This title appears in the Scientific Report :
2018
Theory of Intrinsic Timescales in Spiking Neural Networks
Theory of Intrinsic Timescales in Spiking Neural Networks
We investigate intrinsic timescales, characterized by single unit autocorrelation times, in spiking neuralnetwork models that incorporate exhaustive experimental data about the network architecture [1, 2, 3].In vivo, electrophysiological recordings during the resting state reveal a hierarchical stru...
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Personal Name(s): | van Meegen, Alexander (Corresponding author) |
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van Albada, Sacha | |
Contributing Institute: |
Computational and Systems Neuroscience; IAS-6 Jara-Institut Brain structure-function relationships; INM-10 Computational and Systems Neuroscience; INM-6 |
Imprint: |
2018
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Conference: | INM/ICS Retreat 2018, Juelich (Germany), 2018-07-02 - 2018-07-03 |
Document Type: |
Conference Presentation |
Research Program: |
Human Brain Project Specific Grant Agreement 2 Human Brain Project Specific Grant Agreement 1 Connectivity and Activity |
Publikationsportal JuSER |
We investigate intrinsic timescales, characterized by single unit autocorrelation times, in spiking neuralnetwork models that incorporate exhaustive experimental data about the network architecture [1, 2, 3].In vivo, electrophysiological recordings during the resting state reveal a hierarchical structure of intrinsictimescales that matches anatomical hierarchies remarkably well [4]. Using dynamical mean field theory,we try to elucidate this apparent interrelation between network structure and intrinsic timescales.In a first step, we reduce the dynamics of the recurrent network of spiking neurons to a set of self-consistent, one-dimensional stochastic differential equations. To this end, we make use of a dynamicalmean-field theory originally developed for spin glasses [5]. The starting point of this theory is the system’scharacteristic functional and it proceeds with a disorder average, a Hubbard-Stratonovich transformation,and a saddle point approximation. Although technically involved, the result is quite intuitive: The massiverecurrent input each neuron receives is replaced by an effective Gaussian process.To obtain the intrinsic timescale from the reduced dynamics, we have to calculate the correlation functionof a spiking neuron driven by a non-Markovian Gaussian process. In the low firing rate regime where themean interspike interval exceeds the correlation time of the input, a renewal approximation is admissible.As a renewal process is fully characterized by its hazard function, we derive novel approximations forthe hazard function of a leaky integrate-and-fire neuron driven by a non-Markovian Gaussian process.This enables us to obtain an analytically closed system of self-consistent equations for the autocorrelationfunctions of single neurons in recurrent networks. By formulating these analytical expressions, a thoroughinvestigation of the effect of network architecture on intrinsic timescales becomes possible. |