  Artificial neural networks can harness stochasticity in multiple ways to
enable a vast class of computationally powerful models. Electronic
implementation of such stochastic networks is currently limited to addition of
algorithmic noise to digital machines which is inherently inefficient; albeit
recent efforts to harness physical noise in devices for stochasticity have
shown promise. To succeed in fabricating electronic neuromorphic networks we
need experimental evidence of devices with measurable and controllable
stochasticity which is complemented with the development of reliable
statistical models of such observed stochasticity. Current research literature
has sparse evidence of the former and a complete lack of the latter. This
motivates the current article where we demonstrate a stochastic neuron using an
insulator-metal-transition (IMT) device, based on electrically induced
phase-transition, in series with a tunable resistance. We show that an IMT
neuron has dynamics similar to a piecewise linear FitzHugh-Nagumo (FHN) neuron
and incorporates all characteristics of a spiking neuron in the device
phenomena. We experimentally demonstrate spontaneous stochastic spiking along
with electrically controllable firing probabilities using Vanadium Dioxide
(VO$_2$) based IMT neurons which show a sigmoid-like transfer function. The
stochastic spiking is explained by two noise sources - thermal noise and
threshold fluctuations, which act as precursors of bifurcation. As such, the
IMT neuron is modeled as an Ornstein-Uhlenbeck (OU) process with a fluctuating
boundary resulting in transfer curves that closely match experiments. As one of
the first comprehensive studies of a stochastic neuron hardware and its
statistical properties, this article would enable efficient implementation of a
large class of neuro-mimetic networks and algorithms.
