The covariance perceptron: A new paradigm for classification and processing of time series in recurrent neuronal networks

PLoS Computational Biology, vol. 16, pp. e1008127

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.

Authors 5

1. Matthieu Gilson corresponding

   Universitat Pompeu Fabra · Forschungszentrum Jülich · Jülich Aachen Research Alliance

   Affiliation as printed

   Center for Brain and Cognition, Department of Information and Telecommunication technologies, Universitat Pompeu Fabra, Barcelona, Spain

   Institute of Neuroscience and Medicine (INM-6) and Institute for Advanced Simulation (IAS-6) and JARA Institute Brain Structure-Function Relationships (INM-10), Jülich Research Centre, Jülich, Germany

2. David Dahmen

   Forschungszentrum Jülich · Jülich Aachen Research Alliance

   Affiliation as printed

   Institute of Neuroscience and Medicine (INM-6) and Institute for Advanced Simulation (IAS-6) and JARA Institute Brain Structure-Function Relationships (INM-10), Jülich Research Centre, Jülich, Germany

3. Rubén Moreno‐Bote

   Institució Catalana de Recerca i Estudis Avançats · Universitat Pompeu Fabra

   Affiliation as printed

   Center for Brain and Cognition, Department of Information and Telecommunication technologies, Universitat Pompeu Fabra, Barcelona, Spain

   ICREA, Barcelona, Spain

4. Andrea Insabato

   Consorci Institut D'Investigacions Biomediques August Pi I Sunyer

   Affiliation as printed

   IDIBAPS (Institut d'Investigacions Biomèdiques August Pi i Sunyer), Barcelona, Spain

5. Moritz Helias Aachen Department of Physics Faculty 1

   Forschungszentrum Jülich · Jülich Aachen Research Alliance · RWTH Aachen University

   Affiliation as printed

   Department of Physics, Faculty 1, RWTH Aachen University, Aachen, Germany

   Institute of Neuroscience and Medicine (INM-6) and Institute for Advanced Simulation (IAS-6) and JARA Institute Brain Structure-Function Relationships (INM-10), Jülich Research Centre, Jülich, Germany