  Emerging non-volatile memories have been proposed for a wide range of
applications from easing the von-Neumann bottleneck to neuromorphic
applications. Specifically, scalable RRAMs based on Pr$_{1-x}$Ca$_x$MnO$_3$
(PCMO) exhibit analog switching have been demonstrated as an integrating
neuron, an analog synapse, and a voltage-controlled oscillator. More recently,
the inherent stochasticity of memristors has been proposed for efficient
hardware implementations of Boltzmann Machines. However, as the problem size
scales, the number of neurons increase and controlling the stochastic
distribution tightly over many iterations is necessary. This requires
parametric control over stochasticity. Here, we characterize the stochastic Set
in PCMO RRAMs. We identify that the Set time distribution depends on the
internal state of the device (i.e., resistance) in addition to external input
(i.e., voltage pulse). This requires the confluence of contradictory properties
like stochastic switching as well as deterministic state control in the same
device. Unlike, "stochastic-everywhere" filamentary memristors, in PCMO RRAMs,
we leverage the (i) stochastic Set in negative polarity and (ii) deterministic
analog Reset in positive polarity to demonstrate 100x reduced Set time
distribution drift. The impact on Boltzmann Machines' performance is analyzed
and as opposed to the "fixed external input stochasticity", the
"state-monitored stochasticity" can solve problems 20x larger in size. State
monitoring also tunes out the device-to-device variability effect on
distributions providing 10x better performance. In addition to the physical
insights, this study establishes the use of experimental stochasticity in PCMO
RRAMs in stochastic recurrent neural networks reliably over many iterations.
