arXiv:2608. 06971v1 Announce Type: cross Abstract: This paper introduces Mixtures of Geodesic Factor Analyzers (MGFA) on Riemannian homogeneous spaces.
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arXiv:2505. 04338v3 Announce Type: replace Abstract: We propose Riemannian Denoising Diffusion Probabilistic Models (RDDPMs) for learning distributions on submanifolds of Euclidean space that are level sets of functions, including most of the manifolds relevant to applications.
The paper introduces a pullback Riemannian geometry tailored for multimodal data by employing a latent Gaussian mixture model. It defines a smooth, positive‑definite metric based on responsibility‑weighted component precision, extending the standard single‑Gaussian construction. Experiments on synthetic, multi‑view image, and MNIST datasets demonstrate reduced transport distortion, accurate trajectory recovery, and more realistic interpolation.
The paper introduces Constant‑Curvature Sliced Gromov‑Wasserstein (CCSGW), a new divergence for aligning probability distributions on heterogeneous constant‑curvature spaces such as hyperbolic and spherical manifolds. It extends sliced Gromov‑Wasserstein by adding geodesic‑based one‑dimensional projections for spherical spaces, enabling efficient and principled comparison across manifolds with different curvatures while preserving intrinsic geometric relationships. The authors provide theoretical analysis showing that CCSGW controls intrinsic geometric discrepancy and demonstrate consistent performance gains when integrated into mixed‑curvature learning tasks like graph anomaly detection, node classification, and multimodal learning.
arXiv:2510.26266v3 Announce Type: replace Abstract: The geometry of generative models serves as the basis for interpolation, model inspection, and more. Unfortunately, most generative models lack a p...
The study introduces a Riemannian shape‑space framework for analyzing age‑related morphological changes in the midsagittal corpus callosum (CC) using 128 landmarks embedded in Kendall shape space. Applied to the OASIS‑1 cohort, multivariate geodesic regression identifies anterior sub‑regions (Genu and Anterior Body) as the primary sites of age‑related deformation, outperforming Euclidean benchmarks. In Alzheimer’s patients, age explains less than 0.5% of shape variance, and a tangent‑space classifier achieves an age‑group AUC of 0.791 from 2D contour data alone.
arXiv:2610.33731v1 Announce Type: cross Abstract: On Riemannian manifolds, generative-model evaluation is geometry-dependent since curvature and dimension jointly determine distances and volume growt...