The geometry of robustness in spiking neural networks

  1. Nuno Calaim
  2. Florian Alexander Dehmelt
  3. Pedro J Gonçalves
  4. Christian K Machens  Is a corresponding author
  1. Champalimaud Research, Portugal
  2. University of Tübingen, Germany

Abstract

Neural systems are remarkably robust against various perturbations, a phenomenon that still requires a clear explanation. Here, we graphically illustrate howneural networks can become robust. We study spiking networks that generate low-dimensional representations, and we show that the neurons; subthreshold voltages are confined to a convex region in a lower-dimensional voltage subspace, which we call a 'bounding box'. Any changes in network parameters (such as number of neurons, dimensionality of inputs, firing thresholds, synapticweights, or transmission delays) can all be understood as deformations of this bounding box. Using these insights, we showthat functionality is preserved as long as perturbations do not destroy the integrity of the bounding box. We suggest that the principles underlying robustness in these networks-low-dimensional representations, heterogeneity of tuning, and precise negative feedback-may be key to understanding the robustness of neural systems at the circuit level.

Data availability

The current manuscript is a computational study, so no data have been generated for this manuscript. Modelling code is uploaded on https://github.com/machenslab/boundingbox

The following data sets were generated

Article and author information

Author details

  1. Nuno Calaim

    Champalimaud Research, Lisbon, Portugal
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-0317-3276
  2. Florian Alexander Dehmelt

    Centre for Integrative Neuroscience, University of Tübingen, Tübingen, Germany
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-6135-4652
  3. Pedro J Gonçalves

    Department of Electrical and Computer Engineering, University of Tübingen, Tübingen, Germany
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-6987-4836
  4. Christian K Machens

    Champalimaud Research, Lisbon, Portugal
    For correspondence
    christian.machens@neuro.fchampalimaud.org
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-1717-1562

Funding

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Reviewing Editor

  1. Markus Meister, California Institute of Technology, United States

Publication history

  1. Received: August 23, 2021
  2. Accepted: May 22, 2022
  3. Accepted Manuscript published: May 30, 2022 (version 1)

Copyright

© 2022, Calaim et al.

This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.

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  1. Nuno Calaim
  2. Florian Alexander Dehmelt
  3. Pedro J Gonçalves
  4. Christian K Machens
(2022)
The geometry of robustness in spiking neural networks
eLife 11:e73276.
https://doi.org/10.7554/eLife.73276

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