Beyond Gradient Descent: Adam for Analog Ising Machines
2026-06-02 • Machine Learning
Machine Learning
AI summaryⓘ
The authors studied a special type of computer called an analog Ising machine, which tries to solve tough optimization problems. They looked at ways to make these machines work faster and find better solutions by using improved optimization methods called momentum and Adam. Since these methods usually work step-by-step, the authors adapted them to work smoothly over continuous time, which is how these machines operate. Their experiments showed that using Adam in continuous time helped the machines solve problems quicker and better than older methods. They also created a simpler version of Adam that might be easier to build in real devices and still worked well.
Moore's lawIsing machineoptimizationgradient descentmomentum optimizationAdam optimizercontinuous-time dynamicsMax-Cut problemanalog computingdiscrete-time optimization
Authors
Stijn Van Vooren, Guy Van der Sande, Guy Verschaffelt
Abstract
As Moore's law reaches its limits, Ising machines offer a promising alternative computing approach for difficult optimization problems. However, many analog, time-continuous Ising machines rely on gradient-descent-like dynamics to find solutions, which can limit speed and robustness. We investigate whether momentum and Adam optimization can improve these systems. Since these optimizers are traditionally formulated in discrete time, we derive continuous-time versions suitable for analog, time-continuous Ising-machine dynamics. On Max-Cut benchmarks, we find that Adam-based dynamics substantially reduce time-to-target and improve solution quality compared with gradient-descent- and momentum-based dynamics. We further introduce a first-order continuous-time approximation of Adam that is intended as a simpler starting point for future physical implementations and while performing better than the full Adam formulation in a continuous-time setting. We also study a purely algorithmic discrete-time setting, where the performance gap is reduced on easier problem instances, while the Adam-based update rule performs best on harder weighted problem instances. These results identify continuous-time Adam dynamics as a powerful design principle for analog Ising machines.