  The Coherent Ising Machine (CIM) is a non-conventional architecture that
takes inspiration from physical annealing processes to solve Ising problems
heuristically. Its dynamics are naturally continuous and described by a set of
ordinary differential equations that have been proven to be useful for the
optimization of continuous variables non-convex quadratic optimization
problems. The dynamics of such Continuous Variable CIMs (CV-CIM) encourage
optimization via optical pulses whose amplitudes are determined by the negative
gradient of the objective; however, standard gradient descent is known to be
trapped by local minima and hampered by poor problem conditioning. In this
work, we propose to modify the CV-CIM dynamics using more sophisticated pulse
injections based on tried-and-true optimization techniques such as momentum and
Adam. Through numerical experiments, we show that the momentum and Adam updates
can significantly speed up the CV-CIM's convergence and improve sample
diversity over the original CV-CIM dynamics. We also find that the
Adam-CV-CIM's performance is more stable as a function of feedback strength,
especially on poorly conditioned instances, resulting in an algorithm that is
more robust, reliable, and easily tunable. More broadly, we identify the CIM
dynamical framework as a fertile opportunity for exploring the intersection of
classical optimization and modern analog computing.
