mailitics

Category: math.FA

  • Generalized infinite dimensional Alpha-Procrustes based geometries

    Generalized infinite dimensional Alpha-Procrustes based geometries arXiv:2511.09801v1 Announce Type: new Abstract: This work extends the recently introduced Alpha-Procrustes family of Riemannian metrics for symmetric positive definite (SPD) matrices by incorporating generalized versions of the Bures-Wasserstein (GBW), Log-Euclidean, and Wasserstein distances. While the Alpha-Procrustes framework has unified many classical metrics in both finite- and infinite- dimensional…

  • Infinite-Dimensional Operator/Block Kaczmarz Algorithms: Regret Bounds and $lambda$-Effectiveness

    Infinite-Dimensional Operator/Block Kaczmarz Algorithms: Regret Bounds and $lambda$-Effectiveness arXiv:2511.07604v1 Announce Type: new Abstract: We present a variety of projection-based linear regression algorithms with a focus on modern machine-learning models and their algorithmic performance. We study the role of the relaxation parameter in generalized Kaczmarz algorithms and establish a priori regret bounds with explicit $lambda$-dependence to…

  • Distributionally robust approximation property of neural networks

    Distributionally robust approximation property of neural networks arXiv:2510.09177v1 Announce Type: new Abstract: The universal approximation property uniformly with respect to weakly compact families of measures is established for several classes of neural networks. To that end, we prove that these neural networks are dense in Orlicz spaces, thereby extending classical universal approximation theorems even beyond…

  • Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learning

    Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learning arXiv:2509.11070v1 Announce Type: new Abstract: We develop a stochastic approximation framework for learning nonlinear operators between infinite-dimensional spaces utilizing general Mercer operator-valued kernels. Our framework encompasses two key classes: (i) compact kernels, which admit discrete spectral decompositions, and (ii) diagonal kernels of the form $K(x,x’)=k(x,x’)T$, where $k$…

  • Learning Operators by Regularized Stochastic Gradient Descent with Operator-valued Kernels

    Learning Operators by Regularized Stochastic Gradient Descent with Operator-valued Kernels arXiv:2504.18184v1 Announce Type: new Abstract: This paper investigates regularized stochastic gradient descent (SGD) algorithms for estimating nonlinear operators from a Polish space to a separable Hilbert space. We assume that the regression operator lies in a vector-valued reproducing kernel Hilbert space induced by an operator-valued…

  • Optimal Scheduling of Dynamic Transport

    Optimal Scheduling of Dynamic Transport arXiv:2504.14425v1 Announce Type: new Abstract: Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a {transport map} that pushes forward a source measure to a target measure. The introduction of a time axis provides considerable design freedom, and a central question is how to exploit this…

  • Smoothed Distance Kernels for MMDs and Applications in Wasserstein Gradient Flows

    Smoothed Distance Kernels for MMDs and Applications in Wasserstein Gradient Flows arXiv:2504.07820v1 Announce Type: new Abstract: Negative distance kernels $K(x,y) := – |x-y|$ were used in the definition of maximum mean discrepancies (MMDs) in statistics and lead to favorable numerical results in various applications. In particular, so-called slicing techniques for handling high-dimensional kernel summations profit…

  • Positivity sets of hinge functions

    Positivity sets of hinge functions arXiv:2503.13512v1 Announce Type: new Abstract: In this paper we investigate which subsets of the real plane are realisable as the set of points on which a one-layer ReLU neural network takes a positive value. In the case of cones we give a full characterisation of such sets. Furthermore, we give…

  • Online Learning Algorithms in Hilbert Spaces with $beta-$ and $phi-$Mixing Sequences

    Online Learning Algorithms in Hilbert Spaces with $beta-$ and $phi-$Mixing Sequences arXiv:2502.03551v1 Announce Type: new Abstract: In this paper, we study an online algorithm in a reproducing kernel Hilbert spaces (RKHS) based on a class of dependent processes, called the mixing process. For such a process, the degree of dependence is measured by various mixing…

  • Deep Networks are Reproducing Kernel Chains

    Deep Networks are Reproducing Kernel Chains arXiv:2501.03697v1 Announce Type: cross Abstract: Identifying an appropriate function space for deep neural networks remains a key open question. While shallow neural networks are naturally associated with Reproducing Kernel Banach Spaces (RKBS), deep networks present unique challenges. In this work, we extend RKBS to chain RKBS (cRKBS), a new…