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

Version history

  1. Preprint posted: June 15, 2020 (view preprint)
  2. Received: August 23, 2021
  3. Accepted: May 22, 2022
  4. Accepted Manuscript published: May 30, 2022 (version 1)
  5. Version of Record published: July 22, 2022 (version 2)

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.

Metrics

  • 2,639
    views
  • 789
    downloads
  • 12
    citations

Views, downloads and citations are aggregated across all versions of this paper published by eLife.

Download links

A two-part list of links to download the article, or parts of the article, in various formats.

Downloads (link to download the article as PDF)

Open citations (links to open the citations from this article in various online reference manager services)

Cite this article (links to download the citations from this article in formats compatible with various reference manager tools)

  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

Share this article

https://doi.org/10.7554/eLife.73276

Further reading

    1. Computational and Systems Biology
    2. Medicine
    Seo-Gyeong Bae, Guo Nan Yin ... Jihwan Park
    Research Article

    Erectile dysfunction (ED) affects a significant proportion of men aged 40–70 and is caused by cavernous tissue dysfunction. Presently, the most common treatment for ED is phosphodiesterase 5 inhibitors; however, this is less effective in patients with severe vascular disease such as diabetic ED. Therefore, there is a need for development of new treatment, which requires a better understanding of the cavernous microenvironment and cell-cell communications under diabetic condition. Pericytes are vital in penile erection; however, their dysfunction due to diabetes remains unclear. In this study, we performed single-cell RNA sequencing to understand the cellular landscape of cavernous tissues and cell type-specific transcriptional changes in diabetic ED. We found a decreased expression of genes associated with collagen or extracellular matrix organization and angiogenesis in diabetic fibroblasts, chondrocytes, myofibroblasts, valve-related lymphatic endothelial cells, and pericytes. Moreover, the newly identified pericyte-specific marker, Limb Bud-Heart (Lbh), in mouse and human cavernous tissues, clearly distinguishing pericytes from smooth muscle cells. Cell-cell interaction analysis revealed that pericytes are involved in angiogenesis, adhesion, and migration by communicating with other cell types in the corpus cavernosum; however, these interactions were highly reduced under diabetic conditions. Lbh expression is low in diabetic pericytes, and overexpression of LBH prevents erectile function by regulating neurovascular regeneration. Furthermore, the LBH-interacting proteins (Crystallin Alpha B and Vimentin) were identified in mouse cavernous pericytes through LC-MS/MS analysis, indicating that their interactions were critical for maintaining pericyte function. Thus, our study reveals novel targets and insights into the pathogenesis of ED in patients with diabetes.

    1. Computational and Systems Biology
    Rebecca A Deek, Siyuan Ma ... Hongzhe Li
    Review Article

    Large-scale microbiome studies are progressively utilizing multiomics designs, which include the collection of microbiome samples together with host genomics and metabolomics data. Despite the increasing number of data sources, there remains a bottleneck in understanding the relationships between different data modalities due to the limited number of statistical and computational methods for analyzing such data. Furthermore, little is known about the portability of general methods to the metagenomic setting and few specialized techniques have been developed. In this review, we summarize and implement some of the commonly used methods. We apply these methods to real data sets where shotgun metagenomic sequencing and metabolomics data are available for microbiome multiomics data integration analysis. We compare results across methods, highlight strengths and limitations of each, and discuss areas where statistical and computational innovation is needed.