Stationarity properties of neural networks

Asmussen, Søren; Turova, Tatyana S.

doi:10.1239/jap/1032438374

Cited by 1 publication

(1 citation statement)

References 8 publications

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“…It was first introduced by Cottrell (1992), studied by Fricker et al (1994) and then instantiated and studied in Asmussen and Turova (1998), Cottrell and Turova (2000) and Turova (1996Turova ( , 2000. Time-discrete versions of such systems were studied by Cessac (2008Cessac ( , 2010 with a particular focus on stationary spike distributions.…”

Section: Proposition 21mentioning

confidence: 99%

A Markovian event-based framework for stochastic spiking neural networks

Touboul

Faugeras²

2011

J Comput Neurosci

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In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature of the sequence of spike times in stochastic neural networks, and in particular the ability to deduce from a spike train the next spike time, and therefore produce a description of the network activity only based on the spike times regardless of the membrane potential process. To study this question in a rigorous manner, we introduce and study an event-based description of networks of noisy integrate-and-fire neurons, i.e. that is based on the computation of the spike times. We show that the firing times of the neurons in the networks constitute a Markov chain, whose transition probability is related to the probability distribution of the interspike interval of the neurons in the network. In the cases where the Markovian model can be developed, the transition probability is explicitly derived in such classical cases of neural networks as the linear integrate-and-fire neuron models with excitatory and inhibitory interactions, for different types of synapses, possibly featuring noisy synaptic integration, transmission delays and absolute and relative refractory period. This covers most of the cases that have been investigated in the event-based description of spiking deterministic neural networks.

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