{"id":"https://openalex.org/W4386066414","doi":"https://doi.org/10.1109/isit54713.2023.10206652","title":"Lower Bounds for Multiclass Classification with Overparameterized Linear Models","display_name":"Lower Bounds for Multiclass Classification with Overparameterized Linear Models","publication_year":2023,"publication_date":"2023-06-25","ids":{"openalex":"https://openalex.org/W4386066414","doi":"https://doi.org/10.1109/isit54713.2023.10206652"},"language":"en","primary_location":{"id":"doi:10.1109/isit54713.2023.10206652","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit54713.2023.10206652","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE International Symposium on Information Theory (ISIT)","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/A5045114235","display_name":"David X. Wu","orcid":"https://orcid.org/0000-0003-4863-4689"},"institutions":[{"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":"David X. Wu","raw_affiliation_strings":["UC Berkeley,Department of EECS,Berkeley,California,94720"],"affiliations":[{"raw_affiliation_string":"UC Berkeley,Department of EECS,Berkeley,California,94720","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079317491","display_name":"Anant Sahai","orcid":"https://orcid.org/0000-0001-9263-7719"},"institutions":[{"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":"Anant Sahai","raw_affiliation_strings":["UC Berkeley,Department of EECS,Berkeley,California,94720"],"affiliations":[{"raw_affiliation_string":"UC Berkeley,Department of EECS,Berkeley,California,94720","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5045114235"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":0.3477,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.62863049,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"334","last_page":"339"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.996399998664856,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9896000027656555,"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/mathematics","display_name":"Mathematics","score":0.6106577515602112},{"id":"https://openalex.org/keywords/converse","display_name":"Converse","score":0.605383574962616},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.5801831483840942},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5586437582969666},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.502907931804657},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.4615594744682312},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44066762924194336},{"id":"https://openalex.org/keywords/lp-space","display_name":"Lp space","score":0.43169859051704407},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3853726387023926},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3580882251262665},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3425062596797943},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.34057730436325073},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.31506139039993286},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1242673397064209}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6106577515602112},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.605383574962616},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.5801831483840942},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5586437582969666},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.502907931804657},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.4615594744682312},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44066762924194336},{"id":"https://openalex.org/C172294467","wikidata":"https://www.wikidata.org/wiki/Q305936","display_name":"Lp space","level":3,"score":0.43169859051704407},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3853726387023926},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3580882251262665},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3425062596797943},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34057730436325073},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31506139039993286},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1242673397064209},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"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/isit54713.2023.10206652","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit54713.2023.10206652","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.44999998807907104}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W581334404","https://openalex.org/W1570089119","https://openalex.org/W2032291279","https://openalex.org/W2098346479","https://openalex.org/W2133214726","https://openalex.org/W2152471841","https://openalex.org/W2169891049","https://openalex.org/W2295172321","https://openalex.org/W2566079294","https://openalex.org/W2587788201","https://openalex.org/W2626872000","https://openalex.org/W2922153390","https://openalex.org/W2923764619","https://openalex.org/W2963480332","https://openalex.org/W2975960188","https://openalex.org/W3001279689","https://openalex.org/W3014316192","https://openalex.org/W3018252856","https://openalex.org/W3020361330","https://openalex.org/W3104101844","https://openalex.org/W3162172987","https://openalex.org/W3172995164","https://openalex.org/W3178606210","https://openalex.org/W3191067499","https://openalex.org/W3197744105","https://openalex.org/W3213378669","https://openalex.org/W4212774754","https://openalex.org/W4224815527","https://openalex.org/W4226022860","https://openalex.org/W4250954493","https://openalex.org/W4286984660","https://openalex.org/W4287777768","https://openalex.org/W4299785371","https://openalex.org/W4312426305","https://openalex.org/W6745276634","https://openalex.org/W6748155593","https://openalex.org/W6766887723","https://openalex.org/W6772383348","https://openalex.org/W6776071938","https://openalex.org/W6777730395","https://openalex.org/W6780266352","https://openalex.org/W6800070934","https://openalex.org/W6804307206","https://openalex.org/W6810017755","https://openalex.org/W6839194757"],"related_works":["https://openalex.org/W2387449261","https://openalex.org/W2418518962","https://openalex.org/W2963377682","https://openalex.org/W2043159103","https://openalex.org/W2391769344","https://openalex.org/W2359260952","https://openalex.org/W2977059567","https://openalex.org/W4289099368","https://openalex.org/W2036857931","https://openalex.org/W2321724992"],"abstract_inverted_index":{"Subramanian":[0],"et":[1],"al.":[2],"[1]":[3],"introduced":[4],"an":[5],"asymptotic":[6],"Gaussian-features":[7],"model":[8,66],"for":[9,59],"overparameterized":[10],"multiclass":[11],"classification":[12],"in":[13,64],"which":[14,67],"the":[15,43,47,81,88],"number":[16],"of":[17,46,80],"classes,":[18],"training":[19],"points,":[20],"and":[21],"parameters":[22],"all":[23],"go":[24],"to":[25,87],"infinity.":[26],"They":[27],"provided":[28],"some":[29],"achievable":[30],"regions":[31],"where":[32],"min-norm":[33,61],"interpolating":[34,62],"classifiers":[35,63],"successfully":[36],"asymptotically":[37],"generalize":[38],"as":[39,41],"well":[40],"conjecturing":[42],"full":[44],"form":[45],"region":[48],"based":[49],"on":[50],"a":[51,57,78],"heuristic":[52],"analysis.":[53],"Here,":[54],"we":[55],"introduce":[56],"converse":[58],"such":[60],"their":[65,70],"fully":[68],"matches":[69],"conjectured":[71],"regions.":[72],"The":[73],"key":[74],"technical":[75],"tool":[76],"is":[77],"variant":[79],"Hanson-Wright":[82],"concentration":[83],"inequality":[84],"that":[85,92],"applies":[86],"sparse":[89],"bilinear":[90],"forms":[91],"arise.":[93]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}