Related papers: Multiresolution analysis and Zygmund dilations

Multimodal learning enhances the performance of various machine learning tasks by leveraging complementary information across different modalities. However, existing methods often learn multimodal representations that retain substantial…

Let $V$ be a quasi-conformal grading-restricted vertex algebra, $W$ be its module, and $\W_{z_1, \ldots, z_n}$ be the space of rational differential forms with complex parameters $(z_1, \ldots, z_n)$ for $n \ge 0$. Using geometric…

Mixed-precision arithmetic offers significant computational advantages for large-scale matrix computation tasks, yet preserving accuracy and stability in eigenvalue problems and the singular value decomposition (SVD) remains challenging.…

Generalized Functions play a central role in the understanding of differential equations containing singularities and nonlinearities. Introducing infinitesimals and infinities to deal with these obstructions leads to controversies…

Classical linear metric learning methods have recently been extended along two distinct lines: deep metric learning methods for learning embeddings of the data using neural networks, and Bregman divergence learning approaches for extending…

We propose and analyze the moving median absolute deviation (MMAD) as a robust depth construction based on the median absolute distance functional with particular emphasis on its local geometry and probabilistic structure. In the univariate…

Leveraging machine learning (ML) to predict an initial solution for mixed-integer linear programming (MILP) has gained considerable popularity in recent years. These methods predict a solution and fix a subset of variables to reduce the…

Researchers in the behavioral and social sciences use linear discriminant analysis (LDA) for predictions of group membership (classification) and for identifying the variables most relevant to group separation among a set of continuous…

Mixed-integer linear programming (MILP) stands as a notable NP-hard problem pivotal to numerous crucial industrial applications. The development of effective algorithms, the tuning of solvers, and the training of machine learning models for…

Motivated by modern data applications such as cryo-electron microscopy, the goal of classic multi-reference alignment (MRA) is to recover an unknown signal $f: \mathbb{R} \to \mathbb{R}$ from many observations that have been randomly…

Divergence measures play a central role and become increasingly essential in deep learning, yet efficient measures for multiple (more than two) distributions are rarely explored. This becomes particularly crucial in areas where the…

In this paper we give a multiresolution construction in Bergman space. The successful application of rational orthogonal bases needs a priori knowledge of the poles of the transfer function that may cause a drawback of the method. We give a…

The squared singular values of the product of $M$ complex Ginibre matrices form a biorthogonal ensemble, and thus their distribution is fully determined by a correlation kernel. The kernel permits a hard edge scaling to a form specified in…

Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…

The warped product $N_1\times_f N_2$ of two Riemannian manifolds $(N_1,g_1)$ and $(N_2,g_2)$ is the product manifold $N_1\times N_2$ equipped with the warped product metric $g=g_1+f^2 g_2$, where $f$ is a positive function on $N_1$. The…

We obtain weighted mixed inequalities for operators associated to a critical radius function. We consider Schr\"odinger Calder\'on-Zygmund operators of $(s,\delta)$ type, for $1<s\leq \infty$ and $0<\delta \leq 1$. We also give estimates of…

Triple Differences (DDD) designs are widely used in empirical work to relax parallel trends assumptions in Difference-in-Differences (DiD) settings. This paper highlights that common DDD implementations -- such as taking the difference…

Many vision-related tasks benefit from reasoning over multiple modalities to leverage complementary views of data in an attempt to learn robust embedding spaces. Most deep learning-based methods rely on a late fusion technique whereby…

Pointwise estimates for the gradient of solutions to the $p$-Laplace system with right-hand side in divergence form are established. They enable us to develop a nonlinear counterpart of the classical Calder\'on-Zygmund theory in terms of…

Autoregressive language models, despite their impressive capabilities, struggle with complex reasoning and long-term planning tasks. We introduce discrete diffusion models as a novel solution to these challenges. Through the lens of subgoal…