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@ARTICLE{Cramer:917558,
      author       = {Cramer, Eike and Rauh, Felix and Mitsos, Alexander and
                      Tempone, Raúl and Dahmen, Manuel},
      title        = {{N}onlinear {I}sometric {M}anifold {L}earning for
                      {I}njective {N}ormalizing {F}lows},
      publisher    = {arXiv},
      reportid     = {FZJ-2023-00760},
      year         = {2022},
      abstract     = {To model manifold data using normalizing flows, we propose
                      to employ the isometric autoencoder to design nonlinear
                      encodings with explicit inverses. The isometry allows us to
                      separate manifold learning and density estimation and train
                      both parts to high accuracy. Applied to the MNIST data set,
                      the combined approach generates high-quality images.},
      keywords     = {Machine Learning (cs.LG) (Other) / FOS: Computer and
                      information sciences (Other)},
      cin          = {IEK-10},
      cid          = {I:(DE-Juel1)IEK-10-20170217},
      pnm          = {1121 - Digitalization and Systems Technology for
                      Flexibility Solutions (POF4-112) / HDS LEE - Helmholtz
                      School for Data Science in Life, Earth and Energy (HDS LEE)
                      (HDS-LEE-20190612)},
      pid          = {G:(DE-HGF)POF4-1121 / G:(DE-Juel1)HDS-LEE-20190612},
      typ          = {PUB:(DE-HGF)25},
      doi          = {10.48550/ARXIV.2203.03934},
      url          = {https://juser.fz-juelich.de/record/917558},
}