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@INPROCEEDINGS{Bouss:1041674,
      author       = {Bouss, Peter and Nestler, Sandra and Fischer, Kirsten and
                      Merger, Claudia Lioba and Rene, Alexandre and Helias,
                      Moritz},
      title        = {{E}xploring {N}eural {M}anifold {C}haracteristics {U}sing
                      {A}dapted {N}ormalizing {F}lows},
      reportid     = {FZJ-2025-02379},
      year         = {2024},
      abstract     = {Despite the large number of active neurons in the cortex,
                      the activity of neural populations fordifferent brain
                      regions is expected to live on a low-dimensional manifold
                      [1]. Variants of principalcomponent analysis (PCA) are
                      frequently employed to estimate this manifold. However,
                      thesemethods are limited by the assumption that the data
                      conforms to a Gaussian distribution, neglectingadditional
                      features such as the curvature of the manifold.
                      Consequently, their performance asgenerative models tends to
                      be subpar.To fully learn the statistics of neural activity
                      and to generate artificial samples, we use NormalizingFlows
                      (NFs) [2, 3]. These neural networks learn a
                      dimension-preserving estimator of the
                      probabilitydistribution of the data. They differ from other
                      generative networks by their simplicity and by theirability
                      to compute the likelihood exactly.Our adaptation of NFs
                      focuses on distinguishing between relevant (in manifold) and
                      noisedimensions (out of manifold). This is achieved by
                      training the NF to represent maximal datavariance
                      representation in minimal dimensions, akin to PCA's linear
                      model but allowing fornonlinear mappings. Our adaptation
                      allows us to estimate the dimensionality of the neural
                      manifold.As every layer is a bijective mapping, the network
                      can describe the manifold without losinginformation – a
                      distinctive advantage of NFs.We validate our adaptation on
                      artificial datasets of varying complexity where the
                      underlyingdimensionality is known. Our approach can
                      reconstruct data using only a few latent variables, and
                      ismore efficient than linear methods, such as PCA.Following
                      this approach, we identify manifolds in electrophysiological
                      recordings from macaqueV1 and V4 [4]. Our approach
                      faithfully represents not only the variance but also higher
                      orderfeatures, such as the skewness and kurtosis of the
                      data, using fewer dimensions than PCA.[1] J. Gallego et al.,
                      Neuron, 94, 5, 978-984, 2017.[2] L. Dinh et al., ICLR,
                      2015.[3] L. Dinh et al., ICLR, 2017.[4] X. Chen et al., Sci.
                      Data, 9, 1, 77, 2022.},
      month         = {Jun},
      date          = {2024-06-03},
      organization  = {International Conference on
                       Neuromorphic Computing and Engineering,
                       Aachen (Germany), 3 Jun 2024 - 6 Jun
                       2024},
      subtyp        = {After Call},
      cin          = {IAS-6},
      cid          = {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/1041674},
}