<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-04664174v2</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-05T04:49:52+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Differentially Private Gradient Flow based on the Sliced Wasserstein Distance</title>
            <author role="aut">
              <persName>
                <forename type="first">Ilana</forename>
                <surname>Sebag</surname>
              </persName>
              <email type="md5">5e11a757ef77030485f08949c93cb636</email>
              <email type="domain">criteo.com</email>
              <idno type="idhal" notation="numeric">1405367</idno>
              <idno type="halauthorid" notation="string">3205757-1405367</idno>
              <affiliation ref="#struct-1001229"/>
              <affiliation ref="#struct-552996"/>
              <affiliation ref="#struct-989"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Muni</forename>
                <surname>Sreenivas</surname>
              </persName>
              <idno type="halauthorid">3205758-0</idno>
              <affiliation ref="#struct-552996"/>
              <affiliation ref="#struct-989"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Jean-Yves</forename>
                <surname>Franceschi</surname>
              </persName>
              <email type="md5">0ab0008c2d9e71c490b6ef6be1da0e9c</email>
              <email type="domain">criteo.com</email>
              <idno type="idhal" notation="string">jean-yves-franceschi</idno>
              <idno type="idhal" notation="numeric">17956</idno>
              <idno type="halauthorid" notation="string">39162-17956</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-3631-5349</idno>
              <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=IL2OzksAAAAJ</idno>
              <idno type="IDREF">https://www.idref.fr/260654086</idno>
              <affiliation ref="#struct-1001229"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Alain</forename>
                <surname>Rakotomamonjy</surname>
              </persName>
              <email type="md5">f0cb04a59a3aeed7cf6a13d9e868107a</email>
              <email type="domain">criteo.com</email>
              <idno type="idhal" notation="numeric">1102415</idno>
              <idno type="halauthorid" notation="string">3668-1102415</idno>
              <affiliation ref="#struct-1001229"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Mike</forename>
                <surname>Gartrell</surname>
              </persName>
              <email type="md5">673fc789292aa488270e730e5d158e84</email>
              <email type="domain">acm.org</email>
              <idno type="idhal" notation="numeric">1405368</idno>
              <idno type="halauthorid" notation="string">2707607-1405368</idno>
              <affiliation ref="#struct-1221400"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Jamal</forename>
                <surname>Atif</surname>
              </persName>
              <email type="md5">f3ee6f6f7dfa9e21c2c36b9640f22d2c</email>
              <email type="domain">lamsade.dauphine.fr</email>
              <idno type="idhal" notation="numeric">1080031</idno>
              <idno type="halauthorid" notation="string">19015-1080031</idno>
              <affiliation ref="#struct-552996"/>
              <affiliation ref="#struct-989"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Alexandre</forename>
                <surname>Allauzen</surname>
              </persName>
              <email type="md5">0124166ad70f06a6272745c1e04cfb46</email>
              <email type="domain">dauphine.psl.eu</email>
              <idno type="idhal" notation="string">alexandre-allauzen</idno>
              <idno type="idhal" notation="numeric">171266</idno>
              <idno type="halauthorid" notation="string">13659-171266</idno>
              <idno type="IDREF">https://www.idref.fr/078187621</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-8627-1965</idno>
              <idno type="VIAF">https://viaf.org/viaf/218292984</idno>
              <idno type="ISNI">http://isni.org/isni/0000000140297249</idno>
              <affiliation ref="#struct-552996"/>
              <affiliation ref="#struct-301585"/>
              <affiliation ref="#struct-989"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Ilana</forename>
                <surname>Sebag</surname>
              </persName>
              <email type="md5">fbf5855f88f69901f2bf88cfb955d5f0</email>
              <email type="domain">gmail.com</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2024-07-29 19:02:56</date>
            </edition>
            <edition n="v2" type="current">
              <date type="whenSubmitted">2025-01-20 11:44:51</date>
              <date type="whenWritten">2025-01</date>
              <date type="whenModified">2025-06-13 11:38:14</date>
              <date type="whenReleased">2025-01-28 17:19:16</date>
              <date type="whenProduced">2025-01</date>
              <date type="whenEndEmbargoed">2025-01-20</date>
              <ref type="file" target="https://hal.science/hal-04664174v2/document">
                <date notBefore="2025-01-20"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-04664174v2/file/DP_SW_GF%20%286%29.pdf" id="file-4900792-4255635">
                <date notBefore="2025-01-20"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="1564456">
                <persName>
                  <forename>Ilana</forename>
                  <surname>Sebag</surname>
                </persName>
                <email type="md5">fbf5855f88f69901f2bf88cfb955d5f0</email>
                <email type="domain">gmail.com</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-04664174</idno>
