arXiv:2606. 11263v1 Announce Type: cross Abstract: Spectral methods rely fundamentally on the stability of principal eigenspaces under random perturbations.
arXiv:2511. 11927v2 Announce Type: replace-cross Abstract: Principal Component Analysis (PCA) is a standard tool for extracting a low-rank signal from noisy observations.
arXiv:2510. 02308v2 Announce Type: replace Abstract: Estimating the tangent spaces of a data manifold is a fundamental problem in geometric data analysis.
arXiv:2606. 29675v1 Announce Type: new Abstract: Bogomolny, Bohigas and Schmit (BBS) found that the spectrum of the pairwise distance matrix on N points sampled from a smooth d-dimensional manifold encodes a signature of the underlying geometry.
arXiv:2505. 10882v2 Announce Type: replace Abstract: Principal component analysis classically requires full $d$-dimensional samples, yet in various applications hardware limits acquisition to a few scalar measurements per sample.
arXiv:2606. 19411v3 Announce Type: replace Abstract: Selecting a fixed-size subset that maximizes the determinant of a positive semidefinite kernel is the MAP problem for a size-constrained determinantal point process and the classical maximum-entropy sampling problem.
arXiv:2602. 02908v2 Announce Type: replace-cross Abstract: Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed.
arXiv:2604. 08625v3 Announce Type: replace-cross Abstract: Benign overfitting describes the ability of minimum norm interpolating estimators to generalize despite fitting noisy data exactly.
arXiv:2511. 19513v4 Announce Type: replace Abstract: Decentralized learning often involves a weighted global loss with heterogeneous node weights $\lambda$.
arXiv:2606. 15679v1 Announce Type: cross Abstract: Stochastic trace estimation is a standard tool for approximating the trace of a large-scale matrix available only through matrix-vector products.
arXiv:2606. 00500v1 Announce Type: cross Abstract: We present a simple and efficient algorithm for robust approximate message passing (AMP) in the spiked matrix setting.
arXiv:2604. 08625v2 Announce Type: replace-cross Abstract: We develop a theoretical framework for generalization in the interpolating regime of statistical learning.
arXiv:2605. 11607v2 Announce Type: replace-cross Abstract: Probabilistic partial least squares (PPLS) is a central likelihood-based model for two-view learning when one needs both interpretable latent factors and calibrated uncertainty.