Linear response for spiking neuronal networks with unbounded memory
arXiv:1704.05344
Abstract
We establish a general linear response relation for spiking neuronal networks, based on chains with unbounded memory. This relation allows us to predict the influence of a weak amplitude time-dependent external stimuli on spatio-temporal spike correlations, from the spontaneous statistics (without stimulus) in a general context where the memory in spike dynamics can extend arbitrarily far in the past. Using this approach, we show how linear response is explicitly related to neuronal dynamics with an example, the gIF model, introduced by M. Rudolph and A. Destexhe. This example illustrates the collective effect of the stimuli, intrinsic neuronal dynamics, and network connectivity on spike statistics. We illustrate our results with numerical simulations.
60 pages, 8 figures
References in corpus (7)
- A discrete time neural network model with spiking neurons II. Dynamics with noise
- Maximum entropy models reveal the excitatory and inhibitory correlation structures in cortical neuronal activity
- Learning to make external sensory stimulus predictions using internal correlations in populations of neurons
- Linear response, or else
- Learning Maximum Entropy Models from finite size datasets: a fast Data-Driven algorithm allows sampling from the posterior distribution
- Large Deviations Properties of Maximum Entropy Markov Chains from Spike Trains
- Introduction to (generalized) Gibbs measures