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.

翻译：我们展示了图形神经网络如何用于解决卡通图形颜色问题。 我们将图形颜色标定为一个多级节点分类问题, 并使用基于统计物理波茨模型的不受监督的培训策略。 对社区检测、数据组合和最小分类覆盖问题等其他多级问题的概括化是直截了当的。 我们提供了数字基准结果, 并用一个端到端应用程序来说明我们的方法, 用于在全面的编码- 进程解码框架内真实世界列表使用案例。 我们的优化方法在平方或优于现有解答器上演化, 能够与数以百万计的变量相容。