Related papers: Universality of Gaussian-Mixture Reverse Kernels i…

Used as priors for Bayesian inverse problems, diffusion models have recently attracted considerable attention in the literature. Their flexibility and high variance enable them to generate multiple solutions for a given task, such as…

Finite-width one hidden layer networks with multiple neurons in the readout layer display non-trivial output-output correlations that vanish in the lazy-training infinite-width limit. In this manuscript we leverage recent progress in the…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

Kernel sparsity ("dying ReLUs") and lack of diversity are commonly observed in CNN kernels, which decreases model capacity. Drawing inspiration from information theory and wireless communications, we demonstrate the intersection of coding…

Conditional kernel mean embeddings form an attractive nonparametric framework for representing conditional means of functions, describing the observation processes for many complex models. However, the recovery of the original underlying…

We propose a data-driven framework to learn interaction kernels in stochastic multi-agent systems. Our approach aims at identifying the functional form of nonlocal interaction and diffusion terms directly from trajectory data, without any a…

This paper proves the mean field limit and quantitative estimates for many-particle systems with singular attractive interactions between particles. As an important example, a full rigorous derivation (with quantitative estimates) of the…

We derive necessary density conditions for sampling and for interpolation in general reproducing kernel Hilbert spaces satisfying some natural conditions on the geometry of the space and the reproducing kernel. If the volume of shells is…

An implicit Euler finite-volume scheme for a nonlocal cross-diffusion system on the one-dimensional torus, arising in population dynamics, is proposed and analyzed. The kernels are assumed to be in detailed balance and satisfy a weak…

We study integration and $L^2$-approximation in the worst-case setting for deterministic linear algorithms based on function evaluations. The underlying function space is a reproducing kernel Hilbert space with a Gaussian kernel of tensor…

We consider the problem of clustering datasets in the presence of arbitrary outliers. Traditional clustering algorithms such as k-means and spectral clustering are known to perform poorly for datasets contaminated with even a small number…

Existing statistical learning guarantees for general kernel regressors often yield loose bounds when used with finite-rank kernels. Yet, finite-rank kernels naturally appear in several machine learning problems, e.g.\ when fine-tuning a…

We derive a new theoretical interpretation of the reweighted losses that are widely used for training diffusion models. Our method is based on constructing a cascade of time-dependent variational lower bounds on the data log-likelihood,…

This paper presents a method for building a preconditioner for a kernel ridge regression problem, where the preconditioner is not only effective in its ability to reduce the condition number substantially, but also efficient in its…

We show that geometric inference of a point cloud can be calculated by examining its kernel density estimate with a Gaussian kernel. This allows one to consider kernel density estimates, which are robust to spatial noise, subsampling, and…

In this work, we consider the problem of learning nonlinear operators that correspond to discrete-time nonlinear dynamical systems with inputs. Given an initial state and a finite input trajectory, such operators yield a finite output…

Recent diffusion models have achieved promising performances in audio-denoising tasks. The unique property of the reverse process could recover clean signals. However, the distribution of real-world noises does not comply with a single…

In this paper, we consider parameter recovery for non-overlapping convolutional neural networks (CNNs) with multiple kernels. We show that when the inputs follow Gaussian distribution and the sample size is sufficiently large, the squared…

We present a conditional diffusion model for electromagnetic inverse design that generates structured media geometries directly from target differential scattering cross-section profiles, bypassing expensive iterative optimization. Our 1D…

Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…