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: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
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: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
arXiv:2608. 19914v1 Announce Type: new Abstract: Network topology inference from graph signals is central to graph signal processing with applications in neuroscience, sensor, and social networks.
By Chuansen Peng, Yifan Xia, Jinshan Zhong, Xiaojing Shen
The paper investigates how signed graph filters respond to structural changes such as edge additions, deletions, and sign flips. It shows that both the nature of the edge perturbation and the correlation among node features jointly influence the stability of learned representations. Leveraging this insight, the authors propose a perturbation strategy that targets structurally influential signed edges, and experiments demonstrate that this approach causes greater embedding drift, polarity change, and link‑prediction degradation than baseline methods.
By Ning Zhang, Li Zhang