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@ARTICLE{Gilson:885723,
      author       = {Gilson, Matthieu and Dahmen, David and Moreno-Bote, Rubén
                      and Insabato, Andrea and Helias, Moritz},
      title        = {{T}he covariance perceptron: {A} new paradigm for
                      classification and processing of time series in recurrent
                      neuronal networks},
      journal      = {PLoS Computational Biology},
      volume       = {16},
      number       = {10},
      issn         = {1553-7358},
      address      = {San Francisco, Calif.},
      publisher    = {Public Library of Science},
      reportid     = {FZJ-2020-04035},
      pages        = {e1008127},
      year         = {2020},
      abstract     = {Learning in neuronal networks has developed in many
                      directions, in particular to reproduce cognitive tasks like
                      image recognition and speech processing. Implementations
                      have been inspired by stereotypical neuronal responses like
                      tuning curves in the visual system, where, for example,
                      ON/OFF cells fire or not depending on the contrast in their
                      receptive fields. Classical models of neuronal networks
                      therefore map a set of input signals to a set of activity
                      levels in the output of the network. Each category of inputs
                      is thereby predominantly characterized by its mean. In the
                      case of time series, fluctuations around this mean
                      constitute noise in this view. For this paradigm, the high
                      variability exhibited by the cortical activity may thus
                      imply limitations or constraints, which have been discussed
                      for many years. For example, the need for averaging neuronal
                      activity over long periods or large groups of cells to
                      assess a robust mean and to diminish the effect of noise
                      correlations. To reconcile robust computations with variable
                      neuronal activity, we here propose a conceptual change of
                      perspective by employing variability of activity as the
                      basis for stimulus-related information to be learned by
                      neurons, rather than merely being the noise that corrupts
                      the mean signal. In this new paradigm both afferent and
                      recurrent weights in a network are tuned to shape the
                      input-output mapping for covariances, the second-order
                      statistics of the fluctuating activity. When including time
                      lags, covariance patterns define a natural metric for time
                      series that capture their propagating nature. We develop the
                      theory for classification of time series based on their
                      spatio-temporal covariances, which reflect dynamical
                      properties. We demonstrate that recurrent connectivity is
                      able to transform information contained in the temporal
                      structure of the signal into spatial covariances. Finally,
                      we use the MNIST database to show how the covariance
                      perceptron can capture specific second-order statistical
                      patterns generated by moving digits.},
      cin          = {INM-6 / IAS-6 / INM-10},
      ddc          = {610},
      cid          = {I:(DE-Juel1)INM-6-20090406 / I:(DE-Juel1)IAS-6-20130828 /
                      I:(DE-Juel1)INM-10-20170113},
      pnm          = {571 - Connectivity and Activity (POF3-571) / 574 - Theory,
                      modelling and simulation (POF3-574) / MSNN - Theory of
                      multi-scale neuronal networks (HGF-SMHB-2014-2018) /
                      neuroIC002 - Recurrence and stochasticity for neuro-inspired
                      computation (EXS-SF-neuroIC002) / HBP SGA2 - Human Brain
                      Project Specific Grant Agreement 2 (785907) / HBP SGA3 -
                      Human Brain Project Specific Grant Agreement 3 (945539)},
      pid          = {G:(DE-HGF)POF3-571 / G:(DE-HGF)POF3-574 /
                      G:(DE-Juel1)HGF-SMHB-2014-2018 / G:(DE-82)EXS-SF-neuroIC002
                      / G:(EU-Grant)785907 / G:(EU-Grant)945539},
      typ          = {PUB:(DE-HGF)16},
      pubmed       = {33044953},
      UT           = {WOS:000581784900003},
      doi          = {10.1371/journal.pcbi.1008127},
      url          = {https://juser.fz-juelich.de/record/885723},
}