{"id":"https://openalex.org/W3098085121","doi":"https://doi.org/10.1109/tnnls.2020.3030565","title":"SurReal: Complex-Valued Learning as Principled Transformations on a Scaling and Rotation Manifold","display_name":"SurReal: Complex-Valued Learning as Principled Transformations on a Scaling and Rotation Manifold","publication_year":2020,"publication_date":"2020-11-10","ids":{"openalex":"https://openalex.org/W3098085121","doi":"https://doi.org/10.1109/tnnls.2020.3030565","mag":"3098085121","pmid":"https://pubmed.ncbi.nlm.nih.gov/33170785"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2020.3030565","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2020.3030565","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025100345","display_name":"Rudrasis Chakraborty","orcid":"https://orcid.org/0000-0002-0448-911X"},"institutions":[{"id":"https://openalex.org/I1297971548","display_name":"International Computer Science Institute","ror":"https://ror.org/01ewh7m12","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I1297971548"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Rudrasis Chakraborty","raw_affiliation_strings":["International Computer Science Institute (ICSI), University of California at Berkeley (UC Berkeley), Berkeley, CA, USA"],"affiliations":[{"raw_affiliation_string":"International Computer Science Institute (ICSI), University of California at Berkeley (UC Berkeley), Berkeley, CA, USA","institution_ids":["https://openalex.org/I1297971548","https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045346394","display_name":"Yifei Xing","orcid":"https://orcid.org/0000-0002-5206-9515"},"institutions":[{"id":"https://openalex.org/I1297971548","display_name":"International Computer Science Institute","ror":"https://ror.org/01ewh7m12","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I1297971548"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yifei Xing","raw_affiliation_strings":["International Computer Science Institute (ICSI), University of California at Berkeley (UC Berkeley), Berkeley, CA, USA"],"affiliations":[{"raw_affiliation_string":"International Computer Science Institute (ICSI), University of California at Berkeley (UC Berkeley), Berkeley, CA, USA","institution_ids":["https://openalex.org/I1297971548","https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042014034","display_name":"Stella X. Yu","orcid":"https://orcid.org/0000-0002-3507-5761"},"institutions":[{"id":"https://openalex.org/I1297971548","display_name":"International Computer Science Institute","ror":"https://ror.org/01ewh7m12","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I1297971548"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stella X. Yu","raw_affiliation_strings":["International Computer Science Institute (ICSI), University of California at Berkeley (UC Berkeley), Berkeley, CA, USA"],"affiliations":[{"raw_affiliation_string":"International Computer Science Institute (ICSI), University of California at Berkeley (UC Berkeley), Berkeley, CA, USA","institution_ids":["https://openalex.org/I1297971548","https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5025100345"],"corresponding_institution_ids":["https://openalex.org/I1297971548","https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":1.7833,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.88336008,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"33","issue":"3","first_page":"940","last_page":"951"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9900000095367432,"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":0.9900000095367432,"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/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9879999756813049,"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/T12946","display_name":"Fractal and DNA sequence analysis","score":0.9801999926567078,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.6001535654067993},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5897389650344849},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5625768899917603},{"id":"https://openalex.org/keywords/equivariant-map","display_name":"Equivariant map","score":0.5073444247245789},{"id":"https://openalex.org/keywords/tangent-bundle","display_name":"Tangent bundle","score":0.49624425172805786},{"id":"https://openalex.org/keywords/tangent-space","display_name":"Tangent space","score":0.47500669956207275},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4570072591304779},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.44967252016067505},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3971134424209595},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3570649027824402},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.33180299401283264},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30207210779190063},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.24313384294509888},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10657927393913269}],"concepts":[{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.6001535654067993},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5897389650344849},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5625768899917603},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.5073444247245789},{"id":"https://openalex.org/C28903235","wikidata":"https://www.wikidata.org/wiki/Q746550","display_name":"Tangent