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In addition, we replace the widely adopted isotropic Gaussian prior distribution by the sparse Laplacian distribution to further enhance the disentanglement of representations. From a theoretical perspective, our proposed method has\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mi>O<\/mml:mi>\n                          <mml:mo stretchy=\"false\">(<\/mml:mo>\n                          <mml:mi>log<\/mml:mi>\n                          <mml:mi>L<\/mml:mi>\n                          <mml:mo stretchy=\"false\">)<\/mml:mo>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                      <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"mlstac8393ieqn1.gif\" xlink:type=\"simple\"\/>\n                    <\/jats:inline-formula>\n                    complexity for inpainting of an image with edge length\n                    <jats:italic>L<\/jats:italic>\n                    , compared to previous generative models with\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi>O<\/mml:mi>\n                        <mml:mo stretchy=\"false\">(<\/mml:mo>\n                        <mml:msup>\n                          <mml:mi>L<\/mml:mi>\n                          <mml:mn>2<\/mml:mn>\n                        <\/mml:msup>\n                        <mml:mo stretchy=\"false\">)<\/mml:mo>\n                      <\/mml:math>\n                      <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"mlstac8393ieqn2.gif\" xlink:type=\"simple\"\/>\n                    <\/jats:inline-formula>\n                    complexity.\n                  <\/jats:p>","DOI":"10.1088\/2632-2153\/ac8393","type":"journal-article","created":{"date-parts":[[2022,7,22]],"date-time":"2022-07-22T18:24:37Z","timestamp":1658514277000},"page":"035009","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":8,"title":["RG-Flow: a hierarchical and explainable flow model based on renormalization group and sparse prior"],"prefix":"10.1088","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5841-831X","authenticated-orcid":false,"given":"Hong-Ye","family":"Hu","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3888-5003","authenticated-orcid":true,"given":"Dian","family":"Wu","sequence":"additional","affiliation":[]},{"given":"Yi-Zhuang","family":"You","sequence":"additional","affiliation":[]},{"given":"Bruno","family":"Olshausen","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8930-3512","authenticated-orcid":false,"given":"Yubei","family":"Chen","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2022,8,3]]},"reference":[{"key":"mlstac8393bib1","author":"Dinh","year":"2017"},{"key":"mlstac8393bib2","first-page":"pp 10236","author":"Kingma","year":"2018"},{"key":"mlstac8393bib3","first-page":"pp 6572","author":"Chen","year":"2018"},{"key":"mlstac8393bib4","first-page":"pp 9913","author":"Chen","year":"2019"},{"key":"mlstac8393bib5","first-page":"pp 573","volume":"vol 97","author":"Behrmann","year":"2019"},{"key":"mlstac8393bib6","first-page":"pp 2771","volume":"vol 97","author":"Hoogeboom","year":"2019"},{"key":"mlstac8393bib7","first-page":"pp 442","author":"Brehmer","year":"2020"},{"key":"mlstac8393bib8","first-page":"pp 8083","volume":"vol 119","author":"Rezende","year":"2020"},{"key":"mlstac8393bib9","first-page":"pp 5636","author":"Karami","year":"2019"},{"key":"mlstac8393bib10","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1038\/381607a0","volume":"381","author":"Olshausen","year":"1996","journal-title":"Nature"},{"key":"mlstac8393bib11","doi-asserted-by":"publisher","first-page":"3311","DOI":"10.1016\/S0042-6989(97)00169-7","volume":"37","author":"Olshausen","year":"1997","journal-title":"Vis. 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