Improving the Robustness of Graph Neural Networks Against Node Feature Attacks

Core Concepts

Graph Neural Networks (GNNs) are vulnerable to adversarial attacks targeting node features. This work introduces a theoretically grounded approach, called Graph Convolutional Orthonormal Robust Networks (GCORN), that enhances the expected robustness of Graph Convolutional Networks (GCNs) against such attacks while maintaining their performance.

Abstract

The paper focuses on improving the robustness of Graph Neural Networks (GNNs) against adversarial attacks targeting node features. It makes the following key contributions:

Defines the concept of "Expected Adversarial Robustness" for graph-based functions and relates it to the classical definition of adversarial robustness. This allows for a more comprehensive assessment of a model's robustness.

Derives an upper bound on the expected robustness of Graph Convolutional Networks (GCNs) and Graph Isomorphism Networks (GINs) subject to node feature attacks. The bound depends on the graph structure and the propagation scheme.

Proposes a novel GCN variant called Graph Convolutional Orthonormal Robust Networks (GCORN) that enhances robustness to feature-based attacks by encouraging orthonormality of the weight matrices. This is achieved through an iterative weight projection scheme.

Introduces a probabilistic method to estimate the expected robustness of GNNs, which allows for a more realistic and comprehensive evaluation of defense approaches.

Empirically evaluates GCORN on benchmark node and graph classification datasets, demonstrating its superior ability to defend against feature-based attacks compared to existing methods. GCORN also shows improved certified robustness against structural perturbations.

Stats

The sum of normalized walks of length (L-1) starting from node u in a graph is denoted as ŵu.
The maximum of the sum of normalized walks of length (L-1) across all nodes in a graph is denoted as ŵG.
The L1 and L∞ norms of the weight matrix W in the l-th layer of a GCN are denoted as ∥W(l)∥1 and ∥W(l)∥∞, respectively.
The L2 norm of the node feature matrix X is denoted as ∥X∥2.

Quotes

"Our definition allows us to derive an upper bound of the expected robustness of Graph Convolutional Networks (GCNs) and Graph Isomorphism Networks subject to node feature attacks."
"Motivated by our theoretical results, we propose a refined learning scheme, called Graph Convolutional Orthonormal Robust Network (GCORN), for the GCN, to improve its robustness to feature-based perturbations while maintaining its expressive power."
"To overcome this limitation, we propose a novel probabilistic method for evaluating the expected robustness of GNNs, which is based on our introduced robustness definition."

Key Insights Distilled From

Bounding the Expected Robustness of Graph Neural Networks Subject to Node Feature Attacks

by Yass... at arxiv.org 04-30-2024

https://arxiv.org/pdf/2404.17947.pdf

Deeper Inquiries

How can the proposed GCORN architecture be extended to other GNN models beyond GCNs to improve their robustness against feature-based attacks

The proposed GCORN architecture can be extended to other GNN models beyond GCNs by incorporating the orthonormalization technique into their weight matrices. This approach aims to control the norms of the weight matrices in each layer of the GNN, thereby enhancing the model's robustness against feature-based attacks. By applying the iterative orthonormalization process during training, other GNN models can also benefit from improved robustness. The key idea is to modify the mathematical formulation of the GNN to encourage the orthonormality of the weights, leading to a more robust architecture. This extension can be applied to various GNN models, such as Graph Isomorphism Networks (GINs) and Graph Attention Networks (GATs), by integrating the orthonormalization process into their training procedures. By enforcing the orthonormality of weight matrices, these models can potentially exhibit enhanced robustness to feature-based attacks while maintaining their performance in graph representation tasks.

What are the potential limitations of the introduced expected robustness definition, and how can it be further generalized to capture other aspects of a model's robustness

The introduced expected robustness definition has certain potential limitations that can be addressed to further generalize and enhance its applicability. One limitation is the focus on node feature-based attacks, which may not fully capture the overall robustness of a GNN model. To address this limitation, the definition can be extended to encompass a broader range of adversarial scenarios, including structural attacks and other types of perturbations. By incorporating multiple attack vectors and evaluating the model's robustness across different dimensions, the expected robustness definition can provide a more comprehensive assessment of a GNN's resilience to adversarial threats. Additionally, the definition could be further generalized by considering the impact of hyperparameters, model architecture, and dataset characteristics on the model's robustness. By incorporating these factors into the definition, a more holistic understanding of a GNN's robustness can be achieved, leading to more effective defense strategies and evaluation metrics.

Can the insights gained from the theoretical analysis of GNNs' robustness be leveraged to develop new adversarial attack strategies that are more effective against existing defense methods

The insights gained from the theoretical analysis of GNNs' robustness can be leveraged to develop new adversarial attack strategies that are more effective against existing defense methods. By understanding the vulnerabilities and limitations of GNN models, attackers can devise targeted adversarial attacks that exploit specific weaknesses in the model's architecture. For example, the analysis of the upper bound on the expected robustness of GNNs can guide attackers in identifying optimal attack strategies that maximize the model's vulnerability within a given input neighborhood. Additionally, the theoretical findings can inform the development of sophisticated adversarial attacks that bypass existing defense mechanisms, such as orthonormalization techniques or robust training strategies. By leveraging the insights from the theoretical analysis, attackers can design more potent and challenging adversarial attacks that pose a greater threat to GNN models, ultimately driving advancements in adversarial attack strategies and defense mechanisms.