bundle","level":3,"score":0.49624425172805786},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.47500669956207275},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4570072591304779},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.44967252016067505},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3971134424209595},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3570649027824402},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.33180299401283264},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30207210779190063},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24313384294509888},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10657927393913269},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2020.3030565","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2020.3030565","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:33170785","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33170785","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W1578621147","https://openalex.org/W1974778413","https://openalex.org/W1978524241","https://openalex.org/W1991605728","https://openalex.org/W1993482030","https://openalex.org/W2010853190","https://openalex.org/W2026892575","https://openalex.org/W2032802519","https://openalex.org/W2034470681","https://openalex.org/W2044738244","https://openalex.org/W2048446345","https://openalex.org/W2072072671","https://openalex.org/W2075649259","https://openalex.org/W2087640086","https://openalex.org/W2112796928","https://openalex.org/W2116341502","https://openalex.org/W2120435280","https://openalex.org/W2126602610","https://openalex.org/W2134563598","https://openalex.org/W2135858797","https://openalex.org/W2143572124","https://openalex.org/W2194775991","https://openalex.org/W2261689926","https://openalex.org/W2272847350","https://openalex.org/W2558748708","https://openalex.org/W2576915720","https://openalex.org/W2890212406","https://openalex.org/W2919115771","https://openalex.org/W2956119932","https://openalex.org/W2962996460","https://openalex.org/W2963482031","https://openalex.org/W2963630186","https://openalex.org/W2966844953","https://openalex.org/W2982973723","https://openalex.org/W3106050203","https://openalex.org/W4231109964","https://openalex.org/W4360620679","https://openalex.org/W6631603772","https://openalex.org/W6637178625","https://openalex.org/W6679349780","https://openalex.org/W6694954494","https://openalex.org/W6717575008","https://openalex.org/W6738884980","https://openalex.org/W6743757654","https://openalex.org/W6744291033","https://openalex.org/W6748579715","https://openalex.org/W6752004172","https://openalex.org/W6753878646","https://openalex.org/W6755221244","https://openalex.org/W6755848407","https://openalex.org/W6763956835","https://openalex.org/W6768943855","https://openalex.org/W6769504725"],"related_works":["https://openalex.org/W1979300328","https://openalex.org/W2050728860","https://openalex.org/W2013051270","https://openalex.org/W1993056240","https://openalex.org/W4377864461","https://openalex.org/W2096403660","https://openalex.org/W2735816623","https://openalex.org/W4225110265","https://openalex.org/W2400724917","https://openalex.org/W2755430707"],"abstract_inverted_index":{"Complex-valued":[0,48],"data":[1,49],"are":[2],"ubiquitous":[3],"in":[4,13],"signal":[5],"and":[6,10,62,98,151,180,202,214],"image":[7],"processing":[8],"applications,":[9],"complex-valued":[11,27,45,56,102,215],"representations":[12],"deep":[14,28,46],"learning":[15,29],"have":[16,23],"appealing":[17],"theoretical":[18],"properties.":[19],"While":[20],"these":[21],"aspects":[22],"long":[24],"been":[25],"recognized,":[26],"continues":[30],"to":[31,44,54,116,127,145,161,171],"lag":[32],"far":[33],"behind":[34],"its":[35],"real-valued":[36,125],"counterpart.":[37],"We":[38,114,131,192],"propose":[39,115],"a":[40,59,92,106,209],"principled":[41],"geometric":[42],"approach":[43],"learning.":[47],"could":[50,65],"often":[51],"be":[52],"subject":[53],"arbitrary":[55],"scaling;":[57],"as":[58,72,91,134,177,183,185,197],"result,":[60],"real":[61,77],"imaginary":[63],"components":[64],"covary.":[66],"Instead":[67],"of":[68,76,88,95,108,121,124,148,212],"treating":[69],"complex":[70,89,129],"values":[71],"two":[73],"independent":[74],"channels":[75],"values,":[78],"we":[79,84],"recognize":[80],"their":[81],"underlying":[82],"geometry:":[83],"model":[85,195],"the":[86,118,122,128,135,140,146,156,162,189],"space":[87],"numbers":[90],"product":[93],"manifold":[94,141,157,166],"nonzero":[96],"scaling":[97,103],"planar":[99],"rotations.":[100],"Arbitrary":[101],"naturally":[104],"becomes":[105],"group":[107,147],"transitive":[109],"actions":[110,150],"on":[111,139,155,188,200],"this":[112],"manifold.":[113],"extend":[117],"property":[119],"instead":[120],"form":[123],"functions":[126],"domain.":[130],"define":[132,152,172],"convolution":[133],"weighted":[136],"Fr\u00e9chet":[137],"mean":[138],"that":[142,158],"is":[143,159],"equivariant":[144],"scaling/rotation":[149],"distance":[153],"transform":[154],"invariant":[160],"action":[163],"group.":[164],"The":[165],"perspective":[167],"also":[168],"allows":[169],"us":[170],"nonlinear":[173],"activation":[174],"functions,":[175],"such":[176],"tangent":[178],"ReLU":[179],"G":[181],"-transport,":[182],"well":[184],"residual":[186],"connections":[187],"manifold-valued":[190],"data.":[191],"dub":[193],"our":[194,198],"SurReal,":[196],"experiments":[199],"MSTAR":[201],"RadioML":[203],"deliver":[204],"high":[205],"performance":[206],"with":[207],"only":[208],"fractional":[210],"size":[211],"real-":[213],"baseline":[216],"models.":[217]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
