arXiv:2410. 01669v3 Announce Type: replace Abstract: Covariance Neural Networks (VNNs) perform graph convolutions on the covariance matrix of input data to leverage correlation information as pairwise connections.
This review discusses how neuroimaging data can be represented as symmetric positive-definite (SPD) matrices and analyzed using the Riemannian geometry of the SPD manifold. It surveys the evolution from modality-specific SPD representations to geometric shallow and deep learning methods, emphasizing how these approaches maintain structural constraints while integrating modern AI techniques. The paper frames SPD matrix learning as a bridge between classical geometric statistics and contemporary machine learning in neuroimaging and brain‑computer interface research.
arXiv:2608.20380v1 Announce Type: cross Abstract: Resting-state functional magnetic resonance imaging (rs-fMRI) has enabled non-invasive mapping of functional brain interactions for computer-aided di...
arXiv:2601. 10199v2 Announce Type: replace Abstract: Multivariate data often exhibit complex dependencies that violate the assumption of isotropic residual noise.
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:2608. 15266v1 Announce Type: cross Abstract: Functional connectome analysis examines brain-region interactions to understand and identify disorders such as autism spectrum disorder and Alzheimer's disease.
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.
arXiv:2510. 10101v4 Announce Type: replace Abstract: Understanding the interplay between generalization, expressivity, and the geometry of the input space is a central challenge in graph learning.
arXiv:2506. 13139v3 Announce Type: replace-cross Abstract: Modern Machine Learning (ML) and Deep Neural Networks (DNNs) often operate on high-dimensional data and rely on overparameterized models, where classical low-dimensional intuitions break down.
arXiv:2608.28853v1 Announce Type: cross Abstract: Equivariant graph neural networks provide a principled way to model geometric systems, but efficient first-order architectures remain limited in how...
The paper introduces COVER, a multi‑task learning framework that regularizes covariate overlap to mitigate the negative effects of sharing information across tasks with differing covariate distributions and response relationships. COVER blends a common component function, a shared neural representation, and low‑dimensional task‑specific coefficients, using taskwise second‑moment matrices to guide coefficient integration. The authors provide theoretical bias‑variance analysis, oracle inequalities, and neural‑network convergence rates, and demonstrate that COVER outperforms existing deep‑learning and statistical integration methods in simulations and a GTEx central‑nervous‑system study.
arXiv:2607. 28681v1 Announce Type: cross Abstract: Functional magnetic resonance imaging (fMRI) is a widely used technique for studying the brain.