Graph Neural Networks (GNNs) have proven to be highly effective in various graph learning tasks. A key characteristic of GNNs is their use of a fixed number of message-passing steps for all nodes in the graph, regardless of each node's diverse computational needs and characteristics. Through empirical real-world data analysis, we demonstrate that the optimal number of message-passing layers varies for nodes with different characteristics. This finding is further supported by experiments conducted on synthetic datasets. To address this, we propose Adaptive Depth Message Passing GNN (ADMP-GNN), a novel framework that dynamically adjusts the number of message passing layers for each node, resulting in improved performance. This approach applies to any model that follows the message passing scheme. We evaluate ADMP-GNN on the node classification task and observe performance improvements over baseline GNN models. Our code is publicly available at: https://github.com/abbahaddou/ADMP-GNN

Graph Neural Networks (GNNs) have shown great promise in tasks like node and graph classification, but they often struggle to generalize, particularly to unseen or out-of-distribution (OOD) data. These challenges are exacerbated when training data is limited in size or diversity. To address these issues, we introduce a theoretical framework using Rademacher complexity to compute a regret bound on the generalization error and then characterize the effect of data augmentation. This framework informs the design of GRATIN, an efficient graph data augmentation algorithm leveraging the capability of Gaussian Mixture Models (GMMs) to approximate any distribution. Our approach not only outperforms existing augmentation techniques in terms of generalization but also offers improved time complexity, making it highly suitable for real-world applications.

Generative models such as Generative Adversarial Networks (GANs), Variational Autoencoders (VAEs), and diffusion models often suffer from mode collapse, failing to reproduce the full diversity of their training data. While this problem has been extensively studied in image generation, it remains largely unaddressed for time series. We introduce a formal definition of mode collapse for time series and propose DMD-GEN, a geometry-aware metric that quantifies its severity. DMD-GEN leverages Dynamic Mode Decomposition (DMD) to extract coherent temporal structures and uses Optimal Transport between DMD eigenvectors to measure discrepancies in underlying dynamics. By representing the subspaces spanned by the DMD eigenvectors as point structures on a Grassmann manifold, and comparing them via Wasserstein distances computed from principal angles, DMD-GEN enables a principled geometric comparison between real and generated sequences. The metric is efficient, requiring no additional training, supports mini-batch evaluation, and is easily parallelizable. Beyond quantification, DMD-GEN offers interpretability by revealing which dynamical modes are distorted or missing in the generated data. Experiments on synthetic and real-world datasets using TimeGAN, TimeVAE, and DiffusionTS show that DMD-GEN aligns with existing metrics while providing the first principled framework for detecting and interpreting mode collapse in time series.

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 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.

Graph Neural Networks (GNNs) have emerged as the dominant approach for machine learning on graph-structured data. However, concerns have arisen regarding the vulnerability of GNNs to small adversarial perturbations. Existing defense methods against such perturbations suffer from high time complexity and can negatively impact the model's performance on clean graphs. To address these challenges, this paper introduces NoisyGNNs, a novel defense method that incorporates noise into the underlying model's architecture. We establish a theoretical connection between noise injection and the enhancement of GNN robustness, highlighting the effectiveness of our approach. We further conduct extensive empirical evaluations on the node classification task to validate our theoretical findings, focusing on two popular GNNs: the GCN and GIN. The results demonstrate that NoisyGNN achieves superior or comparable defense performance to existing methods while minimizing added time complexity. The NoisyGNN approach is model-agnostic, allowing it to be integrated with different GNN architectures. Successful combinations of our NoisyGNN approach with existing defense techniques demonstrate even further improved adversarial defense results. Our code is publicly available at: https://github.com/Sennadir/NoisyGNN.

Graph Neural Networks (GNNs) have demonstrated state-of-the-art performance in various graph representation learning tasks. Recently, studies revealed their vulnerability to adversarial attacks. In this work, we theoretically define the concept of expected robustness in the context of attributed graphs and relate it to the classical definition of adversarial robustness in the graph representation learning literature. 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. Building on these findings, we connect the expected robustness of GNNs to the orthonormality of their weight matrices and consequently propose an attack-independent, more robust variant of the GCN, called the Graph Convolutional Orthonormal Robust Networks (GCORNs). We further introduce a probabilistic method to estimate the expected robustness, which allows us to evaluate the effectiveness of GCORN on several real-world datasets. Experimental experiments showed that GCORN outperforms available defense methods. Our code is publicly available at: https://github.com/Sennadir/GCORN .