Title: Moving Past Gradient Descent: Integrating Adam Optimization into Analog Ising Machines

Abstract:

As the limitations of Moore’s Law become increasingly apparent, Ising machines have emerged as a compelling alternative for tackling complex optimization challenges. Yet, many time-continuous, analog variants of these machines depend on gradient-descent-like dynamics, a constraint that can hinder both their speed and robustness. This study explores whether incorporating momentum and Adam optimization can enhance the performance of these systems. Because Adam and similar optimizers are typically defined in discrete time, we have developed continuous-time formulations specifically tailored to the dynamics of analog, time-continuous Ising machines.

Testing on Max-Cut benchmarks reveals that dynamics driven by Adam significantly outperform those based on gradient descent or momentum, yielding superior solution quality and reduced time-to-target. Additionally, we propose a first-order continuous-time approximation of Adam, designed to serve as a more practical foundation for future physical hardware implementations. Although this simplified approach does not match the full Adam formulation’s performance in a continuous-time context, it still offers distinct advantages. In purely algorithmic, discrete-time experiments, we observe that the performance disparity narrows on simpler problem instances; however, Adam-based updates demonstrate the highest efficacy on more challenging, weighted problems. Ultimately, these findings highlight continuous-time Adam dynamics as a potent design strategy for next-generation analog Ising machines.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC