arXiv:2601. 20970v3 Announce Type: replace-cross Abstract: The maximum-entropy remote sampling problem (MERSP) is to select a subset of $s$ random variables from a set of $n$ random variables, so as to maximize the information concerning a set of target random variables that are not directly observable.
arXiv:2609.39855v1 Announce Type: new Abstract: We study the width required for a randomly initialized hidden layer of a neural network to achieve rank lifting. Namely, given a dataset $X \in \mathbb...
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: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:2606.07124v2 Announce Type: replace-cross Abstract: We study the minimax estimation error for distributed covariance matrix estimation in the vertical-split (feature-split) setting, where two a...
arXiv:2604. 08438v2 Announce Type: replace Abstract: The Shapley value, and its broader family of semi-values, has received much attention in various attribution problems.
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.
arXiv:2604. 10727v2 Announce Type: replace-cross Abstract: Classical information-theoretic learning bounds typically rely on KL mutual information and moment-generating-function (MGF) arguments, which are well matched to bounded or sub-Gaussian losses but can be ineffective when losses or rewards are heavy-tailed.
For an arbitrary isotropic log-concave distribution $P$ on $\mathbb{R}^d$, we prove that the polynomial $(Cm)^m\|v\|_2^m - \mathbb{E}_{X\sim P}\langle X,v\rangle^m$ is a sum of squares for every even $m\ge2$, where $C>0$ is a universal constant. This removes the dependence on the Poincaré constant in the theorem of Kothari and Steinhardt (arXiv:1711.
arXiv:2609. 30105v1 Announce Type: new Abstract: For an arbitrary isotropic log-concave distribution $P$ on $\mathbb{R}^d$, we prove that the polynomial $(Cm)^m\|v\|_2^m - \mathbb{E}_{X\sim P}\langle X,v\rangle^m$ is a sum of squares for every even $m\ge2$, where $C>0$ is a universal constant.
arXiv:2607. 22889v1 Announce Type: new Abstract: Learning the natural parameters $z \in \mathbb{R}^n$ of discrete distributions $\mu_z$ from independent samples constrained to a subset $S \subseteq \{0,1\}^n$ is a foundational challenge in high-dimensional statistics.
arXiv:2605. 03283v2 Announce Type: replace-cross Abstract: We provide a unified theoretical analysis of Linear Discriminant Analysis with simultaneous multilabel scatter matrix formulations and Stiefel orthogonality constraints.
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...