arXiv:2606. 24956v1 Announce Type: new Abstract: Spectral graph neural networks (GNNs) interpret message passing as frequency-selective filtering.
arXiv:2602. 10031v2 Announce Type: replace Abstract: Graph neural networks (GNNs) are commonly divided into message-passing neural networks (MPNNs) and spectral GNNs, reflecting two largely separate research traditions in machine learning and signal processing.
The paper introduces HermNet, a spectral graph neural network that uses Hermite polynomials for nodewise prediction and normalized propagation, avoiding eigendecomposition or learned bases. It compares HermNet to other complete polynomial bases, examining how coordinate choices affect optimization under limited training. Experiments on synthetic and real data show regimes where HermNet outperforms alternatives, and analyze the impact of calibration, regularization, and training duration on performance.
arXiv:2607. 06546v1 Announce Type: cross Abstract: Denoising graphs is a fundamental problem in graph learning and the core operation of graph diffusion models.
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:2607. 19042v1 Announce Type: cross Abstract: Neural hypergraphs are a natural generalization of neural networks, the reference models in modern machine learning.
arXiv:2607. 22381v1 Announce Type: new Abstract: Curvature notions on graphs, particularly Ollivier-Ricci and Forman, have emerged as powerful tools for addressing fundamental issues in Graph Neural Networks (GNNs) such as oversmoothing and oversquashing, but rely almost exclusively on local edge-level comparisons and therefore fail to certify how information actually propagates over long distances.
arXiv:2609.14977v1 Announce Type: cross Abstract: Finite element stress fields often exhibit strong local non-smoothness, where stress concentrations near holes, notches, and loading regions induce s...
The paper introduces the Long‑Range Ising Model (LRIM) benchmark, which ensures long‑range dependence by defining each label as a node’s spin multiplied by a power‑law coupled spin field. It proves that polynomial filters on the adjacency matrix—used in isotropic message passing and spectral graph networks—cannot reduce the error floor because the target lies on a spectral level set where such filters are constant. The authors show that a strided filter with about fifty coefficients, trained on the labels, achieves a test error 52 times lower than the best published network, while a dilated convolutional network outperforms prior results at 256 nodes and matches them at 1,024 nodes, providing the first in‑domain results for larger sizes.
arXiv:2607.11577v2 Announce Type: replace-cross Abstract: Conventional Graph Neural Networks (GNNs) couple feature transformation and neighborhood aggregation, which often renders them vulnerable to...
arXiv:2607. 11577v1 Announce Type: cross Abstract: We introduce a constrained two-view framework for node prediction that aligns structure-conditioned GNN embeddings with a structure-free feature prior learned by an anchor model.
The paper introduces CTQW-GNN, a graph neural network that uses Continuous‑Time Quantum Walks (CTQW) to address two common GNN problems: low‑pass bias on heterophilic graphs and over‑smoothing with deep layers. By exploiting the unitary nature of the CTQW propagator, the model preserves high‑frequency signals and maintains feature norms across layers. Three aggregation modules—CTQW‑based, CTQW‑attention, and a low‑pass GAT branch—combine to handle both heterophilic and homophilic graph structures, supported by spectral‑gap analysis and a Lieb–Robinson‑type bound for walk‑time selection.
arXiv:2601. 02451v2 Announce Type: replace-cross Abstract: Graph Neural Networks (GNNs) suffer from over-smoothing in deep architectures and expressiveness bounded by the 1-Weisfeiler-Leman (1-WL) test.