Graph neural networks (GNNs) are powerful machine learning models for various graph learning tasks. Recently, the limitations of the expressive power of various GNN models have been revealed. For example, GNNs cannot distinguish some non-isomorphic graphs and they cannot learn efficient graph algorithms, and several GNN models have been proposed to overcome these limitations. In this paper, we demonstrate that GNNs become powerful just by adding a random feature to each node. We prove that the random features enable GNNs to learn almost optimal polynomial-time approximation algorithms for the minimum dominating set problem and maximum matching problem in terms of the approximation ratio. The main advantage of our method is that it can be combined with off-the-shelf GNN models with slight modifications. Through experiments, we show that the addition of random features enables GNNs to solve various problems that normal GNNs, including GCNs and GINs, cannot solve.

本文研究了图神经网络的表达能力，发现其存在局限性。作者提出为每个节点添加随机特征，这样GNN就能够学习一些最优多项式时间近似算法，同时该方法方便与其他GNN模型结合使用。经实验证明，加入随机特征的GNN能够解决一些无法被传统的GNN模型解决的问题。

随机特征增强图神经网络