The seemingly stochastic transient dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference. In vitro neurons, on the other hand, exhibit a highly deterministic response to various types of stimulation. We show that an ensemble of deterministic leaky integrate-and-fire neurons embedded in a spiking noisy environment can attain the correct firing statistics in order to sample from a well-defined target distribution. We provide an analytical derivation of the activation function on the single cell level; for recurrent networks, we examine convergence towards stationarity in computer simulations and demonstrate sample-based Bayesian inference in a mixed graphical model. This establishes a rigorous link between deterministic neuron models and functional stochastic dynamics on the network level.
@article{arxiv.1311.3211,
title = {Stochastic inference with deterministic spiking neurons},
author = {Mihai A. Petrovici and Johannes Bill and Ilja Bytschok and Johannes Schemmel and Karlheinz Meier},
journal= {arXiv preprint arXiv:1311.3211},
year = {2017}
}