Oversmoothing is a fundamental limitation of deep graph neural networks (GNNs), where repeated message passing causes node representations to become increasingly similar, eventually collapsing toward a low-dimensional subspace. This phenomenon limits the effective depth of message-passing architectures and motivates the search for mechanisms that preserve representation diversity.
arXiv:2607. 28185v1 Announce Type: new Abstract: Oversmoothing is a fundamental limitation of deep graph neural networks (GNNs), where repeated message passing causes node representations to become increasingly similar, eventually collapsing toward a low-dimensional subspace.
arXiv:2609.13920v1 Announce Type: cross Abstract: Persistent Gaussian perturbations have been shown to prevent asymptotic oversmoothing in recurrent Graph Neural Networks (GNNs) by ensuring a positiv...
arXiv:2609.39739v1 Announce Type: new Abstract: Graph generative models increasingly rely on Graph Transformers (GT) to capture complex dependencies among nodes and edges. While deeper architectures...
arXiv:2507. 05164v2 Announce Type: replace-cross Abstract: In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms.
arXiv:2608. 16038v1 Announce Type: cross Abstract: Post-hoc Graph Neural Network (GNN) explainers commonly follow a Perturb-Query paradigm, inferring the importance of graph elements based on queried predictions to perturbed inputs.
Generating signals on graphs requires permutation-equivariant models that exhibit stability with respect to relative structural perturbations. While favorable stability properties of Graph Neural Networks (GNNs) have been well documented, it is unclear how structural errors propagate through the dynamics of continuous generative flow models that are gaining traction for graph signal generation.
The paper introduces the Graph Dynamics Model (GDM), a world model that learns stochastic latent dynamics over evolving graph topologies. GDM employs a sparse recurrent adjacency matrix for topology updates and a recurrent state‑space architecture for stochastic transitions, enabling it to handle partially observable, stochastic environments. The authors also propose the Graph Distribution Distance (GDD) metric, using maximum mean discrepancy with a graph kernel, to compare predicted and true joint graph state distributions, and demonstrate GDM’s superior performance and zero‑shot generalisation on large graphs.
The paper explores how information propagates in Deep Graph Networks (DGNs) for both static and dynamic graphs, treating DGNs as dynamical systems. It presents new architectures that better preserve long‑term node dependencies and learn complex spatio‑temporal patterns from irregular, sparsely sampled dynamic graphs. The work combines theoretical analysis with empirical results to demonstrate the effectiveness of these designs.
Denoising graphs is a fundamental problem in graph learning and the core operation of graph diffusion models. Attention-based architectures like graph transformers have recently shown promise in denoising graphs.
arXiv:2607. 06546v1 Announce Type: cross Abstract: Denoising graphs is a fundamental problem in graph learning and the core operation of graph diffusion models.
arXiv:2601. 02451v2 Announce Type: replace-cross Abstract: Graph Neural Networks (GNNs) suffer from over-smoothing in deep architectures and expressiveness bounded by the 1-Weisfeiler-Leman (1-WL) test.
arXiv:2607. 07510v1 Announce Type: cross Abstract: Generating signals on graphs requires permutation-equivariant models that exhibit stability with respect to relative structural perturbations.