Relaxing Graph Transformers for Adversarial Attacks (2407.11764v1)

Abstract: Existing studies have shown that Graph Neural Networks (GNNs) are vulnerable to adversarial attacks. Even though Graph Transformers (GTs) surpassed Message-Passing GNNs on several benchmarks, their adversarial robustness properties are unexplored. However, attacking GTs is challenging due to their Positional Encodings (PEs) and special attention mechanisms which can be difficult to differentiate. We overcome these challenges by targeting three representative architectures based on (1) random-walk PEs, (2) pair-wise-shortest-path PEs, and (3) spectral PEs - and propose the first adaptive attacks for GTs. We leverage our attacks to evaluate robustness to (a) structure perturbations on node classification; and (b) node injection attacks for (fake-news) graph classification. Our evaluation reveals that they can be catastrophically fragile and underlines our work's importance and the necessity for adaptive attacks.

• The paper introduces continuous relaxations to facilitate gradient-based adaptive attacks on Graph Transformers, overcoming challenges from non-differentiable components.
• It evaluates three GT architectures with varied positional encodings, revealing significant vulnerabilities in node classification and fake news detection tasks.
• The study underscores the need for robust positional encodings and architectural innovations to enhance the adversarial resilience of Graph Transformers.

Analyzing the Adversarial Robustness of Graph Transformers Through Relaxations

The paper "Relaxing Graph Transformers for Adversarial Attacks" by Foth et al. offers a thorough exploration of the adversarial robustness of Graph Transformers (GTs). The research builds on the backdrop of existing studies that identified vulnerabilities in Graph Neural Networks (GNNs) such as Graph Convolutional Networks (GCNs). Although GTs outperform traditional GNNs in various benchmarks, the robustness of GTs under adversarial attacks remained unexplored.

The primary contribution of this research is the novel adaptive attack strategies designed for GTs. The authors focus on three representative architectures, each utilizing different Positional Encodings (PEs)—namely: random-walk PEs, pairwise-shortest-path PEs, and spectral PEs. These correspond to the Graph Inductive bias Transformer (GRIT), Graphormer, and Spectral Attention Network (SAN), respectively. They evaluate the robustness of these GT models under structural perturbations for node classification and node injection attacks targeting fake news detection in graph classification.

Architecture Relaxations and Adaptive Attacks

Attacking GTs presents unique challenges due to non-differentiable attention mechanisms and PEs with respect to the graph structure. The authors propose continuous relaxations to overcome these challenges:

1. Random-Walk-Based GRIT: The random-walk PEs are inherently continuous, easing their integration into gradient-based attacks.
2. Distance-Based Graphormer: Interpolation techniques make degree and shortest path distance (SPD) encodings compatible with continuous optimization by enabling gradients over continuous distances.
3. Spectral SAN: Laplacian-based PEs are tackled through matrix perturbation theory approximations, and a continuous relaxation of the attention mechanism accounts for probabilistic edge presence.

These relaxations align with three main principles: equivalence for discrete inputs, smooth interpolation between graph states, and efficient computation.

Robustness Evaluations

The evaluation results uncover significant robustness disparities across the GT models evaluated:

1. CLUSTER Dataset: The inductive node classification dataset offers deceptively straightforward perturbations, primarily through modifications of labeled nodes. Both adaptive and transfer attacks identify labeled nodes as the primary targets, demonstrating the robustness weaknesses regardless of the GT model used.
2. UPFD Datasets (Fake News Detection): The node injection attack results display more variability. Graphormer often shows heightened vulnerability, especially in the gossipcop dataset. The relaxations reveal that certain model components are more susceptible to adversarial perturbations, suggesting differential architectural robustness within GTs.

Implications and Future Developments

The findings underscore the necessity for adversarial robustness research tailored to Graph Transformers. GTs, despite their enhanced performance, exhibit critical vulnerabilities that could undermine practical applications, particularly in sensitive domains such as fake news detection.

Several future research avenues emerge from this paper:

1. Designing Robust PEs: Investigating and developing positional encodings that enhance robustness while maintaining model accuracy.
2. Architectural Innovations: Modifying attention mechanisms and other core components of GTs to inherently resist adversarial perturbations.
3. Adaptive Attack Frameworks: Expanding the proposed continuous relaxations and adaptive attacks to a broader range of GT designs.

Conclusion

This paper by Foth et al. makes a significant contribution to understanding and improving the adversarial robustness of GTs. By proposing effective continuous relaxations and adaptive attacks, the paper lays the groundwork for future research aimed at fortifying the resilience of advanced graph models against adversarial threats. The varied robustness across different GT architectures calls attention to the critical need for tailored defenses in future iterations of graph transformer designs.