图着色满足深度学习：用于组合问题的有效图神经网络模型
Graph Colouring Meets Deep Learning: Effective Graph Neural Network Models for Combinatorial Problems
摘要：
在过去的十年里，深度学习一直在挑战许多领域的最先进技术。然而，我们才刚刚开始了解神经学习在符号领域的能力。在图上使用参数共享的深度学习架构可以生成可以根据关系数据的复杂属性进行训练的模型。这些问题包括高度相关的NP完全问题，如SAT和TSP。在这项工作中，我们展示了如何设计图神经网络（GNN）-用一个非常简单的架构-来解决图着色的基本组合问题。我们的研究结果表明，该模型在随机实例上训练时达到了很高的准确性，能够推广到与训练时不同的图形分布。此外，对于某些分布，它的表现优于Neurosat，Tabucol和greedy基线。此外，我们还展示了顶点嵌入如何在多维空间中聚类以产生建设性的解决方案，即使我们的模型只被训练为二元分类器。总之，我们的研究结果有助于缩短我们对GNN学习算法的理解差距，并为它们在困难的组合问题上的能力积累经验证据。因此，我们的研究结果有助于在深度学习系统中集成鲁棒学习和符号推理的长期挑战。
英文摘要：
Deep learning has consistently defied state-of-the-art techniques in many fields over the last decade. However, we are just beginning to understand the capabilities of neural learning in symbolic domains. Deep learning architectures that employ parameter sharing over graphs can produce models which can be trained on complex properties of relational data. These include highly relevant NP-Complete problems, such as SAT and TSP. In this work, we showcase how Graph Neural Networks (GNN) can be engineered -- with a very simple architecture -- to solve the fundamental combinatorial problem of graph colouring. Our results show that the model, which achieves high accuracy upon training on random instances, is able to generalise to graph distributions different from those seen at training time. Further, it performs better than the Neurosat, Tabucol and greedy baselines for some distributions. In addition, we show how vertex embeddings can be clustered in multidimensional spaces to yield constructive solutions even though our model is only trained as a binary classifier. In summary, our results contribute to shorten the gap in our understanding of the algorithms learned by GNNs, as well as hoarding empirical evidence for their capability on hard combinatorial problems. Our results thus contribute to the standing challenge of integrating robust learning and symbolic reasoning in Deep Learning systems.
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