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

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Abstract

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.

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Aditya Gilra

School of Computer and Communication Sciences, Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland

For correspondence
aditya.gilra@epfl.ch

Competing interests
The authors declare that no competing interests exist.

"This ORCID iD identifies the author of this article:" 0000-0002-8628-1864
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.

Funding

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.

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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.