arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2202.01606cs.LGcond-mat.dis-nncs.AImath.OCquant-ph
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基于物理启发的图神经网络的图着色

Graph Coloring with Physics-Inspired Graph Neural Networks

Amazon Quantum Solutions Lab(亚马逊量子解决方案实验室);AWS Intelligent and Advanced Compute Technologies, Professional Services(AWS智能与高级计算技术专业服务部);AWS Center for Quantum Computing(AWS量子计算中心)

Martin J. A. Schuetz, J. Kyle Brubaker, Zhihuai Zhu, Helmut G. Katzgraber

摘要:

我们展示了如何图神经网络可以用来解决规范的图着色问题。我们框架图着色作为一个多类节点分类问题,并利用基于统计物理Potts模型的无监督训练策略。推广到其他多类问题,如社区发现,数据聚类和最小集团覆盖问题是直接的。我们提供了数值基准测试结果,并在一个全面的编码-处理-解码框架内,用一个端到端的应用程序来说明我们的方法。我们的优化方法与现有的求解器性能相当或优于现有的求解器,能够扩展到具有数百万个变量的问题。

英文摘要:

We show how graph neural networks can be used to solve the canonical graph coloring problem. We frame graph coloring as a multi-class node classification problem and utilize an unsupervised training strategy based on the statistical physics Potts model. Generalizations to other multi-class problems such as community detection, data clustering, and the minimum clique cover problem are straightforward. We provide numerical benchmark results and illustrate our approach with an end-to-end application for a real-world scheduling use case within a comprehensive encode-process-decode framework. Our optimization approach performs on par or outperforms existing solvers, with the ability to scale to problems with millions of variables.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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