2015,"publication_date":"2015-12-06","ids":{"openalex":"https://openalex.org/W2193298673","mag":"2193298673"},"language":"en","primary_location":{"id":"mag:2193298673","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1512.01834","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},"volume":null,"type":"preprint","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/abs/1512.01834","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016533438","display_name":"SueYeon Chung","orcid":"https://orcid.org/0000-0001-5726-4865","observed_orcids":["https://orcid.org/0000-0001-5726-4865"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"SueYeon Chung","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-5726-4865","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001893893","display_name":"Daniel D. Lee","orcid":"https://orcid.org/0000-0002-2163-2686","observed_orcids":["https://orcid.org/0000-0002-2163-2686","https://orcid.org/0000-0003-4239-8777","https://orcid.org/0000-0001-6437-6339"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daniel D. Lee","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-2163-2686","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5073266403","display_name":"Haim Sompolinsky","orcid":"https://orcid.org/0000-0002-0322-0629","observed_orcids":["https://orcid.org/0000-0002-0322-0629"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Haim Sompolinsky","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-0322-0629","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/T10320","display_name":"Neural Networks and Applications","score":0.9916999936103821,"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/T10320","display_name":"Neural Networks and Applications","score":0.9916999936103821,"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/T10581","display_name":"Neural dynamics and brain function","score":0.003599999938160181,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10427","display_name":"Visual perception and processing mechanisms","score":0.0008999999845400453,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/single-layer-perceptron","display_name":"single-layer perceptron","score":0.8859999775886536},{"id":"https://openalex.org/keywords/perceptual-invariance","display_name":"perceptual invariance","score":0.7599999904632568}],"concepts":[{"id":"https://openalex.org/C60908668","wikidata":"https://www.wikidata.org/wiki/Q690207","display_name":"Perceptron","level":3,"score":0.7082436680793762},{"id":"https://openalex.org/C2775937380","wikidata":"https://www.wikidata.org/wiki/Q1232589","display_name":"Replica","level":2,"score":0.6817989945411682},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6572993397712708},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.6483767628669739},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5602390170097351},{"id":"https://openalex.org/C26760741","wikidata":"https://www.wikidata.org/wiki/Q160402","display_name":"Perception","level":2,"score":0.555202305316925},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5157492756843567},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4953292906284332},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4746045470237732},{"id":"https://openalex.org/C2779227376","wikidata":"https://www.wikidata.org/wiki/Q6505497","display_name":"Layer (electronics)","level":2,"score":0.4672643542289734},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.43840667605400085},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.43465954065322876},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.43301281332969666},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.35366448760032654},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3167627453804016},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"score":0.2312471568584442},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.2257208228111267},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.22018355131149292},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12332957983016968},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2193298673","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1512.01834","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}],"best_oa_location":{"id":"mag:2193298673","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1512.01834","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},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3128696818","https://openalex.org/W2766572821","https://openalex.org/W2469085137","https://openalex.org/W4417274023","https://openalex.org/W3004639598","https://openalex.org/W2005524850","https://openalex.org/W4384108749","https://openalex.org/W4408189760","https://openalex.org/W4386936396","https://openalex.org/W7215129698"],"abstract_inverted_index":{"The":[0],"neuronal":[1,34,51],"representation":[2],"of":[3,33,40,50,53,59,61,82],"objects":[4,41],"exhibit":[5],"enormous":[6],"variability":[7,29],"due":[8],"to":[9],"changes":[10],"in":[11],"the":[12,24,28,72,77,83],"object's":[13],"physical":[14],"features":[15],"such":[16],"as":[17],"location,":[18],"size,":[19],"orientation,":[20],"and":[21,36,80],"intensity.":[22],"How":[23],"brain":[25],"copes":[26],"with":[27],"across":[30],"these":[31],"manifolds":[32],"states":[35],"generates":[37],"invariant":[38],"perception":[39],"remains":[42],"poorly":[43],"understood.":[44],"Here":[45],"we":[46],"present":[47],"a":[48,65],"theory":[49,58],"classification":[52,60],"manifolds,":[54],"extending":[55],"Gardner's":[56],"replica":[57],"isolated":[62],"points":[63],"by":[64],"single":[66],"layer":[67],"perceptron.":[68],"We":[69],"evaluate":[70],"how":[71],"perceptron":[73],"capacity":[74],"depends":[75],"on":[76],"dimensionality,":[78],"size":[79],"shape":[81],"classified":[84],"manifolds.":[85]},"counts_by_year":[],"updated_date":"2026-10-17T09:40:24.721904","created_date":"2016-06-24T00:00:00"}
