Back-engineering of spiking neural networks parameters

Horacio Rostro-Gonzalez 1 Bruno Cessac 1 Juan Carlos Vasquez 1 Thierry Vieville 2
1 NEUROMATHCOMP
CRISAM - Inria Sophia Antipolis - Méditerranée , INRIA Rocquencourt, ENS Paris - École normale supérieure - Paris, UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR8548
2 CORTEX - Neuromimetic intelligence
Inria Nancy - Grand Est, LORIA - AIS - Department of Complex Systems, Artificial Intelligence & Robotics
Abstract : We consider the deterministic evolution of a time-discretized spiking network of neurons with connection weights having delays, modeled as a discretized neural network of the generalized integrate and fire (gIF) type. The purpose is to study a class of algorithmic methods allowing to calculate the proper parameters to reproduce exactly a given spike train generated by an hidden (unknown) neural network. This standard problem is known as NP-hard when delays are to be calculated. We propose here a reformulation, now expressed as a Linear-Programming (LP) problem, thus allowing to provide an efficient resolution. This allows us to "back-engineer" a neural network, i.e. to find out, given a set of initial conditions, which parameters (i.e., connection weights in this case), allow to simulate the network spike dynamics. More precisely we make explicit the fact that the back-engineering of a spike train, is a Linear (L) problem if the membrane potentials are observed and a LP problem if only spike times are observed, with a gIF model. Numerical robustness is discussed. We also explain how it is the use of a generalized IF neuron model instead of a leaky IF model that allows us to derive this algorithm. Furthermore, we point out how the L or LP adjustment mechanism is local to each unit and has the same structure as an "Hebbian" rule. A step further, this paradigm is easily generalizable to the design of input-output spike train transformations. This means that we have a practical method to "program" a spiking network, i.e. find a set of parameters allowing us to exactly reproduce the network output, given an input. Numerical verifications and illustrations are provided.
Type de document :
Pré-publication, Document de travail
30 pages, 17 figures, submitted. 2009
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https://hal.inria.fr/hal-00846118
Contributeur : Pierre Kornprobst <>
Soumis le : jeudi 18 juillet 2013 - 15:38:42
Dernière modification le : jeudi 26 avril 2018 - 10:28:51

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  • HAL Id : hal-00846118, version 1
  • ARXIV : 0905.4810

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Horacio Rostro-Gonzalez, Bruno Cessac, Juan Carlos Vasquez, Thierry Vieville. Back-engineering of spiking neural networks parameters. 30 pages, 17 figures, submitted. 2009. 〈hal-00846118〉

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