arXiv:2608. 26552v1 Announce Type: cross Abstract: Randomized sketch-and-solve algorithms accelerate overconstrained $\ell_2$ regression by replacing the input with a smaller problem.
Randomized sketch-and-solve algorithms accelerate overconstrained $\ell_2$ regression by replacing the input with a smaller problem. Standard subspace embeddings guarantee that the cost of the regress...
arXiv:2609.05641v1 Announce Type: cross Abstract: We consider the problem of minimizing error in quantized matrix multiplication $C=AB$. Scalar quantization of the factors introduces rounding errors...
The paper investigates how well two-stage structured Hadamard rotations approximate uniform random rotations in high-dimensional spaces. It establishes nonasymptotic upper bounds of order √{log d/d} for one-dimensional marginals, while showing a persistent Wasserstein-1 discrepancy for the full vector that does not vanish as dimension grows. These results highlight a separation between marginal and joint approximation quality, though they do not directly translate into algorithmic performance guarantees.
arXiv:2607. 00252v1 Announce Type: new Abstract: We present an algorithm for the group distributionally robust (GDR) least squares problem.
arXiv:2609. 02155v1 Announce Type: new Abstract: The Johnson-Lindenstrauss (JL) lemma guarantees that a random projection of $n$ points to $m=O(\varepsilon^{-2}\log n)$ dimensions preserves pairwise squared distances within relative error $\varepsilon$ with high probability, and this dimension order is asymptotically optimal.
arXiv:2606. 15581v1 Announce Type: cross Abstract: We study the graph alignment problem for correlated Gaussian Orthogonal Ensemble (GOE) matrices, where the goal is to recover a hidden vertex permutation given two correlated symmetric Gaussian matrices $(A, B)$ with correlation $1/\sqrt{1+\sigma^2}$.
arXiv:2605. 25303v3 Announce Type: replace-cross Abstract: The $2 \rightarrow q$ norm of a matrix $X \in \mathbb{R}^{n \times d}$ is defined as $\lVert X \rVert_{2 \rightarrow q} = \sup_{\lVert v \rVert_2 = 1} \lVert Xv \rVert_q$.
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. 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:2505. 21460v2 Announce Type: replace Abstract: We study online calibration of multi-dimensional forecasts over an arbitrary convex set $P \subset \mathbb{R}^d$ relative to an arbitrary norm $|\cdot|$.
arXiv:2004. 05813v3 Announce Type: replace-cross Abstract: Suppose that we are given independent, identically distributed random samples $x_1,\cdots,x_n$ from a mixture at most $k$ many $d$-dimensional spherical Gaussian distributions $\mu_1,\cdots,\mu_{k_0}$ of identical and known variance $\sigma^2$ in each coordinate, such that the minimum $\ell^2$ distance between two distinct centers $y_l$ and $y_j$ is greater than $2\Delta\sigma \min\{\sqrt{d},\sqrt k\}$, where $\Delta>C_0$, and $C_0$ is a sufficiently large universal constant.
The paper establishes the optimal incremental first‑order oracle (IFO) complexity for nonconvex finite‑sum optimization under individual smoothness, proving a matching lower bound that closes a previously missing √{n} factor. It also refines the analysis of the PAGE algorithm under the global Polyak‑Lojasiewicz condition, providing tighter guarantees for different ranges of the condition number. The authors introduce a novel dense weak hiding construction that yields these lower bounds and demonstrates the limits of existing methods.