Related papers: Normalizing Flows on Riemannian Manifolds
Geometric data and purpose-built generative models on them have become ubiquitous in high-impact deep learning application domains, ranging from protein backbone generation and computational chemistry to geospatial data. Current geometric…
A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…
We introduce the notion of Fermi flow for hypersurfaces in Riemannian manifolds. It turns out that this is a powerful tool to study the geometry of distance surfaces about a given initial hypersurface. Some of the results in this paper are…
We study the mean curvature flow of smooth $n$-dimensional compact submanifolds with quadratic pinching in a Riemannian manifold $\mathcal{N}^{n+m}$. Our main focus is on the case of high codimension, $m\geq 2$. We establish a codimension…
Point cloud upsampling aims to generate dense point clouds from given sparse ones, which is a challenging task due to the irregular and unordered nature of point sets. To address this issue, we present a novel deep learning-based model,…
Normalizing flows are a class of generative models that enable exact likelihood evaluation. While these models have already found various applications in particle physics, normalizing flows are not flexible enough to model many of the…
Optical flow is a powerful tool for the study and analysis of motion in a sequence of images. In this article we study a Horn-Schunck type spatio-temporal regularization functional for image sequences that have a non-Euclidean, time varying…
Optimization on Riemannian manifolds widely arises in eigenvalue computation, density functional theory, Bose-Einstein condensates, low rank nearest correlation, image registration, and signal processing, etc. We propose an adaptive…
We introduce variational approximations for curve evolutions in two-dimensional Riemannian manifolds that are conformally flat, i.e.\ conformally equivalent to the Euclidean space. Examples include the hyperbolic plane, the hyperbolic disk,…
We tackle unsupervised anomaly detection (UAD), a problem of detecting data that significantly differ from normal data. UAD is typically solved by using density estimation. Recently, deep neural network (DNN)-based density estimators, such…
Normalizing flows model a complex target distribution in terms of a bijective transform operating on a simple base distribution. As such, they enable tractable computation of a number of important statistical quantities, particularly…
We study a normalized version of the second order renormalization group flow on closed Riemannian surfaces. We discuss some general properties of this flow and establish several basic formulas. In particular, we focus on surfaces with zero…
Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent…
Manifold-valued measurements exist in numerous applications within computer vision and machine learning. Recent studies have extended Deep Neural Networks (DNNs) to manifolds, and concomitantly, normalization techniques have also been…
We consider the problem of estimating the density of observations taking values in classical or nonclassical spaces such as manifolds and more general metric spaces. Our setting is quite general but also sufficiently rich in allowing the…
Video anomaly detection is an ill-posed problem because it relies on many parameters such as appearance, pose, camera angle, background, and more. We distill the problem to anomaly detection of human pose, thus decreasing the risk of…
This paper advocates a novel framework for segmenting a dataset in a Riemannian manifold $M$ into clusters lying around low-dimensional submanifolds of $M$. Important examples of $M$, for which the proposed clustering algorithm is…
We introduce novel estimators for computing the curvature, tangent spaces, and dimension of data from manifolds, using tools from diffusion geometry. Although classical Riemannian geometry is a rich source of inspiration for geometric data…
We introduce Statistical Flow Matching (SFM), a novel and mathematically rigorous flow-matching framework on the manifold of parameterized probability measures inspired by the results from information geometry. We demonstrate the…
Emerging sampling algorithms based on normalizing flows have the potential to solve ergodicity problems in lattice calculations. Furthermore, it has been noted that flows can be used to compute thermodynamic quantities which are difficult…