Mean-field theory of graph neural networks in graph partitioning
Mean-field theory of graph neural networks in graph partitioning
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DOI：
10.1088/1742-5468/ab3456
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发表时间：
2019-12-01
影响因子：
2.4
通讯作者：
Obuchi, Tomoyuki
中科院分区：
文献类型：
--
作者：
Kawamoto, Tatsuro;Tsubaki, Masashi;Obuchi, Tomoyuki
对图神经网络（GNN）进行了理论性能分析。对于分类任务，神经网络方法在灵活性方面具有优势，可以以数据驱动的方式使用，而贝叶斯推理需要假设特定的模型。一个基本的问题是，GNN除了这种灵活性之外，是否还具有高精度。此外，所实现的性能主要是反向传播的结果还是架构本身是一个相当感兴趣的问题。为了更好地了解这些问题，一个最小的GNN架构的平均场理论开发的图分割问题。这与数值实验结果吻合较好。
A theoretical performance analysis of the graph neural network (GNN) is presented. For classification tasks, the neural network approach has the advantage in terms of flexibility that it can be employed in a data-driven manner, whereas Bayesian inference requires the assumption of a specific model. A fundamental question is then whether GNN has a high accuracy in addition to this flexibility. Moreover, whether the achieved performance is predominately a result of the backpropagation or the architecture itself is a matter of considerable interest. To gain a better insight into these questions, a mean-field theory of a minimal GNN architecture is developed for the graph partitioning problem. This demonstrates a good agreement with numerical experiments.