arXiv:2410. 09737v2 Announce Type: replace Abstract: A popular way to improve the expressive power of graph neural networks (GNNs) is to use Laplacian eigenvectors as additional node features, since they can serve both as structural identifiers and global coordinates of nodes.
By Junru Zhou, Cai Zhou, Xiyuan Wang, Pan Li, Muhan Zhang
arXiv:2608. 00836v1 Announce Type: new Abstract: While signed-directed graphs have been studied using linear Laplacians in the design of graph neural networks, relatively little research has focused on developing non-linear Laplacian operators for such networks.
By Ali Parviz, Yuichi Yoshida
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.
arXiv:2605.06462v2 Announce Type: replace
Abstract: Progress in graph learning is hindered by benchmark practices that conflate the contributions of node features and graph structure, making it hard...
By Richard von Moos, Mathieu Alain, Bastian Rieck
The paper introduces higher-order positional encodings that enrich graph representations by incorporating topological information from lifted incidence structures, without altering existing graph learning backbones. It theoretically shows that these encodings can mix graph Laplacian frequencies beyond what scalar spectral filters achieve, and demonstrates their effectiveness on Graph Transformers for datasets like ZINC and synthetic benchmarks. The approach bridges graph positional encodings and topological deep learning, enabling standard models to exploit higher-order interactions.
By Caleb Stam, Aagrim Hoysal, Sanjukta Krishnagopal
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