arXiv:2607. 10618v1 Announce Type: cross Abstract: We consider the recovery of a pair of sparse vectors from a limited number of nonlinear observations of their superposition: $y_i=g(\inner{\ba_i}{\bPhi\bw^\ast+\bPsi\bz^\ast})+e_i$, $i=1,\dots,m$, with $m\ll n$, incoherent orthonormal bases $\bPhi,\bPsi$, a scalar link $g$, and noise $e_i$ that may be heavy-tailed or contaminated.
By Raziyeh Takbiri
arXiv:2602. 16568v2 Announce Type: replace-cross Abstract: Sparse recovery is among the most well-studied problems in learning theory and high-dimensional statistics.
By Ziyun Chen, Jerry Li, Kevin Tian, Yusong Zhu
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.
By Misha Ivkov, Tselil Schramm
arXiv:2607. 00252v1 Announce Type: new Abstract: We present an algorithm for the group distributionally robust (GDR) least squares problem.
By Naren Sarayu Manoj, Kumar Kshitij Patel
arXiv:2608. 02588v1 Announce Type: cross Abstract: In [AS21], Axiotis and Sviridenko conjectured that the linear dependence on the restricted condition number in sparse convex optimization cannot be improved by a polynomial-time algorithm.
By Honghao Lin, Vahab Mirrokni, David P. Woodruff
arXiv:2602. 05790v2 Announce Type: replace-cross Abstract: Fast computation of a matrix product $W^\top X$ is a workhorse of modern LLMs.
By Alina Harbuzova, Or Ordentlich, Yury Polyanskiy
arXiv:2512. 17473v3 Announce Type: replace-cross Abstract: We present an algorithm based on the alternating direction method of multipliers (ADMM) for solving nonlinear matrix decompositions (NMD).
By Atharva Awari, Nicolas Gillis, Arnaud Vandaele
arXiv:2606. 06782v1 Announce Type: cross Abstract: Robust Subspace Recovery (RSR) aims to identify an underlying d-dimensional subspace from a dataset heavily corrupted by outliers.
By Gilad Lerman, Teng Zhang
arXiv:2607. 01799v1 Announce Type: cross Abstract: Sparse autoencoders (SAEs) decompose internal activations of neural networks into sparse linear combinations of learned features by fitting an overcomplete dictionary $\mathbf{W}\in\mathbb{R}^{m\times n}$ with $m<n$, and inferring a sparse code $\mathbf{x}\in\mathbb{R}^n$ from $\mathbf{h}\approx\mathbf{W}\mathbf{x}$.
By Rodrigo Mendoza-Smith
arXiv:2605. 29497v2 Announce Type: replace Abstract: We study the problem of robustly learning Gaussian Single Index Models (SIMs) in the presence of heavy-tailed noise and a constant fraction of adversarially corrupted covariates and responses.
By Santanu Das, Sagnik Chatterjee, Jatin Batra
arXiv:2605. 14672v2 Announce Type: replace Abstract: Estimating an $N \times N$ quantum kernel from circuit fidelities requires $\Theta(N^2 S)$ measurement shots, the dominant bottleneck for deployment on near-term hardware.
By Jian Xu, Chao Li, Delu Zeng, John Paisley, Qibin Zhao
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 $\lVert X \rVert_{2 \rightarrow q} = \sup_{\lVert v \rVert_2 = 1} \lVert Xv \rVert_q$.
By Samuel B. Hopkins, Stefan Tiegel