Fisher-Bures Adversary Graph Convolutional Networks

Abstract

In a graph convolutional network, we assume that the graph $G$ is generated wrt some observation noise. During learning, we make small random perturbations $\Delta G$ of the graph and try to improve generalization. Based on quantum information geometry, $\Delta G$ can be characterized by the eigendecomposition of the graph Laplacian matrix. We try to minimize the loss wrt the perturbed $G+\Delta G$ while making $\Delta G$ to be effective in terms of the Fisher information of the neural network. Our proposed model can consistently improve graph convolutional networks on semi-supervised node classification tasks with reasonable computational overhead. We present three different geometries on the manifold of graphs: the intrinsic geometry measures the information theoretic dynamics of a graph; the extrinsic geometry characterizes how such dynamics can affect externally a graph neural network; the embedding geometry is for measuring node embeddings. These new analytical tools are useful in developing a good understanding of graph neural networks and fostering new techniques.

Published in UAI 2019

References in corpus (10)

• Inductive Representation Learning on Large Graphs
• Simplifying Graph Convolutional Networks
• Representation Learning on Graphs with Jumping Knowledge Networks
• Pitfalls of Graph Neural Network Evaluation
• Support Vector Machines under Adversarial Label Contamination
• LanczosNet: Multi-Scale Deep Graph Convolutional Networks
• Derivatives of Multilinear Functions of Matrices
• Convolutional Kernel Networks
• Quantum state discrimination: a geometric approach
• Fisher Information and Natural Gradient Learning of Random Deep Networks

Cited by in corpus (5)

• Bayesian Graph Convolutional Neural Networks using Node Copying
• Bayesian Graph Convolutional Neural Networks Using Non-Parametric Graph Learning
• Node Copying: A Random Graph Model for Effective Graph Sampling
• Graph Self-Supervised Learning with Learnable Structural and Positional Encodings
• Node Copying for Protection Against Graph Neural Network Topology Attacks