{"id":"https://openalex.org/W4403421083","doi":"https://doi.org/10.1109/tit.2024.3481269","title":"The Local Landscape of Phase Retrieval Under Limited Samples","display_name":"The Local Landscape of Phase Retrieval Under Limited Samples","publication_year":2024,"publication_date":"2024-10-15","ids":{"openalex":"https://openalex.org/W4403421083","doi":"https://doi.org/10.1109/tit.2024.3481269"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2024.3481269","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2024.3481269","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"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/A5065868245","display_name":"Kaizhao Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kaizhao Liu","raw_affiliation_strings":["School of Mathematical Sciences, Peking University, Beijing, China"],"raw_orcid":"https://orcid.org/0009-0008-7753-0030","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5115604829","display_name":"Zihao Wang","orcid":"https://orcid.org/0009-0004-9687-5457"},"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":"Zihao Wang","raw_affiliation_strings":["Department of Mathematics, Stanford University, Stanford, CA, USA"],"raw_orcid":"https://orcid.org/0009-0004-9687-5457","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Stanford University, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":null,"display_name":"Lei Wu","orcid":"https://orcid.org/0009-0004-0788-1493"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lei Wu","raw_affiliation_strings":["School of Mathematical Sciences and Center for Machine Learning Research, Peking University, Beijing, China"],"raw_orcid":"https://orcid.org/0009-0004-0788-1493","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and Center for Machine Learning Research, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"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":0.15276836,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"70","issue":"12","first_page":"9012","last_page":"9035"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12157","display_name":"Geochemistry and Geologic Mapping","score":0.9230999946594238,"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/T12157","display_name":"Geochemistry and Geologic Mapping","score":0.9230999946594238,"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/computer-science","display_name":"Computer science","score":0.577186107635498},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.44364985823631287},{"id":"https://openalex.org/keywords/information-retrieval","display_name":"Information retrieval","score":0.3285071551799774},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12022408843040466}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.577186107635498},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.44364985823631287},{"id":"https://openalex.org/C23123220","wikidata":"https://www.wikidata.org/wiki/Q816826","display_name":"Information retrieval","level":1,"score":0.3285071551799774},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12022408843040466},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2024.3481269","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2024.3481269","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/13","display_name":"Climate action","score":0.4000000059604645}],"awards":[{"id":"https://openalex.org/G2252290668","display_name":null,"funder_award_id":"2022YFA1008200","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W1545211435","https://openalex.org/W1981042292","https://openalex.org/W2015911499","https://openalex.org/W2022541060","https://openalex.org/W2093246563","https://openalex.org/W2102019642","https://openalex.org/W2142949395","https://openalex.org/W2145080587","https://openalex.org/W2283023501","https://openalex.org/W2287147025","https://openalex.org/W2542482481","https://openalex.org/W2761315682","https://openalex.org/W2790687101","https://openalex.org/W2955601265","https://openalex.org/W2963073572","https://openalex.org/W2963443408","https://openalex.org/W2969215180","https://openalex.org/W3037508544","https://openalex.org/W3085097441","https://openalex.org/W3094857757","https://openalex.org/W3113425034","https://openalex.org/W3120243577","https://openalex.org/W3123272904","https://openalex.org/W3169803339","https://openalex.org/W4205607078","https://openalex.org/W4205633435","https://openalex.org/W4250954493","https://openalex.org/W4313525046","https://openalex.org/W4378979031","https://openalex.org/W4381806233","https://openalex.org/W6631190155","https://openalex.org/W6637461557","https://openalex.org/W6684191040","https://openalex.org/W6687403782","https://openalex.org/W6696112117","https://openalex.org/W6712153814","https://openalex.org/W6713869322","https://openalex.org/W6734280532","https://openalex.org/W6738373677","https://openalex.org/W6748278370","https://openalex.org/W6748748765","https://openalex.org/W6772055179","https://openalex.org/W6778540096","https://openalex.org/W6779364481","https://openalex.org/W6785059860","https://openalex.org/W6810225657","https://openalex.org/W6849630339"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052","https://openalex.org/W4402327032"],"abstract_inverted_index":{"We":[0,52,89],"present":[1],"a":[2,30,188,220],"fine-grained":[3],"analysis":[4],"of":[5,9,15,190],"the":[6,13,23,45,55,75,78,92,111,118,140,209,223],"local":[7,32,56,76,119,212],"landscape":[8,33,112],"phase":[10],"retrieval":[11],"under":[12,234],"regime":[14],"limited":[16,235],"samples.":[17],"Specifically,":[18],"we":[19,175],"aim":[20],"to":[21,28,163,218,222],"ascertain":[22],"minimal":[24],"sample":[25,46],"size":[26,47],"required":[27],"guarantee":[29],"benign":[31],"surrounding":[34],"global":[35],"minima":[36],"in":[37,74,117,158,208],"high":[38,109],"dimensions.":[39],"Let":[40],"n":[41],"and":[42,48,58,95,143],"d":[43,85],"denote":[44],"input":[49],"dimension,":[50],"respectively.":[51],"first":[53],"explore":[54],"convexity":[57,94,205],"establish":[59,219],"that":[60,151,177,203],"when":[61,178],"<inline-formula":[62,101,121,133,165,179,191,225],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[63,102,122,134,166,180,192,226],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[64,103,123,135,167,181,193,227],"<tex-math":[65,104,124,136,168,182,194,228],"notation=\"LaTeX\">$n=o(d\\log":[66,183],"d)$":[67,184],"</tex-math></inline-formula>,":[68,107,131,185],"for":[69,231],"almost":[70],"every":[71],"fixed":[72],"point":[73,157],"ball,":[77],"Hessian":[79],"matrix":[80],"has":[81],"negative":[82],"eigenvalues,":[83],"provided":[84],"is":[86,113,139,145,187],"sufficiently":[87],"large.":[88],"next":[90],"consider":[91],"one-point":[93,114,204,241],"show":[96,176],"that,":[97],"as":[98,100],"long":[99],"notation=\"LaTeX\">$n=\\omega":[105],"(d)$":[106],"with":[108],"probability,":[110],"strongly":[115],"convex":[116],"annulus:":[120],"notation=\"LaTeX\">$\\{w\\in":[125],"\\mathbb":[126],"{R}^{d}:":[127],"o_{d}({1})\\leqslant":[128],"\\|w-w^{*}\\|\\leqslant":[129],"c\\}$":[130],"where":[132],"notation=\"LaTeX\">$w^{*}$":[137,229],"</tex-math></inline-formula>":[138,201,230],"ground":[141],"truth":[142],"c":[144],"an":[146,164,216],"absolute":[147],"constant.":[148],"This":[149,214],"implies":[150],"gradient":[152,232],"descent,":[153],"initialized":[154],"from":[155],"any":[156],"this":[159],"domain,":[160],"can":[161],"converge":[162],"notation=\"LaTeX\">$o_{d}({1})$":[169],"</tex-math></inline-formula>-loss":[170],"solution":[171],"exponentially":[172],"fast.":[173],"Furthermore,":[174],"there":[186],"radius":[189],"notation=\"LaTeX\">$\\widetilde":[195],"{\\Theta":[196],"}":[197],"\\left":[198],"({{\\sqrt":[199],"{1/d}}}\\right)$":[200],"such":[202],"breaks":[206],"down":[207],"corresponding":[210],"smaller":[211],"ball.":[213],"indicates":[215],"impossibility":[217],"convergence":[221],"exact":[224],"descent":[233],"samples":[236],"by":[237],"relying":[238],"solely":[239],"on":[240],"convexity.":[242]},"counts_by_year":[],"updated_date":"2025-12-27T23:08:20.325037","created_date":"2025-10-10T00:00:00"}
