arXiv Statistics ML
Geometric Feature Learning for Functional Data Valued on the Symmetric Positive Definite Manifold
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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.
arXiv Statistics ML
Sep 4
Online Learning of Functional Principal Component Analysis for Multidimensional Functional Data
The paper introduces an online framework for functional principal component analysis (FPCA) tailored to multidimensional functional data streams. It models functional principal components with tensor product splines, enforcing smoothness and orthonormality via a penalized approach on a Stiefel manifold. The authors present efficient Riemannian stochastic gradient descent and AdaGrad algorithms, along with a dynamic smoothing parameter tuning strategy based on rolling block validation, and provide asymptotic normality results and confidence intervals for the estimators.
arXiv Computer Vision
Aug 24
Aristotelian Manifolds: Leveraging Platonic Perceptual Features for Backpropagation Free Rapid Concept Learning
arXiv:2608.20682v1 Announce Type: new Abstract: This paper formalizes and systematically characterizes Aristotelian Manifolds, a generalized structural framework built upon the Platonic Representatio...
arXiv AI
Jul 22
Riemannian Deep Learning:Modules, Networks, and Geometries
arXiv:2607. 19305v1 Announce Type: cross Abstract: Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations.
arXiv Machine Learning
Aug 11
SPD Learn: A Geometric Deep Learning Python Library for Neural Decoding Through Trivialization
arXiv:2602. 22895v2 Announce Type: replace-cross Abstract: Implementations of symmetric positive definite (SPD) matrix-based neural networks for neural decoding remain fragmented across research codebases and Python packages.
arXiv AI
Jul 24
Riemannian Deep Learning: Modules, Networks, and Geometries
arXiv:2607. 19305v2 Announce Type: replace-cross Abstract: Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations.