arXiv:2608.10488v2 Announce Type: replace-cross Abstract: Let $X_1,\ldots,X_n$ be independent Gaussian tensors in $\mathbb{R}^{d_1}\otimes\cdots\otimes\mathbb{R}^{d_k}$ with a common covariance matri...
arXiv:2606. 00703v1 Announce Type: cross Abstract: Low-precision pretraining (FP8, MXFP4, NVFP4) is now standard for frontier language models, yet the literature is almost entirely achievability -- algorithms and empirical scaling laws -- with no matching characterization of what is information-theoretically possible.
arXiv:2609.05718v1 Announce Type: cross Abstract: We study state tomography when each measurement acts on at most $k$ fresh copies and no quantum memory is retained between blocks. We prove a lower b...
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.
arXiv:2603. 19703v2 Announce Type: replace-cross Abstract: Estimating covariance matrices is fundamental to a wide range of statistical applications.
arXiv:2609. 22783v1 Announce Type: new Abstract: We study differentially private covariance estimation in operator norm for mean-zero sub-Gaussian distributions with unknown covariance support and at most $k$ nonzero entries per row.
arXiv:2307. 07113v2 Announce Type: replace-cross Abstract: In this paper, we consider the decentralized, stochastic nonconvex strongly-concave (NCSC) minimax problem with nonsmooth regularization terms on both primal and dual variables, wherein a network of $m$ computing agents collaborate via peer-to-peer communications.
arXiv:2607. 16966v1 Announce Type: cross Abstract: Estimating entropy from samples is fundamental in information theory and property testing.
arXiv:2609. 18577v1 Announce Type: new Abstract: We consider the problem of estimating the trace of an implicit matrix $\mathbf{A} \in \mathbb{R}^{d^p\times d^p}$ that can only be accessed through matrix-vector products queries.
The paper addresses bias introduced by aggregating local signs in distributed sign-based variance reduction methods, which hampers optimal convergence rates. By proposing an unbiased compression of recursive gradient increments to track the global gradient at the server, the authors achieve optimal convergence rates for both nonconvex stochastic and finite-sum optimization. They provide specific rate bounds for α-norms and demonstrate matching sample complexities to centralized settings for finite-sum problems.
arXiv:2509.01809v2 Announce Type: replace-cross Abstract: We consider the problem of support recovery for sparse binary signals from noisy linear measurements. For sparse Gaussian measurement matrice...
arXiv:2610.33835v1 Announce Type: cross Abstract: What is the round complexity of Hessian-similar optimization when each round can contact at most $s$ of $m$ clients? Prior rates permit a free master...