arXiv:2509. 25228v3 Announce Type: replace Abstract: Accurate density estimation is crucial for understanding complex high-dimensional data, but it becomes challenging when the data lies on or near low-dimensional manifolds.
arXiv:2601.21831v3 Announce Type: replace Abstract: We propose a geometric latent-subspace framework for generative modeling of discrete data. Specifically, we introduce latent subspaces in the expon...
Normalizing flows are powerful generative models that learn an invertible mapping between complex data distributions and simple latent distributions, typically a standard normal density. However, this choice of latent density can impose unnecessary complexity on the learned flow transformation due to the topological mismatch between the latent and data densities, leading to slower training and suboptimal performance.
arXiv:2606. 29724v1 Announce Type: new Abstract: Normalizing flows are powerful generative models that learn an invertible mapping between complex data distributions and simple latent distributions, typically a standard normal density.
arXiv:2602.19600v2 Announce Type: replace Abstract: Many high-dimensional datasets concentrate near a low-dimensional structure embedded in the ambient space. Generative models for such data must con...
arXiv:2607. 19498v1 Announce Type: cross Abstract: Gaussian process (GP) modeling is widely used in computational science and engineering.
arXiv:2609.25659v1 Announce Type: new Abstract: Many scientific datasets, such as molecular conformational ensembles or single-cell tissue measurements, are naturally modeled as meta-distributions: d...
arXiv:2510.25323v4 Announce Type: replace Abstract: Normalizing flows are deep generative models that enable efficient likelihood estimation and sampling through invertible transformations. A key cha...
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.
arXiv:2604. 13230v2 Announce Type: replace Abstract: Exploratory Landscape Analysis (ELA) provides numerical features for characterizing black-box optimization problems.
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:2410. 10137v5 Announce Type: replace Abstract: We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds.
arXiv:2606. 04176v1 Announce Type: new Abstract: We study a distributional generalization of the matrix completion problem in which each entry of the target matrix is a probability distribution rather than a scalar.