From the 1 of 5 linked papers with an AI index.
5 papers
GEORCE: A Fast New Control Algorithm for Computing Geodesics
Frederik Möbius Rygaard, Søren Hauberg
The paper presents GEORCE, a fast algorithm that computes geodesics on Riemannian and Finsler manifolds by reformulating the problem as a discrete control task, and demonstrates gl…
A Likely Geometry of Generative Models
Frederik Möbius Rygaard, Shen Zhu, Yinzhu Jin +2
The geometry of generative models serves as the basis for interpolation, model inspection, and more. Unfortunately, most generative models lack a principal notion of geometry witho…
Simultaneous Optimization of Geodesics and Fréchet Means
Frederik Möbius Rygaard, Søren Hauberg, Steen Markvorsen
A central part of geometric statistics is to compute the Fréchet mean. This is a well-known intrinsic mean on a Riemannian manifold that minimizes the sum of squared Riemannian di…
Time-dependent Zermelo navigation with tacking
Steen Markvorsen, Enrique Pendás-Recondo, Frederik Möbius Rygaard
We address the time- and position-dependent Zermelo navigation problem within the framework of Lorentz-Finsler geometry. Since the initial work of E. Zermelo, the task is to find t…
Score Matching Riemannian Diffusion Means
Frederik Möbius Rygaard, Steen Markvorsen, Søren Hauberg +1
Estimating means on Riemannian manifolds is generally computationally expensive because the Riemannian distance function is not known in closed-form for most manifolds. To overcome…