arXiv:2607. 06497v1 Announce Type: new Abstract: We introduce EntroPath, a manifold learning method that recovers geodesic geometry from data graphs through ensembles of diffusion paths.
By Przemys{\l}aw Rola
arXiv:2606. 24956v1 Announce Type: new Abstract: Spectral graph neural networks (GNNs) interpret message passing as frequency-selective filtering.
By Ranhui Yan, Jia Cai, Mengzhu Chen, Haodong Yang
Detecting communities in heterophilic graphs -- where connected nodes often belong to different classes -- is hard for unsupervised methods: classical modularity and spectral methods are feature agnostic, while deep graph-clustering methods rely on contrastive or generative machinery that is opaque. We propose Curvature-Guided Sheaf Diffusion (CGSD), a fully unsupervised community-detection algorithm that uses the discrete Forman--Ricci curvature of each edge as its single topological signal, propagated through every stage of an end-to-end pipeline.
arXiv:2607. 21607v1 Announce Type: cross Abstract: Graph Neural Networks propagate information through local message passing, but the graph topologies themselves can silently prevent any amount of training from solving long-range tasks.
By Ranjan Veerabhadraswamy, Ajith Jubilson Emerson
arXiv:2102. 09235v3 Announce Type: replace Abstract: Recent studies revealed the mathematical connection between deep neural networks (DNNs) and dynamic systems.
By Kuo Gai, Shihua Zhang
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.
By Mostafa Haghir Chehreghani