            <idno type="halUri">https://hal.science/hal-04664174</idno>
            <idno type="halBibtex">sebag:hal-04664174</idno>
            <idno type="halRefHtml">&lt;i&gt;Transactions on Machine Learning Research Journal&lt;/i&gt;, 2025</idno>
            <idno type="halRef">Transactions on Machine Learning Research Journal, 2025</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-4900792-4255635"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="ESPCI">ESPCI Paris-PSL</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-DAUPHINE">Université Paris Dauphine - Paris IX</idno>
            <idno type="stamp" n="LAMSADE-DAUPHINE" corresp="UNIV-DAUPHINE">LAMSADE (Laboratoire d'Analyse et de Modélisation des Systèmes pour l'Aide à la Décision)</idno>
            <idno type="stamp" n="PSL">Université Paris sciences et lettres</idno>
            <idno type="stamp" n="ESPCI-PSL" corresp="PSL">Ecole Supérieure de Physique et de Chimie Industrielles de la Ville de Paris - PSL</idno>
            <idno type="stamp" n="UNIV-DAUPHINE-PSL" corresp="PSL">Université Paris Dauphine - PSL</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Differentially Private Gradient Flow based on the Sliced Wasserstein Distance</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Ilana</forename>
                    <surname>Sebag</surname>
                  </persName>
                  <email type="md5">5e11a757ef77030485f08949c93cb636</email>
                  <email type="domain">criteo.com</email>
                  <idno type="idhal" notation="numeric">1405367</idno>
                  <idno type="halauthorid" notation="string">3205757-1405367</idno>
                  <affiliation ref="#struct-1001229"/>
                  <affiliation ref="#struct-552996"/>
                  <affiliation ref="#struct-989"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Muni</forename>
                    <surname>Sreenivas</surname>
                  </persName>
                  <idno type="halauthorid">3205758-0</idno>
                  <affiliation ref="#struct-552996"/>
                  <affiliation ref="#struct-989"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Jean-Yves</forename>
                    <surname>Franceschi</surname>
                  </persName>
                  <email type="md5">0ab0008c2d9e71c490b6ef6be1da0e9c</email>
                  <email type="domain">criteo.com</email>
                  <idno type="idhal" notation="string">jean-yves-franceschi</idno>
                  <idno type="idhal" notation="numeric">17956</idno>
                  <idno type="halauthorid" notation="string">39162-17956</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-3631-5349</idno>
                  <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=IL2OzksAAAAJ</idno>
                  <idno type="IDREF">https://www.idref.fr/260654086</idno>
                  <affiliation ref="#struct-1001229"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Alain</forename>
                    <surname>Rakotomamonjy</surname>
                  </persName>
                  <email type="md5">f0cb04a59a3aeed7cf6a13d9e868107a</email>
                  <email type="domain">criteo.com</email>
                  <idno type="idhal" notation="numeric">1102415</idno>
                  <idno type="halauthorid" notation="string">3668-1102415</idno>
                  <affiliation ref="#struct-1001229"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Mike</forename>
                    <surname>Gartrell</surname>
                  </persName>
                  <email type="md5">673fc789292aa488270e730e5d158e84</email>
                  <email type="domain">acm.org</email>
                  <idno type="idhal" notation="numeric">1405368</idno>
                  <idno type="halauthorid" notation="string">2707607-1405368</idno>
                  <affiliation ref="#struct-1221400"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Jamal</forename>
                    <surname>Atif</surname>
                  </persName>
                  <email type="md5">f3ee6f6f7dfa9e21c2c36b9640f22d2c</email>
                  <email type="domain">lamsade.dauphine.fr</email>
                  <idno type="idhal" notation="numeric">1080031</idno>
                  <idno type="halauthorid" notation="string">19015-1080031</idno>
                  <affiliation ref="#struct-552996"/>
                  <affiliation ref="#struct-989"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Alexandre</forename>
                    <surname>Allauzen</surname>
                  </persName>
                  <email type="md5">0124166ad70f06a6272745c1e04cfb46</email>
                  <email type="domain">dauphine.psl.eu</email>
                  <idno type="idhal" notation="string">alexandre-allauzen</idno>
                  <idno type="idhal" notation="numeric">171266</idno>
                  <idno type="halauthorid" notation="string">13659-171266</idno>
                  <idno type="IDREF">https://www.idref.fr/078187621</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-8627-1965</idno>
                  <idno type="VIAF">https://viaf.org/viaf/218292984</idno>
                  <idno type="ISNI">http://isni.org/isni/0000000140297249</idno>
                  <affiliation ref="#struct-552996"/>
                  <affiliation ref="#struct-301585"/>
                  <affiliation ref="#struct-989"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">363201</idno>
                <idno type="issn">2835-8856</idno>
                <title level="j">Transactions on Machine Learning Research Journal</title>
                <imprint>
