Accelerating Continuous Variable Coherent Ising Machines via Momentum

TL;DR

This paper enhances Continuous Variable Coherent Ising Machines (CV-CIM) by integrating momentum-based optimization techniques, significantly improving convergence speed, robustness, and sample diversity in solving non-convex quadratic problems.

Contribution

It introduces momentum and Adam optimization methods into CV-CIM dynamics, demonstrating improved performance and stability over traditional gradient descent approaches.

Findings

Momentum and Adam accelerate convergence.

Enhanced robustness on poorly conditioned problems.

Increased sample diversity and stability.

Abstract

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.