{"id":"https://openalex.org/W7163544890","doi":"https://doi.org/10.48550/arxiv.2606.04280","title":"The Loss Is Not Enough: Sampling Conditions and Inductive Bias in Contrastive Representation Learning","display_name":"The Loss Is Not Enough: Sampling Conditions and Inductive Bias in Contrastive Representation Learning","publication_year":2026,"publication_date":"2026-06-02","ids":{"openalex":"https://openalex.org/W7163544890","doi":"https://doi.org/10.48550/arxiv.2606.04280"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.04280","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.04280","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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.2606.04280","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5122318458","display_name":"Justinas Zaliaduonis","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zaliaduonis, Justinas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005167857","display_name":"Patrick Putzky","orcid":"https://orcid.org/0000-0002-3923-2963"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Putzky, Patrick","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002993826","display_name":"Till Richter","orcid":"https://orcid.org/0000-0001-6008-8209"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Richter, Till","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137825601","display_name":"Sergios Gatidis","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gatidis, Sergios","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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.6262999773025513,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.6262999773025513,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.1720999926328659,"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/T11448","display_name":"Face recognition and analysis","score":0.05169999971985817,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/identifiability","display_name":"Identifiability","score":0.6410999894142151},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.608299970626831},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.5900999903678894},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4553999900817871},{"id":"https://openalex.org/keywords/feature-learning","display_name":"Feature learning","score":0.43529999256134033},{"id":"https://openalex.org/keywords/inductive-bias","display_name":"Inductive bias","score":0.4302000105381012},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.42179998755455017},{"id":"https://openalex.org/keywords/latent-variable","display_name":"Latent variable","score":0.3790000081062317}],"concepts":[{"id":"https://openalex.org/C122770356","wikidata":"https://www.wikidata.org/wiki/Q1656753","display_name":"Identifiability","level":2,"score":0.6410999894142151},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.608299970626831},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5900999903678894},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4950000047683716},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4860000014305115},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46790000796318054},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4553999900817871},{"id":"https://openalex.org/C59404180","wikidata":"https://www.wikidata.org/wiki/Q17013334","display_name":"Feature learning","level":2,"score":0.43529999256134033},{"id":"https://openalex.org/C197352929","wikidata":"https://www.wikidata.org/wiki/Q1074074","display_name":"Inductive bias","level":4,"score":0.4302000105381012},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.42179998755455017},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.382099986076355},{"id":"https://openalex.org/C51167844","wikidata":"https://www.wikidata.org/wiki/Q4422623","display_name":"Latent variable","level":2,"score":0.3790000081062317},{"id":"https://openalex.org/C75917345","wikidata":"https://www.wikidata.org/wiki/Q2725298","display_name":"Sampling bias","level":3,"score":0.35249999165534973},{"id":"https://openalex.org/C118505674","wikidata":"https://www.wikidata.org/wiki/Q42586063","display_name":"Encoder","level":2,"score":0.35179999470710754},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.34630000591278076},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3122999966144562},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.30720001459121704},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.30410000681877136},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.2971999943256378},{"id":"https://openalex.org/C118930307","wikidata":"https://www.wikidata.org/wiki/Q600590","display_name":"Tuple","level":2,"score":0.28209999203681946},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.2619999945163727},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.04280","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.04280","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.04280","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.04280","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Contrastive":[0,96],"learning":[1],"has":[2],"become":[3],"a":[4,26,33,64,92,101],"leading":[5],"paradigm":[6],"for":[7,42],"self-supervised":[8],"representation":[9,161],"learning,":[10],"yet":[11],"the":[12,30,49,56,59,123,132],"conditions":[13],"under":[14],"which":[15],"it":[16],"recovers":[17],"meaningful":[18],"latent":[19,44,71,108],"geometry":[20,72],"remain":[21],"incompletely":[22],"understood.":[23],"We":[24,46,90],"develop":[25],"measure-theoretic":[27],"framework":[28],"formalizing":[29],"diversity":[31,60,144],"condition,":[32],"support":[34],"requirement":[35],"on":[36,119],"positive-pair":[37],"sampling":[38,143,152],"that":[39,48,135],"is":[40,145],"necessary":[41],"isometric":[43],"recovery.":[45],"show":[47],"standard":[50],"full-support":[51],"von":[52],"Mises-Fisher":[53],"setting":[54],"implies":[55],"satisfaction":[57],"of":[58],"condition":[61],"and":[62,126,154],"as":[63,100],"consequence":[65],"global":[66],"contrastive":[67,88,160],"loss":[68],"minimizers":[69],"recover":[70],"up":[73],"to":[74],"orthogonal":[75,107],"transformation,":[76],"while":[77],"restricted":[78],"conditionals":[79],"can":[80],"make":[81],"non-orthogonal":[82],"maps":[83],"attain":[84],"strictly":[85],"lower":[86],"asymptotic":[87],"loss.":[89],"introduce":[91],"support-corrected":[93],"Information":[94],"Noise":[95],"Estimation":[97],"(InfoNCE)":[98],"variant":[99],"theoretical":[102],"fix:":[103],"this":[104],"correction":[105],"makes":[106],"space":[109],"recovery":[110],"achievable":[111],"but":[112],"does":[113],"not":[114],"uniquely":[115],"select":[116],"it.":[117],"Experiments":[118],"synthetic":[120],"benchmarks":[121],"validate":[122],"identifiability":[124],"predictions,":[125],"CIFAR-10":[127],"experiments":[128],"are":[129],"consistent":[130],"with":[131],"qualitative":[133],"prediction":[134],"architectural":[136],"inductive":[137,156],"bias":[138,157],"becomes":[139],"more":[140],"important":[141],"when":[142],"limited.":[146],"Together,":[147],"our":[148],"results":[149],"clarify":[150],"how":[151],"mechanisms":[153],"encoder":[155],"interact":[158],"in":[159],"learning.":[162]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-05T00:00:00"}