图神经网络与组合优化的能量腔方法
Graph neural networks and the energetic cavity method for combinatorial optimization
- University of Cambridge（剑桥大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究通过将平均场启发式融入图神经网络，提升其求解伊辛模型基态的性能，但发现同等计算成本下模拟退火仍具竞争力。
AI中文摘要：
我们研究了使用图神经网络（GNNs）来寻找伊辛模型近似基态的问题。高效地找到这些基态具有广泛的意义，因为许多组合优化问题可以通过适当选择耦合和场来表述为伊辛模型。精确求解这些问题很困难，但存在许多良好的启发式方法。这些启发式方法中的一系列源于平均场近似：一种方法使用适当定义矩阵的主特征向量，另一种是最小和算法，也称为能量腔方法。未经修改的GNN在这两种方法上表现更差。我们考虑对GNN进行小幅修改以融入这些启发式方法，并发现这显著提高了性能。虽然修改后的方法与其他深度学习方法相比具有竞争力，但我们仍然发现，在相同的计算成本下，模拟退火至少与深度学习方法一样可靠。
英文摘要：
We study the use of graph neural networks (GNNs) for finding approximate ground states of Ising models. Efficiently finding these ground states is of broad significance because many combinatorial optimization problems can be formulated as an Ising model with the appropriate choice of couplings and fields. Exactly solving these problems is hard but there are many good heuristic methods. A lineage of these heuristics build from mean-field approximations: one approach uses the leading eigenvector of an appropriately defined matrix, another is the min-sum algorithm, also known as the energetic cavity method. Without modification, GNNs perform worse than both of these methods. We consider small modifications to the GNN to incorporate these heuristics and find that this considerably improves performance. While the modified approach is competitive against other deep-learning approaches, we still find that simulated annealing is reliably at least as good as deep learning methods for the same computational cost.
