The first provably efficient algorithm for learning graph neural networks (GNNs) with one hidden layer for node information convolution is provided in this paper. Two types of GNNs are investigated, depending on whether labels are attached to nodes or graphs. A comprehensive framework for designing and analyzing convergence of GNN training algorithms is developed. The algorithm proposed is applicable to a wide range of activation functions including ReLU, Leaky ReLU, Sigmod, Softplus and Swish. It is shown that the proposed algorithm guarantees a linear convergence rate to the underlying true parameters of GNNs. For both types of GNNs, sample complexity in terms of the number of nodes or the number of graphs is characterized. The impact of feature dimension and GNN structure on the convergence rate is also theoretically characterized. Numerical experiments are further provided to validate our theoretical analysis.

该论文提供了第一个针对具有一个隐层节点信息卷积的图神经网络（GNN）的可证明有效的学习算法，并开发了一种综合性框架来设计和分析GNN训练算法的收敛性。提出的算法适用于各种激活函数，包括ReLU，Leaky ReLU，Sigmoid，Softplus和Swish，并对样本复杂度进行了特征化。数值实验进一步验证了理论分析。

使用近似梯度下降学习图神经网络