The paper proves spectral convergence of the random feature method (RFM) for multidimensional targets across various function classes, providing high‑probability approximation estimates that hold simultaneously for all admissible error norms. It extends these results to strong‑ and weak‑form RFM discretizations, yielding convergence guarantees for multidimensional second‑order elliptic boundary value and eigenvalue problems. Additionally, it demonstrates super‑exponential singular‑value decay for Fourier features and exponential decay for tanh features, while establishing corresponding condition‑number lower bounds, highlighting a trade‑off between accuracy and ill‑conditioning.
By Pingbing Ming, Hao Yu
arXiv:2609. 12594v1 Announce Type: new Abstract: We study the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA) for $\pi(\,\mathrm{d} x)\propto e^{-f(x)-g(x)}\,\mathrm{d} x$, where $f\in C^2(\mathbb{R}^d)$ is $m$-strongly convex with $L_f$-Lipschitz gradient and $g:\mathbb{R}^d\to\mathbb{R}$ is convex and globally $G$-Lipschitz.
By Yuchen Xin, Zhihua Zhang
arXiv:2609.40193v1 Announce Type: new
Abstract: We establish near-linear accuracy bounds for the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA). The target is $\pi\propto e^{-f-g}$, w...
By Yuchen Xin, Zhihua Zhang
arXiv:2608.29152v1 Announce Type: cross
Abstract: We study the empirical Sinkhorn estimator of the entropic optimal transport potentials under the uniform loss. Since the potentials are only unique u...
By Denis Belomestny
arXiv:2608.29265v1 Announce Type: cross
Abstract: Kernel density estimation (KDE) is one of the most fundamental statistical estimators of density functions. Its direct implementation on a dataset of...
By Xie Wang, Nicolas Langren\'e, Wen Chen
arXiv:2507. 12091v2 Announce Type: replace-cross Abstract: This paper presents an improved analysis for sign-based methods with momentum updates.
By Wei Jiang, Dingzhi Yu, Sifan Yang, Wenhao Yang, Zechao Li, Lijun Zhang
arXiv:2606. 14488v1 Announce Type: cross Abstract: Recent finite-time analyses of nonlinear two-time-scale stochastic approximation show that under contractive assumptions the slow iterate $Y_k$ with stepsizes $\beta_k=\Theta(k^{-1})$ and $\alpha_k=\Theta(k^{-a})$, $a\in(1/2,1)$, generally satisfies a mean-square rate of order $k^{-a}$; decoupled $k^{-1}$ rates require strong local linearity.
By Dhruv Sarkar, Vaneet Aggarwal
arXiv:2607. 08779v1 Announce Type: cross Abstract: The signed integer alphabet contains one more negative representable value than positive.
By Ian Colbert, Eashan Dash, Pablo Monteagudo-Lago, Juan Amboage, Srinidhi N, Giuseppe Franco, Nicholas J. Fraser, Arun Ramachandran
arXiv:2606. 17319v1 Announce Type: cross Abstract: Motivated by the optimization of bounded binary black-box functions, we study the problem of learning polynomial surrogates over the Boolean hypercube.
By Jasper van Doornmalen, Mathieu Molina, Victor Verdugo, Jos\'e Verschae
arXiv:2602. 13906v2 Announce Type: replace-cross Abstract: Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise.
By Shaan Ul Haque, Zedong Wang, Zixuan Zhang, Siva Theja Maguluri
arXiv:2607. 04113v1 Announce Type: new Abstract: Diffusion and flow-matching samplers integrate a learned probability-flow ODE from a large noise scale down to a small terminal floor $\sigma_{\min}$, at which the score is stiff and the flow develops a boundary layer.
By Shiheng Zhang
arXiv:2608. 28564v1 Announce Type: cross Abstract: We study kernel ridge regression under anisotropic Gaussian data, where the input covariance decays as a power law with exponent $\alpha\geq 0$ for polynomial inner-product kernels.
By Lorenzo Rizzi, Arie Wortsman Zurich, Bruno Loureiro