The paper introduces Spectral Connectivity-Regularized Graph Learning (SCoGL), a method for learning sparse graphs from limited data by incorporating Laplacian spectral priors that promote global connectivity. SCoGL extends the graphical lasso objective with a connectivity prior derived from Laplacian eigenvalues and uses projected gradient descent with Armijo backtracking for optimization. Experiments demonstrate that SCoGL improves graph recovery and enhances downstream tasks such as graph signal denoising when observations are scarce.
By Mingxiao Liu (Tsinghua University, China), Bahar Oveisgharan (York University, Canada), Bingyan Zou (Tsinghua University, China), Gene Cheung (York University, Canada), H. Vicky Zhao (Tsinghua University, China), Feifei Gao (Tsinghua University, China)
arXiv:2608. 12757v1 Announce Type: cross Abstract: Laplacian-regularized minimization is fundamental in signal processing and machine learning, but is limited by the dense and ill-conditioned nature of the graph Laplacian pseudoinverse.
By Liping Tao, Chee Wei Tan
arXiv:2605.06395v3 Announce Type: replace-cross
Abstract: Modern deep learning architectures increasingly contend with sophisticated signals that are natively infinite-dimensional, such as time serie...
By Kartik Tandon, Julian Gould, Tanishq Bhatia, Francesca Dominici, Alejandro Ribeiro, Claudio Battiloro
arXiv:2510. 03690v4 Announce Type: replace Abstract: Real-world graph datasets often arise from mixtures of populations, where graphs are generated by multiple distinct underlying distributions.
By Ali Azizpour, Reza Ramezanpour, Santiago Segarra
arXiv:2510. 16311v3 Announce Type: replace Abstract: Graph Contrastive Learning (GCL) has emerged as a powerful tool for extracting consistent representations from graphs, independent of labeled information.
By Zhengyu Wu, Daohan Su, Yang Zhang, Xunkai Li, Rong-Hua Li, Guoren Wang
arXiv:2412.08016v3 Announce Type: replace
Abstract: Standard deep learning architectures used for classification generate label predictions with a projection head and softmax activation function. Alt...
By Jason Brown, Bohan Chen, Harris Hardiman-Mostow, Jeff Calder, Andrea L. Bertozzi
The paper introduces an unsupervised framework that merges manifold learning with rank‑based interpretable graph embeddings to address the Geometric and Interpretability Gaps in visual representation learning. By first analyzing contextual information on the dataset manifold and then producing sparse, self‑explainable embeddings, the method achieves dimensionality reduction while preserving or improving performance in image retrieval and semi‑supervised Graph Convolutional Network classification. Experiments across varied datasets confirm that these context‑aware representations maintain high downstream effectiveness.
By Thiago C\'esar Castilho Almeida, Gustavo Rosseto Let\'icio, Vinicius Atsushi Sato Kawai, Daniel Carlos Guimar\~aes Pedronette
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.
By Antonis Vasileiou, Juan Cervino, Pascal Frossard, Charilaos I. Kanatsoulis, Christopher Morris, Michael T. Schaub, Pierre Vandergheynst, Zhiyang Wang, Guy Wolf, Ron Levie
arXiv:2606. 17684v1 Announce Type: cross Abstract: Graph-based learning methods have become increasingly prominent due to their strong performance across diverse applications.
By Arturo P\'erez-Peralta, Sandra Ben\'itez-Pe\~na, Blas Kolic, Rosa E. Lillo
arXiv:2509. 24458v2 Announce Type: replace-cross Abstract: We study $\Gamma$-convergence of graph Dirichlet energies and spectral convergence of graph Laplacians on unions of intersecting manifolds of potentially different dimensions.
By Leon Bungert, Dejan Slep\v{c}ev
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
arXiv:2607. 07513v1 Announce Type: new Abstract: Self-supervised learning matches supervised accuracy from a fraction of the labels, but the labeled-sample efficiency behind this has lacked a theoretical explanation.
By Adam M. Oberman