  The graph neural network (GNN) models have presented impressive achievements
in numerous machine learning tasks. However, many existing GNN models are shown
to be vulnerable to adversarial attacks, which creates a stringent need to
build robust GNN architectures. In this work, we propose a novel interpretable
message passing scheme with adaptive structure (ASMP) to defend against
adversarial attacks on graph structure. Layers in ASMP are derived based on
optimization steps that minimize an objective function that learns the node
feature and the graph structure simultaneously. ASMP is adaptive in the sense
that the message passing process in different layers is able to be carried out
over dynamically adjusted graphs. Such property allows more fine-grained
handling of the noisy (or perturbed) graph structure and hence improves the
robustness. Convergence properties of the ASMP scheme are theoretically
established. Integrating ASMP with neural networks can lead to a new family of
GNN models with adaptive structure (ASGNN). Extensive experiments on
semi-supervised node classification tasks demonstrate that the proposed ASGNN
outperforms the state-of-the-art GNN architectures in terms of classification
performance under various adversarial attacks.
