Fisher-Bures Adversary Graph Convolutional Networks
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In a graph convolutional network, we assume that the graph G is generated with respect to some observation noise. We make small random perturbations ΔG of the graph and try to improve generalization. Based on quantum information geometry, we can have quantitative measurements on the scale of ΔG. We try to maximize the intrinsic scale of the permutation with a small budget while minimizing the loss based on the perturbed G+ΔG. 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.
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