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The generalization error curve of certain kernel regression method aims at determining the exact order of generalization error with various source condition, noise level and choice of the regularization parameter rather than the minimax…

We connect three distinct lines of research that have recently explored extensions of the classical LOCAL model of distributed computing: A. distributed quantum computing and non-signaling distributions [e.g. STOC 2024], B.…

We introduce a novel approach for learning memory kernels in Generalized Langevin Equations. This approach initially utilizes a regularized Prony method to estimate correlation functions from trajectory data, followed by regression over a…

This paper is devoted to the study of stochastic optimization problems under the generalized smoothness assumption. By considering the unbiased gradient oracle in Stochastic Gradient Descent, we provide strategies to achieve in bounds the…

Deep Operator Network (DeepONet), a recently introduced deep learning operator network, approximates linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to…

Few-shot adaptation of vision-language models (VLMs) like CLIP typically relies on learning textual prompts matched to global image embeddings. Recent works extend this paradigm by incorporating local image-text alignment to capture…

Representations by linear integral operators on $L_p$ spaces over measure spaces are investigated for the polynomial covariance type commutation relations and more general two-sided generalizations of covariance commutation relations…

Proximal operators are ubiquitous in inverse problems, commonly appearing as part of algorithmic strategies to regularize problems that are otherwise ill-posed. Modern deep learning models have been brought to bear for these tasks too, as…

Neural operators generalize neural networks to learn mappings between function spaces from data. They are commonly used to learn solution operators of parametric partial differential equations (PDEs) or propagators of time-dependent PDEs.…

We introduce a novel class of localized atomic environment representations, based upon the Coulomb matrix. By combining these functions with the Gaussian approximation potential approach, we present LC-GAP, a new system for generating…

In this work, we broadly connect kernel-based filtering (e.g. approaches such as the bilateral filters and nonlocal means, but also many more) with general variational formulations of Bayesian regularized least squares, and the related…

This paper presents a brief introduction to the key points of the Grey Machine Learning (GML) based on the kernels. The general formulation of the grey system models have been firstly summarized, and then the nonlinear extension of the grey…

Recently the dense Simultaneous Localization and Mapping (SLAM) based on neural implicit representation has shown impressive progress in hole filling and high-fidelity mapping. Nevertheless, existing methods either heavily rely on known…

This article is concerned with some weighted norm inequalities for the so-called horizontal (i.e. involving time derivatives) area integrals associated to a non-negative self-adjoint operator satisfying a pointwise Gaussian estimate for its…

This paper develops a nonparametric density estimator with parametric overtones. Suppose $f(x,\theta)$ is some family of densities, indexed by a vector of parameters $\theta$. We define a local kernel smoothed likelihood function which for…

Bayesian optimization relies on iteratively constructing and optimizing an acquisition function. The latter turns out to be a challenging, non-convex optimization problem itself. Despite the relative importance of this step, most algorithms…

We propose a new optimization method for training feed-forward neural networks. By rewriting the activation function as an equivalent proximal operator, we approximate a feed-forward neural network by adding the proximal operators to the…

Combining Gaussian processes with the expressive power of deep neural networks is commonly done nowadays through deep kernel learning (DKL). Unfortunately, due to the kernel optimization process, this often results in losing their Bayesian…

This paper studies kernel PCA in a decentralized setting, where data are distributively observed with full features in local nodes and a fusion center is prohibited. Compared with linear PCA, the use of kernel brings challenges to the…

We prove Fatou type theorem on almost everywhere convergence of convolution integrals in spaces $L^p\,(1<p<\infty)$ for general kernels, forming an approximate identity. For a wide class of kernels we show that obtained convergence regions…