arXiv:2602. 20376v3 Announce Type: replace-cross Abstract: We study the problem of maximizing a complex-valued quadratic form over the $K^{\text{th}}$ roots of unity.
By Ria Stevens, Fangshuo Liao, Barbara Su, Thanasis Hadjidimoulas, Jianqiang Li, Anastasios Kyrillidis
The paper introduces a method for selecting a small, diverse subset from a large pool by addressing multiple, potentially conflicting notions of diversity. It formulates a fair multi‑view determinant selection problem that maximizes the weakest per‑view log determinant of a size‑k subset, smooths and relaxes the objective to the Stiefel manifold, and derives an adaptive self‑consistent‑field solver with damping and level shifting. The solver operates using only feature‑map products for each view and includes a rounding step via leverage‑score screening followed by fair local refinement.
By Richard Yi Da Xu
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
arXiv:2507.19290v2 Announce Type: replace-cross
Abstract: We study the problem of learning a structured approximation (low-rank, sparse, banded, etc.) to an unknown matrix $A$ given access to matrix-...
By Noah Amsel, Pratyush Avi, Tyler Chen, Feyza Duman Keles, Chinmay Hegde, Cameron Musco, Christopher Musco, David Persson
arXiv:2609.06394v1 Announce Type: cross
Abstract: Massive datasets in modern machine learning have made data reduction a central challenge, particularly for clustering tasks where memory and computat...
By Diptarka Chakraborty, Satyaki Mukherjee, Gaurav Vallabhdas Revankar, Hoang-Son Tran
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.