Learning Graph Neural Networks with Approximate Gradient Descent
This work provides a foundational theoretical understanding and an efficient learning algorithm for GNNs, which is significant for researchers and practitioners working with graph-structured data.
This paper introduces the first provably efficient algorithm for learning one-hidden-layer Graph Neural Networks (GNNs) for both node and graph label prediction. The algorithm guarantees a linear convergence rate to the true GNN parameters, and the paper characterizes sample complexity and the impact of feature dimension and GNN structure on convergence.
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.