arXiv Machine Learning
Aug 4

Sparse Covariance Neural Networks

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.

By Andrea Cavallo, Zhan Gao, Elvin Isufi
arXiv Machine Learning
Sep 25

Pointwise Generalization in Deep Neural Networks

The paper introduces a pointwise generalization theory for fully connected deep neural networks, using a pointwise Riemannian Dimension derived from eigenvalues of learned feature representations across layers. This framework provides hypothesis-dependent, representation-aware generalization bounds that are significantly tighter than traditional size- or norm-based approaches, both theoretically and experimentally. The authors analytically identify structural properties that explain deep networks’ tractability and empirically show that the pointwise Riemannian Dimension captures feature compression, over‑parameterization effects, and optimizer bias.

By Shaojie Li, Yunbei Xu
arXiv AI
Aug 24

SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challenges

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.

By Ce Ju, Reinmar Kobler, Antoine Collas, Motoaki Kawanabe, Cuntai Guan, Bertrand Thirion
arXiv Machine Learning
Sep 23

Spatiotemporal Kronecker Covariance Neural Networks

The paper introduces the Kronecker coVariance Neural Network (KVNN), a temporal graph neural network that models spatiotemporal covariance matrices as sums of Kronecker products, decoupling spatial and temporal dependencies. KVNNs perform filtering on spatial and temporal components, enabling expressive processing, rigorous spectral analysis, and provable stability to finite-sample estimation errors. Experiments on five real-world datasets show that KVNNs deliver strong forecasting performance with fewer trainable parameters than competing methods and maintain consistency under estimation noise.

By Andrea Cavallo, Athanasios Georgoutsos, Elvin Isufi