Fisher-Bures Adversary Graph Convolutional Networks

In a graph convolutional network, we assume that the graph $G$ is generated with respect to some observation noise. We make small random perturbations $\Delta{}G$ of the graph and try to improve generalization. Based on quantum information geometry, we can have quantitative measurements on the scale of $\Delta{}G$. We try to maximize the intrinsic scale of the permutation with a small budget while minimizing the loss based on the perturbed $G+\Delta{G}$. Our proposed model can consistently improve graph convolutional networks on semi-supervised node classification tasks with reasonable computational overhead. We present two different types of geometry on the manifold of graphs: one is for measuring the intrinsic change of a graph; the other is for measuring how such changes can affect externally a graph neural network. These new analytical tools will be useful in developing a good understanding of graph neural networks and fostering new techniques.