arXiv:2606. 00542v1 Announce Type: new Abstract: Shampoo-style optimizers approximate gradient covariance matrices using Kronecker-factored structures.
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arXiv:2609. 17089v1 Announce Type: cross Abstract: The choice of Riemannian metric can strongly influence the convergence of gradient-based optimization over covariance matrices.
arXiv:2609. 17048v1 Announce Type: cross Abstract: We study nonconvex methods for matrix completion, the problem of recovering a low-rank matrix from a subset of its entries.
arXiv:2609. 03762v1 Announce Type: new Abstract: The computation of the Bures-Wasserstein (BW) barycenter of an ensemble of positive definite matrices arises throughout machine learning, optimal transport, and quantum information.
arXiv:2607. 25624v1 Announce Type: new Abstract: Positive quadratic networks admit the low-rank representation f_U(x)=x^top UU^top x, where Uinmathbb{R}^{dtimes r} is identifiable only up to right orthogonal multiplication, representing a rank-r PSD matrix Q=UU^top.
The paper introduces a Projected Riemannian Gradient Descent (RGD) algorithm for computing the Bures‑Wasserstein barycenter of positive definite matrices, achieving dimension‑independent linear convergence at unit step size. It resolves a previous dichotomy by showing that clipping eigenvalues to a fixed interval yields a closed‑form, non‑expansive projection in the BW metric, allowing the algorithm to match the empirical speed of unit‑step RGD while maintaining theoretical guarantees. The method also extends to the invariant matrix projection problem, providing a unified dimension‑independent analysis.
arXiv:2609.14307v1 Announce Type: new Abstract: Low-rank tensor factorization provides a flexible framework for completing multidimensional data from incomplete and corrupted observations. However, u...