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. 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.
Positional encodings (PEs) enhance the power of graph neural networks (GNNs), both theoretically and empirically. Two of the most popular families of PEs - spectral (e.
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:2606. 24956v1 Announce Type: new Abstract: Spectral graph neural networks (GNNs) interpret message passing as frequency-selective filtering.
arXiv:2607. 25169v1 Announce Type: cross Abstract: Message-passing graph neural networks are bounded by the 1-WL test and can miss topological structure that distinguishes non-isomorphic graphs.
arXiv:2607. 19042v1 Announce Type: cross Abstract: Neural hypergraphs are a natural generalization of neural networks, the reference models in modern machine learning.
The paper presents provable guarantees for a spectral method that recovers binary node labels on signed graphs with edge‑flip noise. It provides graph‑structure‑agnostic bounds on approximate inference accuracy and maximum angle deviation, using matrix concentration and eigenvector perturbation techniques. The results connect to the Cheeger constant and are validated with synthetic experiments, marking the first theoretical analysis of this spectral approach.
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.
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.
arXiv:2607. 27891v1 Announce Type: cross Abstract: Temporal graph learning is commonly organized around the evolution of node states or the encoding of interaction histories.
arXiv:2607. 21263v1 Announce Type: new Abstract: Graph signal processing tasks that leverage spectral information typically assume access to the complete graph topology, which is often unavailable in practice.
arXiv:2609.01441v1 Announce Type: new Abstract: Graph neural networks (GNN) based on message passing are provably no more powerful than the one-dimensional Weisfeiler--Leman colour-refinement test (1...