论文标题
图形卷积网络的简单光谱故障模式
A Simple Spectral Failure Mode for Graph Convolutional Networks
论文作者
论文摘要
神经网络在机器学习任务中取得了巨大的成功。最近，使用神经网络将其扩展到图形学习。但是，在理解如何以及何时表现良好的理论工作中，尤其是相对于建立的统计学习技术，例如光谱嵌入。在这篇简短的论文中，我们提出了一个简单的生成模型，其中无监督的图形卷积网络失败，而邻接光谱嵌入成功。具体而言，无监督的图形卷积网络在某些近似规则的图中无法超越第一个特征向量，因此在非领导特征向量中缺少推理信号。视觉插图和全面的模拟证明了这一现象。
Neural networks have achieved remarkable successes in machine learning tasks. This has recently been extended to graph learning using neural networks. However, there is limited theoretical work in understanding how and when they perform well, especially relative to established statistical learning techniques such as spectral embedding. In this short paper, we present a simple generative model where unsupervised graph convolutional network fails, while the adjacency spectral embedding succeeds. Specifically, unsupervised graph convolutional network is unable to look beyond the first eigenvector in certain approximately regular graphs, thus missing inference signals in non-leading eigenvectors. The phenomenon is demonstrated by visual illustrations and comprehensive simulations.
