arXiv:2606. 19411v1 Announce Type: new Abstract: Selecting a small, diverse, high-quality subset from a massive pool of candidates is a recurring primitive in modern machine learning -- data curation and coreset selection for training and fine-tuning large models, active-learning batch acquisition, prompt and exemplar selection for in-context learning, retrieval diversification, and experimental design.
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.
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.
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: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-...
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...
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:2606. 15832v1 Announce Type: new Abstract: Empirical risk minimization on massive datasets naturally exhibits a nested double finite-sum structure, where $N=nm$ total samples are logically or physically partitioned into $n$ blocks of size $m$ (e.
arXiv:2606. 16045v1 Announce Type: new Abstract: In the data selection problem, the objective is to choose a small, representative subset of data that can be used to efficiently train a machine learning model.
arXiv:2605. 18528v2 Announce Type: replace-cross Abstract: A growing lesson from neural network optimization is that optimizer design should respect how the model is parametrized.
arXiv:2406. 10407v3 Announce Type: replace-cross Abstract: Semidefinite programs (SDPs) and their solvers are powerful tools with many applications in machine learning and data science.
The paper proposes using eigenvalue decomposition (or PCA) to denoise noisy cost observations for shortest‑path problems, instead of the traditional predict‑then‑optimize approach. By projecting new cost vectors onto the top‑k eigenvectors of the training covariance matrix before running Dijkstra’s algorithm, the method can recover the true underlying costs. Experiments on a 5×5 grid benchmark show that choosing k equal to the true latent feature dimension (k=5) yields the best performance, outperforming the SPO+ method especially under high model misspecification.
arXiv:2504. 07133v2 Announce Type: replace-cross Abstract: We revisit the problem of estimating $k$ linear regressors with self-selection bias in $d$ dimensions with the maximum selection criterion, as introduced by Cherapanamjeri, Daskalakis, Ilyas, and Zampetakis [CDIZ23, STOC'23].