{"id":"https://openalex.org/W4376639556","doi":"https://doi.org/10.1145/3564246.3585103","title":"Resolving Matrix Spencer Conjecture Up to Poly-logarithmic Rank","display_name":"Resolving Matrix Spencer Conjecture Up to Poly-logarithmic Rank","publication_year":2023,"publication_date":"2023-05-16","ids":{"openalex":"https://openalex.org/W4376639556","doi":"https://doi.org/10.1145/3564246.3585103"},"language":"en","primary_location":{"id":"doi:10.1145/3564246.3585103","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3564246.3585103","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 55th Annual ACM Symposium on Theory of Computing","raw_type":"proceedings-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/A5008689083","display_name":"Nikhil Bansal","orcid":"https://orcid.org/0000-0002-6290-0894"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Nikhil Bansal","raw_affiliation_strings":["University of Michigan, Ann Arbor, USA"],"affiliations":[{"raw_affiliation_string":"University of Michigan, Ann Arbor, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075618349","display_name":"Haotian Jiang","orcid":"https://orcid.org/0000-0002-5952-7689"},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Haotian Jiang","raw_affiliation_strings":["Microsoft Research, USA"],"affiliations":[{"raw_affiliation_string":"Microsoft Research, USA","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044675813","display_name":"Raghu Meka","orcid":"https://orcid.org/0009-0004-7676-2762"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Raghu Meka","raw_affiliation_strings":["University of California at Los Angeles, Los Angeles, USA"],"affiliations":[{"raw_affiliation_string":"University of California at Los Angeles, Los Angeles, USA","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5008689083"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":1.0332,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.80638384,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"1814","last_page":"1819"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9997000098228455,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9997000098228455,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.9994999766349792,"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/conjecture","display_name":"Conjecture","score":0.8432695865631104},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7525954246520996},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.7394422292709351},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6649547219276428},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6488766670227051},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5284666419029236},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4989032745361328},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.4462140202522278},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4424678087234497},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.41064849495887756},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1257321536540985},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.10206696391105652},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05770516395568848}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8432695865631104},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7525954246520996},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.7394422292709351},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6649547219276428},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6488766670227051},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5284666419029236},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4989032745361328},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.4462140202522278},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4424678087234497},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.41064849495887756},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1257321536540985},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.10206696391105652},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05770516395568848},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3564246.3585103","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3564246.3585103","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 55th Annual ACM Symposium on Theory of Computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1498399422","display_name":null,"funder_award_id":"AF:Small 2007682","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3464653562","display_name":"BioPump - Biodegradable MEMS implants for heart failure recovery","funder_award_id":"22170","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G4405413375","display_name":null,"funder_award_id":"639.023.812","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G5072720925","display_name":"AF: Small: Challenges in Communication Complexity and Pseudorandomness","funder_award_id":"2007682","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5455436254","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G6037617637","display_name":null,"funder_award_id":"2217033","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6894402473","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8333547667","display_name":null,"funder_award_id":"VICI grant 639.023.812","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G8398577554","display_name":"Mechanics and Data-Driven Approach for Developing Resilient Asphalt Materials (MEDAS)","funder_award_id":"21703","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309652","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291"},{"id":"https://openalex.org/F4320310094","display_name":"University of Washington","ror":"https://ror.org/00cvxb145"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W596018869","https://openalex.org/W864923667","https://openalex.org/W1518600598","https://openalex.org/W1581497052","https://openalex.org/W2011095973","https://openalex.org/W2067081844","https://openalex.org/W2079002396","https://openalex.org/W2080024126","https://openalex.org/W2084471691","https://openalex.org/W2088402854","https://openalex.org/W2115242663","https://openalex.org/W2116921087","https://openalex.org/W2134348739","https://openalex.org/W2140322654","https://openalex.org/W2144053122","https://openalex.org/W2148195034","https://openalex.org/W2149178517","https://openalex.org/W2558885861","https://openalex.org/W2593701861","https://openalex.org/W2950343740","https://openalex.org/W2962998255","https://openalex.org/W2963046017","https://openalex.org/W2963978809","https://openalex.org/W2964162348","https://openalex.org/W3000895154","https://openalex.org/W3007362474","https://openalex.org/W3035592582","https://openalex.org/W3070214604","https://openalex.org/W3088300790","https://openalex.org/W3104611862","https://openalex.org/W3150597598","https://openalex.org/W3205665995","https://openalex.org/W3214544158","https://openalex.org/W4206039841","https://openalex.org/W4213358110","https://openalex.org/W4255357113","https://openalex.org/W4281886990","https://openalex.org/W4285035123"],"related_works":["https://openalex.org/W2120826334","https://openalex.org/W2038812594","https://openalex.org/W2077251859","https://openalex.org/W384763036","https://openalex.org/W2100600533","https://openalex.org/W3207412727","https://openalex.org/W1880408471","https://openalex.org/W4376639556","https://openalex.org/W2917327790","https://openalex.org/W4288555402"],"abstract_inverted_index":{"We":[0],"give":[1],"a":[2,57],"simple":[3],"proof":[4],"of":[5],"the":[6],"matrix":[7],"Spencer":[8],"conjecture":[9],"up":[10],"to":[11],"poly-logarithmic":[12],"rank:":[13],"given":[14],"symmetric":[15],"d":[16,18],"\u00d7":[17],"matrices":[19],"A1,\u2026,An":[20],"each":[21],"with":[22,74],"||Ai||op":[23],"\u2264":[24],"1":[25,37],"and":[26],"rank":[27],"at":[28],"most":[29],"n/log3":[30],"n,":[31],"one":[32],"can":[33],"efficiently":[34],"find":[35],"\u00b1":[36],"signs":[38],"x1,\u2026,xn":[39],"such":[40],"that":[41],"their":[42],"signed":[43],"sum":[44],"has":[45],"spectral":[46],"norm":[47],"||\u2211i=1n":[48],"xi":[49],"Ai||op":[50],"=":[51],"O(\u221an).":[52],"This":[53],"result":[54],"also":[55],"implies":[56],"logn":[58],"\u2212":[59],"\u03a9(":[60],"loglogn)":[61],"qubit":[62],"lower":[63],"bound":[64],"for":[65],"quantum":[66],"random":[67],"access":[68],"codes":[69],"encoding":[70],"n":[71],"classical":[72],"bits":[73],"advantage":[75],"\u226b":[76],"1/\u221an.":[77]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2023,"cited_by_count":1}],"updated_date":"2026-04-14T08:04:32.555800","created_date":"2025-10-10T00:00:00"}