arXiv Machine Learning
Jun 25
Convex--Concave Quadratic Spectral Filtering for Graph Neural Networks
arXiv:2606. 24956v1 Announce Type: new Abstract: Spectral graph neural networks (GNNs) interpret message passing as frequency-selective filtering.
Spectral Graph Neural Networks with Hermite Polynomials: A Comprehensive Study
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.
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arXiv AI
Jul 7
Learning to Discover Iterative Spectral Algorithms
arXiv:2602. 09530v2 Announce Type: replace-cross Abstract: We introduce AutoSpec, a neural network framework for discovering iterative spectral algorithms for large-scale numerical linear algebra and numerical optimization.
arXiv AI
Jul 22
Spectral Higher-Order Neural Networks Have Sharp Expressivity Bounds
arXiv:2607. 19042v1 Announce Type: cross Abstract: Neural hypergraphs are a natural generalization of neural networks, the reference models in modern machine learning.
arXiv Machine Learning
Jun 17
Geometrical fairness in graph neural networks
arXiv:2606. 17684v1 Announce Type: cross Abstract: Graph-based learning methods have become increasingly prominent due to their strong performance across diverse applications.
Hugging Face Trending Papers
Jul 7
Graph Convolutional Attention: A Spectral Perspective on Graph Denoising and Diffusion
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 AI
Jul 8
Graph Convolutional Attention: A Spectral Perspective on Graph Denoising and Diffusion
arXiv:2607. 06546v1 Announce Type: cross Abstract: Denoising graphs is a fundamental problem in graph learning and the core operation of graph diffusion models.
arXiv Machine Learning
Aug 4
Spectral Reach: Understanding Neural Scaling as Progress into the Spectral Tail
arXiv:2605. 31244v2 Announce Type: replace Abstract: Neural scaling laws describe predictable power-law relationships between model size, dataset size, compute, and performance.
arXiv Machine Learning
Sep 3
Learning Spectral-Like Mesh-Free Discretisations
The paper introduces Spectral-like Neural Discretisation (SpeND), a mesh‑free method that learns stencil weights via a neural network to approximate the modal response of a spectral operator across a specified band of wavenumbers. By projecting the network output onto the space of polynomial‑consistent weights, SpeND ensures exact consistency while minimizing dispersion and dissipation errors in a self‑supervised, physics‑agnostic manner. Experiments on disordered 2‑D node sets demonstrate that the learned fourth‑order operator matches the exact spectral response over a wider band than traditional LABFM or structured‑grid finite differences, and retains fourth‑order convergence upon refinement.
arXiv Machine Learning
Jun 30
Characterizing Optimizer-Dependent Training Dynamics Through Hessian Eigenvector Displacement and Localization
arXiv:2606. 30226v1 Announce Type: new Abstract: Hessian spectral properties are a standard tool in analysing neural-network training, with eigenvalues linked to sharpness, generalization, and optimization dynamics.
arXiv Machine Learning
Jun 16
Graph Learning Should Move Beyond Restrictive Views of Spectral and Message-Passing GNNs
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 Machine Learning
Jun 30
Spectral Gating via Damped Oscillations for Adaptive Implicit Neural Representations
arXiv:2606. 23129v2 Announce Type: replace-cross Abstract: Implicit Neural Representations (INRs) have been proven successful in encoding continuous signals through coordinate-based networks, yet facing a spectral dilemma: periodic activations capture fine details but act as all-pass filters that memorise noise, while spatially compact activations regularise effectively but suffer from low-frequency bias.
arXiv AI
Sep 15
LiftGCN: Efficient Energy-Preserving Graph Learning via Joukowski Spectral Lifting for Finite Element Stress Prediction
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...