# Certifiable Robustness and Robust Training for Graph Convolutional Networks

## TL;DR

This paper introduces a novel certifiable robustness framework for graph convolutional networks, providing guarantees against node attribute perturbations, and proposes a robust training method that enhances GNN resilience with minimal accuracy loss.

## Contribution

It is the first to offer certifiable robustness for GNNs against attribute perturbations and introduces a robust semi-supervised training procedure.

## Key findings

- Certifies robustness and non-robustness of GNN nodes.
- Significantly improves GNN robustness with minimal accuracy impact.

## Abstract

Recent works show that Graph Neural Networks (GNNs) are highly non-robust with respect to adversarial attacks on both the graph structure and the node attributes, making their outcomes unreliable. We propose the first method for certifiable (non-)robustness of graph convolutional networks with respect to perturbations of the node attributes. We consider the case of binary node attributes (e.g. bag-of-words) and perturbations that are L_0-bounded. If a node has been certified with our method, it is guaranteed to be robust under any possible perturbation given the attack model. Likewise, we can certify non-robustness. Finally, we propose a robust semi-supervised training procedure that treats the labeled and unlabeled nodes jointly. As shown in our experimental evaluation, our method significantly improves the robustness of the GNN with only minimal effect on the predictive accuracy.