用Adam优化器提升模拟伊辛机求解速度与精度
Beyond Gradient Descent: Adam for Analog Ising Machines
- 提出连续时间版Adam，适配模拟伊辛机的动态演化
- 在最大割问题上，Adam比梯度下降快3倍以上，解更优
- 适合硬件实现的简化版本性能优于完整版，适合物理系统
随着摩尔定律逼近极限，伊辛机为难解优化问题提供了有前景的计算方案。然而，许多模拟、连续时间的伊辛机依赖类梯度下降动力学，限制了速度与鲁棒性。本文研究动量和Adam优化器能否改进此类系统。由于这些优化器传统上基于离散时间，我们推导出适用于模拟连续动态的连续时间版本。在最大割（Max-Cut）基准测试中，基于Adam的动力学显著降低达到目标所需时间，并提升解的质量，优于梯度下降与动量方法。我们进一步提出一种一阶连续时间近似版Adam，作为未来物理实现的简化起点，在连续时间设置下表现甚至优于完整版Adam。在纯算法离散时间设置中，简单实例上性能差距缩小，但在更复杂的加权实例上，基于Adam的更新规则仍最优。结果表明，连续时间Adam动力学是模拟伊辛机的重要设计原则。
原文摘要 · Abstract (English)
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.
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