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Parameters estimation in spiking neural networks: a reverse-engineering approach

Horacio Rostro-Gonzalez 1 Bruno Cessac 1, 2 Thierry Viéville 3
1 NEUROMATHCOMP - Mathematical and Computational Neuroscience
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
3 CORTEX - Neuromimetic intelligence
Inria Nancy - Grand Est, LORIA - AIS - Department of Complex Systems, Artificial Intelligence & Robotics
Abstract : This paper presents a reverse engineering approach for parameter estimation in spiking neural networks (SNNs). We consider the deterministic evolution of a time-discretized network with spiking neurons, where synaptic transmission has delays, modeled as a neural network of the generalized integrate and fire type. Our approach aims at by-passing the fact that the parameter estimation in SNN results in a non-deterministic polynomial-time hard problem when delays are to be considered. Here, this assumption has been reformulated as a linear programming (LP) problem in order to perform the solution in a polynomial time. Besides, the LP problem formulation makes the fact that the reverse engineering of a neural network can be performed from the observation of the spike times explicit. Furthermore, we point out how the LP adjustment mechanism is local to each neuron and has the same structure as a 'Hebbian' rule. Finally, we present a generalization of this approach to the design of input―output (I/O) transformations as 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.
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Submitted on : Wednesday, July 17, 2013 - 2:13:58 PM
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Horacio Rostro-Gonzalez, Bruno Cessac, Thierry Viéville. Parameters estimation in spiking neural networks: a reverse-engineering approach. Journal of Neural Engineering, IOP Publishing, 2012, 9 (2), pp.026024. ⟨10.1088/1741-2560/9/2/026024⟩. ⟨hal-00845594⟩



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