Global rates of convergence for nonconvex optimization on manifolds
We consider the minimization of a cost function f on a manifold using Riemannian gradient
descent and Riemannian trust regions (RTR). We focus on satisfying necessary optimality …
descent and Riemannian trust regions (RTR). We focus on satisfying necessary optimality …
Metric flow matching for smooth interpolations on the data manifold
Matching objectives underpin the success of modern generative models and rely on
constructing conditional paths that transform a source distribution into a target distribution …
constructing conditional paths that transform a source distribution into a target distribution …
Representation learning via manifold flattening and reconstruction
A common assumption for real-world, learnable data is its possession of some low-
dimensional structure, and one way to formalize this structure is through the manifold …
dimensional structure, and one way to formalize this structure is through the manifold …
Manifold learning with arbitrary norms
Manifold learning methods play a prominent role in nonlinear dimensionality reduction and
other tasks involving high-dimensional data sets with low intrinsic dimensionality. Many of …
other tasks involving high-dimensional data sets with low intrinsic dimensionality. Many of …
On Taylor-like Estimates for Polynomial Approximations
A Wodecki - arXiv preprint arXiv:2401.10169, 2024 - arxiv.org
Polynomial series approximations are a central theme in approximation theory. Two types of
series, which are featured most prominently in pure and applied mathematics, are Taylor …
series, which are featured most prominently in pure and applied mathematics, are Taylor …
Elucidating Flow Matching ODE Dynamics with respect to Data Geometries
Diffusion-based generative models have become the standard for image generation. ODE-
based samplers and flow matching models improve efficiency, in comparison to diffusion …
based samplers and flow matching models improve efficiency, in comparison to diffusion …
Application of Hertzian theory to torus on plane contacts
J Kelley, K Babaalihaghighi, N Bader… - Proceedings of the …, 2022 - journals.sagepub.com
Hertzian theory includes a well-known analytical solution for the calculation of the contact
area and pressure between two bodies. Hertzian theory is not unconditionally applicable, in …
area and pressure between two bodies. Hertzian theory is not unconditionally applicable, in …
Warped geometric information on the optimisation of Euclidean functions
We consider the fundamental task of optimizing a real-valued function defined in a
potentially high-dimensional Euclidean space, such as the loss function in many machine …
potentially high-dimensional Euclidean space, such as the loss function in many machine …
The one-sided isometric extension problem
N Hungerbühler, M Wasem - Results in Mathematics, 2017 - Springer
Let Σ Σ be a codimension one submanifold of an n-dimensional Riemannian manifold M,
n\geqslant 2 n⩾ 2. We give a necessary condition for an isometric immersion of Σ Σ …
n\geqslant 2 n⩾ 2. We give a necessary condition for an isometric immersion of Σ Σ …
Regularity of the geodesic flow on submanifolds
C Lange - arXiv preprint arXiv:2401.03417, 2024 - arxiv.org
arXiv:2401.03417v1 [math.DG] 7 Jan 2024 Page 1 arXiv:2401.03417v1 [math.DG] 7 Jan 2024
REGULARITY OF THE GEODESIC FLOW ON SUBMANIFOLDS CHRISTIAN LANGE Abstract …
REGULARITY OF THE GEODESIC FLOW ON SUBMANIFOLDS CHRISTIAN LANGE Abstract …