Iso-Riemannian Optimization on Learned Data Manifolds

ArXi:2510.21033v2 Announce Type: replace-cross High-dimensional data with intrinsic low-dimensional structure is ubiquitous in machine learning and data science. While various approaches allow one to learn a data manifold with a Riemannian structure from finite samples, performing downstream tasks such as optimization directly on these learned manifolds remains challenging. In particular, Euclidean convex functions cannot be assumed to be geodesically convex, and the associated Riemannian gradient fields are generally not monotone in the classical Riemannian sense.