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@INPROCEEDINGS{Bouss:1041677,
      author       = {Bouss, Peter and Nestler, Sandra and Fischer, Kirsten and
                      Merger, Claudia Lioba and Rene, Alexandre and Helias,
                      Moritz},
      title        = {{N}ormalizing flows for nonlinear dimensionality reduction
                      ofelectrophysiological recordings},
      reportid     = {FZJ-2025-02382},
      year         = {2023},
      abstract     = {Even though the cortex has many active neurons, neuronal
                      populations for different brain areasshould dwell on a
                      low-dimensional manifold [1]. Principal component analysis
                      versions are used toestimate this manifold and its
                      dimension. Although successful, these methods assume that
                      the data iswell described by a Gaussian distribution and
                      ignore features like skewness and bimodality. Therefore,they
                      perform poorly as generative models.Normalizing Flows (NFs)
                      allow us to learn neural activity statistics and generate
                      artificial samples [2,3]. These neural networks learn a
                      dimension-preserving estimator of the data’s probability
                      distribution.They are simpler than generative adversarial
                      networks (GANs) and variational autoencoders (VAEs)since
                      they learn only one bijective mapping and can compute the
                      likelihood correctly due to tractableJacobians at each
                      building block.NFs are trained to distinguish relevant (in
                      manifold) from noisy dimensions (out of manifold). To
                      dothis, we break the original symmetry of the latent space
                      by pushing maximal variance of the data to becaptured by as
                      few dimensions as possible — the same idea underpinning
                      PCA, a linear model, adoptedhere for nonlinear mappings.
                      NFs’ unique characteristics allows us to estimate the
                      neural manifold’sdimensions and describe the underlying
                      manifold without discarding any information.Our adaptation
                      is validated on simulated datasets of various complexity
                      created using a hidden man-ifold model with specified
                      dimensions. Reconstructing data with a few latent NF
                      dimensions shows ourapproach’s capability. In this case,
                      our nonlinear approaches outperform linear ones. We identify
                      mani-folds in high-gamma EEG recordings using the
                      aforementioned technique. In the experiment of [4],
                      128electrodes recorded during four movement tasks. These
                      data show a heavy-tailed distribution along someof the first
                      principal components. NFs can learn higher-order
                      correlations while linear models like PCAare limited to
                      Gaussian statistics. We can also better match features to
                      latent dimensions by flatteningthe latent space. We now have
                      fewer latent dimensions that explain most data
                      variance.References[1] J. A. Gallego, M. G. Perich, L. E.
                      Miller, and S. A. Solla, Neuron, 94(5), 978-984 (2017).[2]
                      L. Dinh, D. Krueger, and Y. Bengio, In Conference on
                      Learning Representations, ICLR (2015).[3] L. Dinh, J.
                      Sohl-Dickstein, and S. Bengio, In Conference on Learning
                      Representations, ICLR (2017).[4] R. T. Schirrmeister, J. T.
                      Springenberg, L. D. J. Fiederer, M. Glasstetter, K.
                      Eggensperger, M. Tanger-mann, ... and T. Ball, Human brain
                      mapping, 38(11), 5391-5420 (2017).},
      month         = {Jul},
      date          = {2025-07-17},
      organization  = {Computational Neuroscience Academy,
                       Krakow (Poland), 17 Jul 2025 - 23 Jul
                       2025},
      subtyp        = {After Call},
      cin          = {INM-6 / IAS-6},
      cid          = {I:(DE-Juel1)INM-6-20090406 / I:(DE-Juel1)IAS-6-20130828},
      pnm          = {5232 - Computational Principles (POF4-523) / 5234 -
                      Emerging NC Architectures (POF4-523) / GRK 2416 - GRK 2416:
                      MultiSenses-MultiScales: Neue Ansätze zur Aufklärung
                      neuronaler multisensorischer Integration (368482240) /
                      RenormalizedFlows - Transparent Deep Learning with
                      Renormalized Flows (BMBF-01IS19077A)},
      pid          = {G:(DE-HGF)POF4-5232 / G:(DE-HGF)POF4-5234 /
                      G:(GEPRIS)368482240 / G:(DE-Juel-1)BMBF-01IS19077A},
      typ          = {PUB:(DE-HGF)24},
      url          = {https://juser.fz-juelich.de/record/1041677},
}