arXiv Machine Learning
Jul 20

From Diffusion to Reaction-Diffusion: A Dynamical-Systems View of Oversmoothing in Hypergraph Neural Networks

arXiv:2607. 15773v1 Announce Type: new Abstract: Higher-order couplings enhance the expressive power of hypergraph neural networks (HGNNs), but they also intensify representation collapse in deep propagation due to strong multi-way feature mixing.

By Zhiheng Zhou, Mengyao Zhou, Yancheng Chen, Dengyi Zhao, Xingqin Qi, Guiying Yan
arXiv Machine Learning
Sep 17

Stable Filters for Generative Modeling of Graph Signals

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 Machine Learning
1d ago

Information propagation dynamics in Deep Graph Networks

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.

By Alessio Gravina