Stochastic inference with deterministic spiking neurons

TL;DR

This paper demonstrates that deterministic spiking neuron models, when embedded in noisy environments, can perform stochastic inference by sampling from target distributions, linking deterministic neuron behavior to stochastic network dynamics.

Contribution

It provides an analytical framework showing how deterministic neurons can achieve stochastic sampling, bridging the gap between deterministic neuron models and stochastic inference.

Findings

Deterministic neurons can sample from target distributions in noisy environments.

Recurrent networks converge to stationary distributions suitable for Bayesian inference.

Sample-based Bayesian inference demonstrated in simulated neural networks.

Abstract

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.