Yassine Abbahaddou

Graph Neural Networks (GNNs) have emerged as powerful tools for learning representations from structured data. Despite their growing popularity and success across various applications, GNNs encounter several challenges that limit their performance. in their generalization, robustness to adversarial perturbations, and the effectiveness of their representation learning capabilities. In this dissertation, I investigate these core aspects through three main contributions: (1) developing new representation learning techniques based on Graph Shift Operators (GSOs, aiming for enhanced performance across various contexts and applications, (2) introducing generalization-enhancing methods through graph data augmentation, and (3) developing more robust GNNs by leveraging orthonormalization techniques and noise-based defenses against adversarial attacks. By addressing these challenges, my work provides a more principled understanding of the limitations and potential of GNNs.

Graph Neural Networks (GNNs) have achieved strong performance across a range of graph representation learning tasks, yet their adversarial robustness in graph classification remains underexplored compared to node classification. While most existing defenses focus on the message-passing component, this work investigates the overlooked role of pooling operations in shaping robustness. We present a theoretical analysis of standard flat pooling methods (sum, average and max), deriving upper bounds on their adversarial risk and identifying their vulnerabilities under different attack scenarios and graph structures. Motivated by these insights, we propose \textit{Robust Singular Pooling (RS-Pool)}, a novel pooling strategy that leverages the dominant singular vector of the node embedding matrix to construct a robust graph-level representation. We theoretically investigate the robustness of RS-Pool and interpret the resulting bound leading to improved understanding of our proposed pooling operator. While our analysis centers on Graph Convolutional Networks (GCNs), RS-Pool is model-agnostic and can be implemented efficiently via power iteration. Empirical results on real-world benchmarks show that RS-Pool provides better robustness than the considered pooling methods when subject to state-of-the-art adversarial attacks while maintaining competitive clean accuracy. Our code is publicly available at:\href{https://github.com/king/rs-pool}{https://github.com/king/rs-pool}.