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@INPROCEEDINGS{Bouss:1041671,
      author       = {Bouss, Peter and Nestler, Sandra and Fischer, Kirsten and
                      Merger, Claudia Lioba and Rene, Alexandre and Helias,
                      Moritz},
      title        = {{E}mploying normalizing flows to examine neural manifold
                      characteristics and curvatures},
      reportid     = {FZJ-2025-02376},
      year         = {2025},
      abstract     = {Despite the vast number of active neurons, neuronal
                      population activity supposedly lies on low-dimensional
                      manifolds (Gallego et al., 2017). To learn the statistics of
                      neural activity, we use Normalizing Flows (NFs) (Dinh et
                      al., 2014). These neural networks are trained to estimate
                      the probability distribution by learning an invertible map
                      to a latent distribution.We adjust NF’s training
                      objectives to distinguish between relevant and noise
                      dimensions, by using a nested dropout procedure in the
                      latent space (Bekasov $\&$ Murray, 2020). An approximation
                      of the network for each mixture component as a quadratic
                      mapping enables us to calculate the Riemannian curvature
                      tensors of the neural manifold. We focus mainly on the
                      directions in the tangent space, in which the sectional
                      curvature shows local extrema.Finally, we apply the method
                      to electrophysiological recordings of the visual cortex in
                      macaques (Chen et al., 2022). We show that manifolds deviate
                      significantly from being flat. Analyzing the curvature of
                      the manifolds yields insights into the regimes where neuron
                      groups interact in a non-linear manner.},
      month         = {Mar},
      date          = {2025-03-16},
      organization  = {DPG Spring Meeting of the Condensed
                       Matter Section, Regensburg (Germany),
                       16 Mar 2025 - 21 Mar 2025},
      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)6},
      url          = {https://juser.fz-juelich.de/record/1041671},
}