The paper studies the stability of graph-aware continuous‑time generative models that use a graph filter combined with a learned graph neural network. It derives explicit Wasserstein bounds showing how relative graph perturbations affect the generated distributions, and proposes a principled framework for designing stable graph filters that preserve heat‑diffusion smoothing while improving structural stability. Experiments on synthetic and fMRI data demonstrate that these stable filters enhance robustness and match or surpass the generative quality of a heat‑equation baseline.
By Martin Schmidt, Gonzalo Mateos
arXiv:2604. 19465v3 Announce Type: replace-cross Abstract: Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering.
By Chengyun Wang, Liwei Chen, Nils Thuerey
arXiv:2507. 10005v2 Announce Type: replace Abstract: In recent years, graph-based machine learning techniques, such as reinforcement learning and graph neural networks, have garnered significant attention.
By Yash Arya, Sang Hoon Lee
arXiv:2508. 18173v2 Announce Type: replace Abstract: The discovery of symbolic governing equations is a central goal in science; yet, it remains challenging particularly for graph dynamical systems, where the network topology further shapes the system behavior.
By Riccardo Cappi, Paolo Frazzetto, Nicol\`o Navarin, Alessandro Sperduti
arXiv:2501. 02436v5 Announce Type: replace Abstract: Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning.
By Yuchen Lin, Yong Zhang, Sihan Feng, Hong Zhao
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. 16494v1 Announce Type: cross Abstract: Modern power systems face growing operational complexity driven by the integration of renewable energy sources, decentralization, and the need for real-time decision-making across a wide range of timescales.
By Martin Sadric, Sebastian P\"utz, Christian Nauck, Veit Hagenmeyer, Frank Hellmann, Dirk Witthaut, Benjamin Sch\"afer
arXiv:2507.10383v5 Announce Type: replace-cross
Abstract: Recurrent neural networks are canonical models of biological memory. In these models, memories are represented by distributed patterns of neu...
By Uri Cohen, M\'at\'e Lengyel
arXiv:2608. 03696v1 Announce Type: new Abstract: This work focuses on the problem of learning on temporal graphs, with particular emphasis on the task of clustering: obtaining coarse-grained representations by aggregating information from nodes, edges, and temporal dynamics - a task related to pooling in machine learning on graphs, or community detection in network science.
By Nelson Aloysio Reis de Almeida Passos, Emanuele Carlini, Salvatore Trani
The paper extends the neural network verification framework to graph neural networks by introducing GraphStar sets, which model uncertainty over both node and edge features. This allows sound propagation of linear message‑passing operations and ReLU nonlinearities for GCN and GINE layers. Experiments on power system tasks (PF, OPF, CFA) and graph classification benchmarks (ENZYMES, PROTEINS) show that the method, called GNNV, yields tighter robustness guarantees than CORA and provides, for the first time, edge‑aware guarantees for GINE‑based models under joint node and edge perturbations.
By Anne M. Tumlin, Ben Wooding, Zhenxuan Shao, Diego Manzanas Lopez, Tyler Derr, Taylor T. Johnson
arXiv:2609.10490v2 Announce Type: replace
Abstract: This feature article provides an overview of the theoretical foundations for coVariance neural networks (VNNs), i.e., graph neural networks (GNNs)...
By Saurabh Sihag, Andrea Cavallo, Elvin Isufi, Gonzalo Mateos, Alejandro Ribeiro
arXiv:2607. 07510v1 Announce Type: cross Abstract: Generating signals on graphs requires permutation-equivariant models that exhibit stability with respect to relative structural perturbations.
By Martin Schmidt, Gonzalo Mateos