{"id":"https://openalex.org/W7160987705","doi":"https://doi.org/10.48550/arxiv.2605.11291","title":"Optimal Representations for Generalized Contrastive Learning with Imbalanced Datasets","display_name":"Optimal Representations for Generalized Contrastive Learning with Imbalanced Datasets","publication_year":2026,"publication_date":"2026-05-11","ids":{"openalex":"https://openalex.org/W7160987705","doi":"https://doi.org/10.48550/arxiv.2605.11291"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.11291","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.11291","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,"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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.11291","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114062732","display_name":"Thuan Nguyen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nguyen, Thuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004738943","display_name":"Shuchin Aeron","orcid":"https://orcid.org/0000-0002-1049-9795"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aeron, Shuchin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043521380","display_name":"Donna Brown","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Brown, D. Richard","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5036913803","display_name":"Prakash Ishwar","orcid":"https://orcid.org/0000-0002-2621-1549"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ishwar, Prakash","raw_affiliation_strings":[],"raw_orcid":null,"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/T11652","display_name":"Imbalanced Data Classification Techniques","score":0.4934999942779541,"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/T11652","display_name":"Imbalanced Data Classification Techniques","score":0.4934999942779541,"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/T10057","display_name":"Face and Expression Recognition","score":0.10559999942779541,"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/T10136","display_name":"Statistical Methods and Inference","score":0.10509999841451645,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.7110999822616577},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5758000016212463},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5421000123023987},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5360000133514404},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.4666999876499176},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.4169999957084656},{"id":"https://openalex.org/keywords/frame","display_name":"Frame (networking)","score":0.37529999017715454},{"id":"https://openalex.org/keywords/convex-geometry","display_name":"Convex geometry","score":0.353300005197525}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7213000059127808},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.7110999822616577},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5758000016212463},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5421000123023987},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5360000133514404},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.4666999876499176},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.4169999957084656},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.37529999017715454},{"id":"https://openalex.org/C110202963","wikidata":"https://www.wikidata.org/wiki/Q1783542","display_name":"Convex geometry","level":5,"score":0.353300005197525},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3508000075817108},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.33640000224113464},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32899999618530273},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3215000033378601},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.29179999232292175},{"id":"https://openalex.org/C133978748","wikidata":"https://www.wikidata.org/wiki/Q15955882","display_name":"Reflection symmetry","level":2,"score":0.2856000065803528},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C143271835","wikidata":"https://www.wikidata.org/wiki/Q254515","display_name":"Similitude","level":2,"score":0.2651999890804291},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2565999925136566},{"id":"https://openalex.org/C41779539","wikidata":"https://www.wikidata.org/wiki/Q2543717","display_name":"Equiangular polygon","level":3,"score":0.2558000087738037},{"id":"https://openalex.org/C2776230367","wikidata":"https://www.wikidata.org/wiki/Q7314222","display_name":"Representation theorem","level":2,"score":0.2524000108242035},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.25200000405311584},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.2515999972820282}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.11291","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.11291","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,"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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.11291","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.11291","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,"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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"score":0.6174677610397339,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0,115],"this":[1,132],"paper,":[2],"we":[3,81,117,135],"provide":[4],"a":[5,74,127,138,151,170,178,217],"computable":[6],"characterization":[7],"of":[8,11,36,78,87,188,197,219],"the":[9,19,28,34,42,52,61,84,91,111,120,161,174,185,189,195,210],"geometry":[10,101,121],"optimal":[12,43,85],"representations":[13,44,50,86],"in":[14,181],"Contrastive":[15],"Learning":[16],"(CL)":[17],"when":[18],"classes":[20,24,72,163],"are":[21,25,202],"imbalanced.":[22],"When":[23],"balanced":[26],"and":[27,60,73,99,146,193,208],"representation":[29],"dimension":[30],"is":[31,39,108,144],"greater":[32],"than":[33],"number":[35,196,218],"classes,":[37],"it":[38],"well-known":[40],"that":[41,83,107,119,148],"exhibit":[45],"Neural":[46],"Collapse":[47,155],"(NC),":[48],"i.e.,":[49],"from":[51,90,160],"same":[53,92],"class":[54,58,62,93,97,113,142,175],"collapse":[55,94,168],"to":[56,95,204],"their":[57,96,100],"means":[59,63,98],"form":[64],"an":[65,103],"Equiangular":[66],"Tight":[67],"Frame":[68],"(ETF).":[69],"For":[70],"imbalanced":[71],"large,":[75],"generalized":[76],"family":[77],"CL":[79,149,190],"losses,":[80],"prove":[82,147],"all":[88,158],"samples":[89,159],"exhibits":[102,150],"angular":[104],"symmetry":[105,133],"structure":[106],"determined":[109,124],"by":[110,125,215],"relative":[112],"proportions.":[114],"general,":[116],"show":[118],"can":[122],"be":[123],"solving":[126],"convex":[128],"optimization":[129],"problem.":[130],"Exploiting":[131],"structure,":[134],"analytically":[136],"investigate":[137],"special":[139],"case":[140],"where":[141,157],"imbalance":[143,176],"extreme":[145],"phenomenon":[152],"called":[153],"Minority":[154],"(MC)":[156],"minority":[162],"(classes":[164],"with":[165],"small":[166],"probabilities)":[167],"into":[169],"single":[171],"vector,":[172],"whenever":[173],"exceeds":[177],"threshold,":[179],"which":[180],"turn":[182],"depends":[183],"on":[184,194],"regularity":[186],"properties":[187],"loss":[191],"used":[192],"negative":[198],"samples.":[199],"Numerical":[200],"results":[201],"provided":[203],"illustrate":[205],"these":[206],"phenomena":[207],"corroborate":[209],"theoretical":[211],"results.":[212],"We":[213],"conclude":[214],"identifying":[216],"open":[220],"problems.":[221]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-14T00:00:00"}
