1. Neuroscience
Download icon

Predicting non-linear dynamics by stable local learning in a recurrent spiking neural network

  1. Aditya Gilra  Is a corresponding author
  2. Wulfram Gerstner
  1. Ecole Polytechnique Federale de Lausanne, Switzerland
Research Article
  • Cited 25
  • Views 3,811
  • Annotations
Cite this article as: eLife 2017;6:e28295 doi: 10.7554/eLife.28295


The brain needs to predict how the body reacts to motor commands, but how a network of spiking neurons can learn non-linear body dynamics using local, online and stable learning rules is unclear. Here, we present a supervised learning scheme for the feedforward and recurrent connections in a network of heterogeneous spiking neurons. The error in the output is fed back through fixed random connections with a negative gain, causing the network to follow the desired dynamics. The rule for Feedback-based Online Local Learning Of Weights (FOLLOW) is local in the sense that weight changes depend on the presynaptic activity and the error signal projected onto the postsynaptic neuron. We provide examples of learning linear, non-linear and chaotic dynamics, as well as the dynamics of a two-link arm. Under reasonable approximations, we show, using the Lyapunov method, that FOLLOW learning is uniformly stable, with the error going to zero asymptotically.

Article and author information

Author details

  1. Aditya Gilra

    School of Computer and Communication Sciences, Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland
    For correspondence
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-8628-1864
  2. Wulfram Gerstner

    School of Computer and Communication Sciences, Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland
    Competing interests
    The authors declare that no competing interests exist.


European Research Council (Multirules 268 689)

  • Aditya Gilra
  • Wulfram Gerstner

Swiss National Science Foundation (CRSII2_147636)

  • Aditya Gilra
  • Wulfram Gerstner

European Commission Horizon 2020 Framework Program (Human Brain Project 720270)

  • Wulfram Gerstner

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

Reviewing Editor

  1. Peter Latham, University College London, United Kingdom

Publication history

  1. Received: May 3, 2017
  2. Accepted: November 22, 2017
  3. Accepted Manuscript published: November 27, 2017 (version 1)
  4. Version of Record published: December 14, 2017 (version 2)
  5. Version of Record updated: February 23, 2018 (version 3)


© 2017, Gilra & Gerstner

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.


  • 3,811
    Page views
  • 690
  • 25

Article citation count generated by polling the highest count across the following sources: Crossref, Scopus, PubMed Central.

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)

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

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

Further reading

    1. Neuroscience
    Rebecca A Mount et al.
    Research Article

    Trace conditioning and extinction learning depend on the hippocampus, but it remains unclear how neural activity in the hippocampus is modulated during these two different behavioral processes. To explore this question, we performed calcium imaging from a large number of individual CA1 neurons during both trace eye-blink conditioning and subsequent extinction learning in mice. Our findings reveal that distinct populations of CA1 cells contribute to trace conditioned learning versus extinction learning, as learning emerges. Furthermore, we examined network connectivity by calculating co-activity between CA1 neuron pairs and found that CA1 network connectivity patterns also differ between conditioning and extinction, even though the overall connectivity density remains constant. Together, our results demonstrate that distinct populations of hippocampal CA1 neurons, forming different sub-networks with unique connectivity patterns, encode different aspects of learning.

    1. Neuroscience
    Mahmood S Hoseini et al.
    Research Article

    Visual perception in natural environments depends on the ability to focus on salient stimuli while ignoring distractions. This kind of selective visual attention is associated with gamma activity in the visual cortex. While the nucleus reticularis thalami (nRT) has been implicated in selective attention, its role in modulating gamma activity in the visual cortex remains unknown. Here we show that somatostatin- (SST) but not parvalbumin-expressing (PV) neurons in the visual sector of the nRT preferentially project to the dorsal lateral geniculate nucleus (dLGN), and modulate visual information transmission and gamma activity in primary visual cortex (V1). These findings pinpoint the SST neurons in nRT as powerful modulators of the visual information encoding accuracy in V1, and represent a novel circuit through which the nRT can influence representation of visual information.