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: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...
By Mostafa Haghir Chehreghani
The paper presents a theoretical study of how intrinsic noise affects learning dynamics in noisy linear recurrent neural networks. It demonstrates that noise can break degeneracies in the solution space, influence the alignment of read-in, readout, and recurrent weights, and even induce a phase transition where a non-degenerate solution becomes suboptimal under high noise and parameter constraints. These findings suggest that noise is not merely a nuisance but can fundamentally shape representation learning in RNNs.
By John J. Vastola, Kanaka Rajan
arXiv:2507. 05164v2 Announce Type: replace-cross Abstract: In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms.
By Dennis Chemnitz, Maximilian Engel, Christian Kuehn, Sara-Viola Kuntz
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...
By Luca Miglior, Alessio Gravina, Davide Bacciu
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.
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.
By Ziluowen Luo, Jun Yin, Ruochen Liu, Ming Cheng, Shirui Pan, Chengqi Zhang, Senzhang Wang
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.
By Alex Schutz, Nick Hawes, Victor-Alexandru Darvariu
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.
The paper introduces RGC‑Net, a Reservoir‑Based Graph Convolutional Network that combines fixed‑random reservoir dynamics with a structured convolutional framework for graph learning. It addresses limitations of existing reservoir‑based GNNs by adding a leaky integrator for better feature retention and a robust, adaptable architecture for graph classification and generation. Experiments demonstrate state‑of‑the‑art performance on classification and generative tasks, including dynamic brain connectivity, with faster convergence and reduced over‑smoothing.
By Mayssa Soussia, Gita Ayu Salsabila, Mohamed Ali Mahjoub, Islem Rekik
arXiv:2607. 06546v1 Announce Type: cross Abstract: Denoising graphs is a fundamental problem in graph learning and the core operation of graph diffusion models.
By Shervin Khalafi, Igor Krawczuk, Sergio Rozada, Charilaos Kanatsoulis, Antonio G Marques, Alejandro Ribeiro
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.
By Subhankar Mishra