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Conference Papers Year : 2009

## Back-engineering of spiking neural networks parameters

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Horacio Rostro
• Function : Author
• PersonId : 854706
Bruno Cessac
Juan Carlos Vasquez
• Function : Author
• PersonId : 854707
Thierry Viéville
• Function : Author
• PersonId : 830072

#### 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.

#### Domains

Cognitive science Neuroscience

### Dates and versions

inria-00407911 , version 1 (27-07-2009)

### Identifiers

• HAL Id : inria-00407911 , version 1

### Cite

Horacio Rostro, Bruno Cessac, Juan Carlos Vasquez, Thierry Viéville. Back-engineering of spiking neural networks parameters. Eighteenth Annual Computational Neuroscience Meeting CNS*2009, 2009, Berlin, Germany. ⟨inria-00407911⟩

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