From the 1 of 4 linked papers with an AI index.
4 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…
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…