Iso-Riemannian Optimization on Learned Data Manifolds

Excerpt

arXiv:2510.21033v3 Announce Type: replace-cross Abstract: We develop a theory of iso-Riemannian optimization for problems constrained to learned data manifolds, a setting in which classical Riemannian optimization - and Riemannian gradient descent in particular - can be poorly suited. That is, favorable Euclidean properties of an objective need not translate into geodesic convexity or L-smoothness, and the Riemannian gradient may provide an unsuitable search direction. We instead combine the man