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@INPROCEEDINGS{Fischer:910329,
      author       = {Fischer, Kirsten and Rene, Alexandre and Keup, Christian
                      and Layer, Moritz and Dahmen, David and Helias, Moritz},
      title        = {{S}tatistical decomposition of feed-forward neural
                      networks: {T}ransfer of information between correlation
                      functions},
      reportid     = {FZJ-2022-03755},
      year         = {2022},
      abstract     = {Uncovering principles of information processing in neural
                      systems continues to be an active field of research. For the
                      visual system it is well known that it processes signals in
                      a hierarchical manner [1,2]. Feed-forward networks are
                      commonly used models in machine learning that perform
                      hierarchical computations. We here study deep feed-forward
                      networks with the aim of deducing general functional aspects
                      of such systems. These networks implement mappings between
                      probability distributions, where the probability
                      distribution are iteratively transformed from layer to
                      layer. We develop a formalism for expressing signal
                      transformations in each layer as information transfers
                      between different orders of correlation functions. We show
                      that the processing within internal network layers is
                      captured by correlations up to second order. In addition, we
                      demonstrate how the input layer also extracts higher order
                      correlations from the data. Thus, by presenting different
                      correlation orders in the input, we identify key statistics
                      in the data. As a next step, we consider recurrent
                      time-continuous networks, reminiscent of biological neuronal
                      networks (NeuralODEs, [3]). We derive a Fokker-Planck
                      equation describing the evolution of the probability
                      distribution. This formulation allows us to study
                      time-dependent information flow between different
                      interaction terms. In summary, this work provides insights
                      into functional principles of information processing in
                      neural networks.References[1] Hubel, D. H., $\&$ Wiesel, T.
                      N. (1962). Receptive fields, binocular interaction and
                      functional architecture in the cat's visual cortex. The
                      Journal of physiology, 160(1), 106.[2] Zhuang, C., Yan, S.,
                      Nayebi, A., Schrimpf, M., Frank, M. C., DiCarlo, J. J., $\&$
                      Yamins, D. L. (2021). Unsupervised neural network models of
                      the ventral visual stream. Proceedings of the National
                      Academy of Sciences, 118(3), e2014196118.[3] Chen, R. T.,
                      Rubanova, Y., Bettencourt, J., $\&$ Duvenaud, D. K. (2018).
                      Neural ordinary differential equations. Advances in neural
                      information processing systems, 31.},
      month         = {Oct},
      date          = {2022-10-18},
      organization  = {INM IBI Retreat 2022, Juelich
                       (Germany), 18 Oct 2022 - 19 Oct 2022},
      subtyp        = {After Call},
      cin          = {INM-6 / IAS-6 / INM-10},
      cid          = {I:(DE-Juel1)INM-6-20090406 / I:(DE-Juel1)IAS-6-20130828 /
                      I:(DE-Juel1)INM-10-20170113},
      pnm          = {5232 - Computational Principles (POF4-523) / 5234 -
                      Emerging NC Architectures (POF4-523) / RenormalizedFlows -
                      Transparent Deep Learning with Renormalized Flows
                      (BMBF-01IS19077A) / MSNN - Theory of multi-scale neuronal
                      networks (HGF-SMHB-2014-2018) / ACA - Advanced Computing
                      Architectures (SO-092) / neuroIC002 - Recurrence and
                      stochasticity for neuro-inspired computation
                      (EXS-SF-neuroIC002)},
      pid          = {G:(DE-HGF)POF4-5232 / G:(DE-HGF)POF4-5234 /
                      G:(DE-Juel-1)BMBF-01IS19077A /
                      G:(DE-Juel1)HGF-SMHB-2014-2018 / G:(DE-HGF)SO-092 /
                      G:(DE-82)EXS-SF-neuroIC002},
      typ          = {PUB:(DE-HGF)24},
      url          = {https://juser.fz-juelich.de/record/910329},
}