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This research proposes continuous-time adaptations of Adam optimization for analog Ising machines, demonstrating significant improvements in solution speed and quality over traditional gradient-descent methods on Max-Cut benchmarks. By deriving first-order approximations suitable for physical implementation, the study offers a viable design principle to enhance the robustness of non-digital computing architectures as Moore's Law wanes. The findings suggest that integrating advanced discrete-time optimizers into continuous analog dynamics can substantially reduce time-to-target for difficult optimization problems.
Beyond Gradient Descent: Adam for Analog Ising Machines
arXiv:2606.03917v1 Announce Type: cross 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.
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.
Applied Physics (physics.app-ph); Machine Learning (cs.LG)
arXiv:2606.03917 [physics.app-ph]
(or arXiv:2606.03917v1 [physics.app-ph] for this version)
https://doi.org/10.48550/arXiv.2606.03917 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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