{"id":"https://openalex.org/W7214969527","doi":"https://doi.org/10.48550/arxiv.2609.37344","title":"A Sharp Transition in Data Reconstruction under Differential Privacy","display_name":"A Sharp Transition in Data Reconstruction under Differential Privacy","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214969527","doi":"https://doi.org/10.48550/arxiv.2609.37344"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.37344","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37344","pdf_url":"https://arxiv.org/pdf/2609.37344","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.37344","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5125770741","display_name":"Max Cairney-Leeming","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Cairney-Leeming, Max","raw_affiliation_strings":["Institute of Science and Technology Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Science and Technology Austria","institution_ids":["https://openalex.org/I157556583"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043884688","display_name":"Simone Bombari","orcid":"https://orcid.org/0009-0008-9209-349X","observed_orcids":["https://orcid.org/0009-0008-9209-349X"]},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Bombari, Simone","raw_affiliation_strings":["Institute of Science and Technology Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Science and Technology Austria","institution_ids":["https://openalex.org/I157556583"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061114394","display_name":"Marco Mondelli","orcid":"https://orcid.org/0000-0002-3242-7020","observed_orcids":["https://orcid.org/0000-0002-3242-7020","https://orcid.org/0009-0006-3003-1205"]},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Mondelli, Marco","raw_affiliation_strings":["Institute of Science and Technology Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Science and Technology Austria","institution_ids":["https://openalex.org/I157556583"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I157556583"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T10764","display_name":"Privacy-Preserving Technologies in Data","score":1.0,"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/T10764","display_name":"Privacy-Preserving Technologies in Data","score":1.0,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.0,"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/T11614","display_name":"Cloud Data Security Solutions","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/differential-privacy","display_name":"differential privacy","score":0.8370000123977661},{"id":"https://openalex.org/keywords/data-reconstruction-attacks","display_name":"data reconstruction attacks","score":0.9610000252723694},{"id":"https://openalex.org/keywords/privacy-budget","display_name":"privacy budget","score":0.8579999804496765},{"id":"https://openalex.org/keywords/output-perturbation","display_name":"output perturbation","score":0.9900000095367432},{"id":"https://openalex.org/keywords/effective-dimension","display_name":"effective dimension","score":0.6959999799728394}],"concepts":[{"id":"https://openalex.org/C23130292","wikidata":"https://www.wikidata.org/wiki/Q5275358","display_name":"Differential privacy","level":2,"score":0.8499000072479248},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6700999736785889},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.635200023651123},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.5493999719619751},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5389000177383423},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.46299999952316284},{"id":"https://openalex.org/C123201435","wikidata":"https://www.wikidata.org/wiki/Q456632","display_name":"Information privacy","level":2,"score":0.43549999594688416},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.43130001425743103},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.40049999952316284},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.38830000162124634},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.38659998774528503},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.35659998655319214},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3538999855518341},{"id":"https://openalex.org/C58489278","wikidata":"https://www.wikidata.org/wiki/Q1172284","display_name":"Data set","level":2,"score":0.34940001368522644},{"id":"https://openalex.org/C3017597292","wikidata":"https://www.wikidata.org/wiki/Q25052250","display_name":"Privacy protection","level":2,"score":0.3321000039577484},{"id":"https://openalex.org/C8505890","wikidata":"https://www.wikidata.org/wiki/Q605095","display_name":"Budget constraint","level":2,"score":0.3285999894142151},{"id":"https://openalex.org/C99221444","wikidata":"https://www.wikidata.org/wiki/Q1532069","display_name":"Private information