Reliable Graph Neural Networks via Robust Aggregation

TL;DR

This paper introduces Soft Medoid, a robust aggregation function for Graph Neural Networks that significantly enhances their resistance to structural perturbations, especially effective against adversarial attacks.

Contribution

The paper proposes a novel, fully differentiable robust aggregation function with a high breakdown point, improving GNN robustness against adversarial structure perturbations.

Findings

Robust aggregation improves GNN performance under attack by a factor of 3 on Cora ML.

Soft Medoid outperforms traditional aggregation methods in robustness.

Enhanced robustness is especially notable for low-degree nodes.

Abstract

Perturbations targeting the graph structure have proven to be extremely effective in reducing the performance of Graph Neural Networks (GNNs), and traditional defenses such as adversarial training do not seem to be able to improve robustness. This work is motivated by the observation that adversarially injected edges effectively can be viewed as additional samples to a node's neighborhood aggregation function, which results in distorted aggregations accumulating over the layers. Conventional GNN aggregation functions, such as a sum or mean, can be distorted arbitrarily by a single outlier. We propose a robust aggregation function motivated by the field of robust statistics. Our approach exhibits the largest possible breakdown point of 0.5, which means that the bias of the aggregation is bounded as long as the fraction of adversarial edges of a node is less than 50\%. Our novel aggregation function, Soft Medoid, is a fully differentiable generalization of the Medoid and therefore lends itself well for end-to-end deep learning. Equipping a GNN with our aggregation improves the robustness with respect to structure perturbations on Cora ML by a factor of 3 (and 5.5 on Citeseer) and by a factor of 8 for low-degree nodes.