arXiv:2608. 15466v1 Announce Type: new Abstract: Distributional changes can be invisible to means and covariances yet appear in skewness, asymmetric interactions, or other third-order structure.
By Guoqing Zhang, Zhaixin Chen
arXiv:2609.39855v1 Announce Type: new
Abstract: We study the width required for a randomly initialized hidden layer of a neural network to achieve rank lifting. Namely, given a dataset $X \in \mathbb...
By Luca Becchetti, Matteo Russo, Ruben Skorupinski
arXiv:2603. 19703v2 Announce Type: replace-cross Abstract: Estimating covariance matrices is fundamental to a wide range of statistical applications.
By T. Tony Cai, Yicheng Li
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.
By A. Afham
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:2607. 05872v1 Announce Type: new Abstract: Memory-efficient optimizers such as GaLore train large language models by projecting gradients onto a rank-r subspace recomputed every T steps, assuming this subspace is a slowly drifting object that can be tracked.
By Noel Thomas