retrieval","level":2,"score":0.30329999327659607},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3005000054836273},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.2870999872684479},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C2776608160","wikidata":"https://www.wikidata.org/wiki/Q4785462","display_name":"Natural (archaeology)","level":2,"score":0.2745000123977661},{"id":"https://openalex.org/C194232998","wikidata":"https://www.wikidata.org/wiki/Q1606712","display_name":"Transition (genetics)","level":3,"score":0.27390000224113464},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26930001378059387},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.25839999318122864},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.2524999976158142}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.37344","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37344","pdf_url":"https://arxiv.org/pdf/2609.37344","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.37344","doi":"https://doi.org/10.48550/arxiv.2609.37344","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.37344","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,"listed_in":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.37344","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37344","pdf_url":"https://arxiv.org/pdf/2609.37344","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320315473","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214969527.pdf","grobid_xml":"https://content.openalex.org/works/W7214969527.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W2902114605","https://openalex.org/W3211753216","https://openalex.org/W4221145466","https://openalex.org/W4224022788","https://openalex.org/W4225150360","https://openalex.org/W4383987414","https://openalex.org/W4406073497","https://openalex.org/W4416450649","https://openalex.org/W4417275493"],"related_works":["https://openalex.org/W4392012695","https://openalex.org/W4307415497","https://openalex.org/W4221145466","https://openalex.org/W4221142579","https://openalex.org/W4383987414","https://openalex.org/W7133238017","https://openalex.org/W4392781162","https://openalex.org/W4416104487","https://openalex.org/W7221510519","https://openalex.org/W4361865068"],"abstract_inverted_index":{"Data":[0],"reconstruction":[1,128,153],"attacks":[2],"have":[3],"empirically":[4],"been":[5],"successful":[6],"in":[7,170,185],"recovering":[8],"training":[9,77,87],"samples":[10],"from":[11,79],"learned":[12],"models,":[13],"raising":[14],"privacy":[15,30,37,177],"concerns":[16],"and":[17,117,203],"motivating":[18],"defenses":[19],"with":[20,148],"guarantees":[21],"that":[22,152,175],"remain":[23],"valid":[24],"against":[25],"future":[26],"threats.":[27],"While":[28],"differential":[29],"(DP)":[31],"provides":[32],"formal":[33],"protection,":[34],"choosing":[35],"the":[36,55,105,136,161,176,188,192],"budget":[38,56,178],"remains":[39],"a":[40,74,80,95,121,141],"challenge:":[41],"small":[42],"budgets":[43],"severely":[44],"reduce":[45],"utility,":[46],"but":[47],"it":[48],"is":[49,92,129,154],"hard":[50],"to":[51,72,93,164],"quantify":[52],"how":[53],"large":[54],"can":[57],"be":[58,183],"without":[59],"allowing":[60],"accurate":[61],"reconstruction.":[62],"In":[63],"this":[64],"work,":[65],"we":[66,108,139],"study":[67],"informed":[68],"attackers":[69],"who":[70],"aim":[71],"reconstruct":[73],"single":[75],"$d$-dimensional":[76],"sample":[78],"$\u03c1$-zero-concentrated":[81],"DP":[82],"model,":[83],"knowing":[84],"all":[85],"other":[86,137],"data.":[88,193],"Our":[89],"main":[90],"contribution":[91],"establish":[94],"sharp":[96],"transition":[97,162],"at":[98],"$\u03c1\\asymp":[99,165],"d$":[100],"for":[101,113,126,132,157,167],"data":[102,168,202],"reconstruction:":[103],"on":[104,135,144,200],"one":[106],"hand,":[107,138],"derive":[109],"entropy-based":[110],"lower":[111],"bounds":[112],"any":[114,118],"private":[115,145],"mechanism":[116],"attack,":[119],"characterizing":[120],"set":[122],"of":[123,187,191],"target":[124],"priors":[125],"which":[127],"information-theoretically":[130],"impossible":[131],"$\u03c1\\ll":[133],"d$;":[134],"analyze":[140],"simple":[142],"attack":[143],"linear":[146],"regression":[147],"output":[149],"perturbation,":[150],"showing":[151],"practically":[155],"feasible":[156],"$\u03c1\\gg":[158],"d$.":[159],"Remarkably,":[160],"moves":[163],"s$":[166],"lying":[169],"an":[171],"$s$-dimensional":[172],"subspace,":[173],"demonstrating":[174],"guaranteeing":[179],"adequate":[180],"protection":[181],"must":[182],"assessed":[184],"terms":[186],"effective":[189],"dimension":[190],"We":[194],"validate":[195],"our":[196],"findings":[197],"via":[198],"experiments":[199],"synthetic":[201],"natural":[204],"images":[205],"(CIFAR-10,":[206],"ImageNet).":[207]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-01T00:00:00"}