用神经网络学出一种高效求解复杂优化问题的新方法
Neural Ising Machines via Unrolling and Zeroth-Order Training
- 用小型神经网络学习自适应的更新规则，替代传统算法
- 在标准测试中达到与先进方法相当的求解质量与速度
- 适合需要快速求解复杂组合优化问题的研究者
我们提出一种数据驱动的启发式方法，用于求解NP难的伊辛模型与最大割问题。该方法通过学习一个迭代动力系统的更新规则，采用参数量极少的多层感知机来建模节点级更新规则，将局部相互作用场映射为自旋更新。训练使用零阶优化器，因为长程、循环的伊辛机动态会导致不稳定且信息量低的梯度。该方法称为神经网络参数化伊辛机（NPIM）。尽管参数量少，其学习到的动力学仍展现出类似动量的行为和时变调度，能在高度非凸的能量景观中实现高效搜索。在标准伊辛模型和神经组合优化基准上，NPIM在求解质量与求解时间上均表现优异，优于近期学习型方法，并媲美强健的经典伊辛机启发式。
原文摘要 · Abstract (English)
We propose a data-driven heuristic for NP-hard Ising and Max-Cut optimization that learns the update rule of an iterative dynamical system. The method learns a shared, node-wise update rule that maps local interaction fields to spin updates, parameterized by a compact multilayer perceptron with a small number of parameters. Training is performed using a zeroth-order optimizer, since backpropagation through long, recurrent Ising-machine dynamics leads to unstable and poorly informative gradients. We call this approach a neural network parameterized Ising machine (NPIM). Despite its low parameter count, the learned dynamics recover effective algorithmic structure, including momentum-like behavior and time-varying schedules, enabling efficient search in highly non-convex energy landscapes. Across standard Ising and neural combinatorial optimization benchmarks, NPIM achieves competitive solution quality and time-to-solution relative to recent learning-based methods and strong classical Ising-machine heuristics.
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