                  <publisher>[Amherst Massachusetts]: OpenReview.net, 2022</publisher>
                  <date type="datePub">2025-01</date>
                </imprint>
              </monogr>
              <ref target="https://github.com/ilanasebag/dpswgf" type="seeAlso"/>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Machine leaning</term>
                <term xml:lang="en">Differential privacy</term>
                <term xml:lang="en">Generative AI</term>
                <term xml:lang="en">Privacy</term>
              </keywords>
              <classCode scheme="halDomain" n="stat.ml">Statistics [stat]/Machine Learning [stat.ML]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>Safeguarding privacy in sensitive training data is paramount, particularly in the context of generative modeling. This can be achieved through either differentially private stochastic gradient descent or a differentially private metric for training models or generators. In this paper, we introduce a novel differentially private generative modeling approach based on a gradient flow in the space of probability measures. To this end, we define the gradient flow of the Gaussian-smoothed Sliced Wasserstein Distance, including the associated stochastic differential equation (SDE). By discretizing and defining a numerical scheme for solving this SDE, we demonstrate the link between smoothing and differential privacy based on a Gaussian mechanism, due to a specific form of the SDE's drift term. We then analyze the differential privacy guarantee of our gradient flow, which accounts for both the smoothing and the Wiener process introduced by the SDE itself. Experiments show that our proposed model can generate higher-fidelity data at a low privacy budget compared to a generator-based model, offering a promising alternative.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-1001229" status="VALID">
          <orgName>Criteo AI Lab</orgName>
          <desc>
            <address>
              <addrLine>Paris</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-458139" type="direct"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-552996" status="VALID">
          <orgName>Machine Intelligence and Learning Systems</orgName>
          <orgName type="acronym">MILES</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.lamsade.dauphine.fr/miles/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-989" type="direct"/>
            <relation active="#struct-300302" type="indirect"/>
            <relation active="#struct-564132" type="indirect"/>
            <relation name="UMR7243 / FRE3234 / UMR7024" active="#struct-441569" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-989" status="VALID">
          <idno type="IdRef">030107156</idno>
          <idno type="ISNI">0000 0001 2097 7052</idno>
          <idno type="RNSR">201120462Y</idno>
          <idno type="ROR">https://ror.org/052bz7812</idno>
          <idno type="Wikidata">Q3214405</idno>
          <orgName>Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision</orgName>
          <orgName type="acronym">LAMSADE</orgName>
          <desc>
            <address>
              <addrLine>Place de Lattre de Tassigny 75775 PARIS CEDEX 16</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.lamsade.dauphine.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300302" type="direct"/>
            <relation active="#struct-564132" type="indirect"/>
            <relation name="UMR7243 / FRE3234 / UMR7024" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-1221400" status="INCOMING">
          <orgName>Sigma Nova</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-301585" status="VALID">
          <idno type="IdRef">028114779</idno>
          <idno type="ISNI">000000009591493X</idno>
          <idno type="ROR">https://ror.org/03zx86w41</idno>
          <orgName>Ecole Superieure de Physique et de Chimie Industrielles de la Ville de Paris</orgName>
          <orgName type="acronym">ESPCI Paris</orgName>
          <date type="start">1882-10-01</date>
          <desc>
            <address>
              <addrLine>10 rue Vauquelin, 75231 Paris cedex 05</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.espci.psl.eu/fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-564132" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-458139" status="VALID">
          <orgName>Criteo [Paris]</orgName>
          <desc>
            <address>
              <addrLine>32 rue Blanche 75 009 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.criteo.com/fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300302" status="VALID">
          <idno type="IdRef">027787109</idno>
          <idno type="ISNI">0000000120977052</idno>
          <idno type="ROR">https://ror.org/052bz7812</idno>
          <idno type="Wikidata">Q1546437</idno>
          <orgName>Université Paris Dauphine-PSL</orgName>
          <desc>
            <address>
              <addrLine>Place du Maréchal de Lattre de Tassigny75775 PARIS Cedex 16</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://dauphine.psl.eu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-564132" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-564132" status="VALID">
          <idno type="IdRef">241597595</idno>
          <idno type="ISNI">0000 0004 1784 3645</idno>
          <idno type="ROR">https://ror.org/013cjyk83</idno>
          <orgName>Université Paris Sciences et Lettres</orgName>
          <orgName type="acronym">PSL</orgName>
          <desc>
            <address>
              <addrLine>60 rue Mazarine 75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.psl.eu/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>