  A Boltzmann machine whose effective "temperature" can be dynamically "cooled"
provides a stochastic neural network realization of simulated annealing, which
is an important metaheuristic for solving combinatorial or global optimization
problems with broad applications in machine intelligence and operations
research. However, the hardware realization of the Boltzmann stochastic element
with "cooling" capability has never been achieved within an individual
semiconductor device. Here we demonstrate a new memristive device concept based
on two-dimensional material heterostructures that enables this critical
stochastic element in a Boltzmann machine. The dynamic cooling effect in
simulated annealing can be emulated in this multi-terminal memristive device
through electrostatic bias with sigmoidal thresholding distributions. We also
show that a machine-learning-based method is efficient for device-circuit
co-design of the Boltzmann machine based on the stochastic memristor devices in
simulated annealing. The experimental demonstrations of the tunable stochastic
memristors combined with the machine-learning-based device-circuit
co-optimization approach for stochastic-memristor-based neural-network circuits
chart a pathway for the efficient hardware realization of stochastic neural
networks with applications in a broad range of electronics and computing
disciplines.
