arXiv:2607. 19305v1 Announce Type: cross Abstract: Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations.
By Chen Ziheng
arXiv:2607. 19305v2 Announce Type: replace-cross Abstract: Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations.
By Chen Ziheng
arXiv:2606. 12120v1 Announce Type: new Abstract: Low-rank optimal transport (OT) mitigates the quadratic scaling of classical solvers, yet existing approaches rely heavily on first-order mirror-descent updates that require careful hyperparameter tuning and ignore the optimization landscape's curvature.
By Pratik Jawanpuria, Bamdev Mishra
arXiv:2503. 24075v4 Announce Type: replace-cross Abstract: Low-rank optimization problems with sparse simplex constraints involve variables that must satisfy nonnegativity, sparsity, and sum-to-1 conditions, making their optimization particularly challenging due to the interplay between low-rank structures and constraints.
By Flavia Esposito, Andersen Ang
arXiv:2608. 06218v1 Announce Type: cross Abstract: We study Muon, a recently proposed matrix-aware optimization method, in the context of the Stiefel manifold.
By Mikhail Solonko, Molozhavenko Alexander, Maxim Rakhuba
arXiv:2606. 02328v1 Announce Type: new Abstract: We explore Riemannian optimization techniques for rank-factored matrix parameters, targeting contemporary deep learning applications.
By Nicholas Knight