相关论文: Constructive Universal High-Dimensional Distributi…

Flow Matching, a promising approach in generative modeling, has recently gained popularity. Relying on ordinary differential equations, it offers a simple and flexible alternative to diffusion models, which are currently the…

In this paper, we consider robust nonparametric regression using deep neural networks with ReLU activation function. While several existing theoretically justified methods are geared towards robustness against identical heavy-tailed noise…

Gaussian distributions are commonly used as a key building block in many generative models. However, their applicability has not been well explored in deep networks. In this paper, we propose a novel deep generative model named as Normal…

We derive upper bounds on the generalization error of learning algorithms based on their \emph{algorithmic transport cost}: the expected Wasserstein distance between the output hypothesis and the output hypothesis conditioned on an input…

The challenge of approximating functions in infinite-dimensional spaces from finite samples is widely regarded as formidable. We delve into the challenging problem of the numerical approximation of Sobolev-smooth functions defined on…

We study the problem of constructing strong approximate unitary $k$-designs on $D$-dimensional grids (and more generally on Cartesian products of graphs), building on the work of Schuster et al. arXiv:2509.26310 which establishes strong…

Analyzing neural network dynamics via stochastic gradient descent (SGD) is crucial to building theoretical foundations for deep learning. Previous work has analyzed structured inputs within the \textit{hidden manifold model}, often under…

We present a novel multiscale super-resolution framework (SRLBM) that applies deep learning directly to the mesoscopic density distribution functions of the lattice Boltzmann method for high-fidelity flow reconstruction. Two neural network…

We present a near linear time algorithm for constructing hierarchical nets in finite metric spaces with constant doubling dimension. This data-structure is then applied to obtain improved algorithms for the following problems: Approximate…

1-Lipschitz neural networks are fundamental for generative modelling, inverse problems, and robust classifiers. In this paper, we focus on 1-Lipschitz residual networks (ResNets) based on explicit Euler steps of negative gradient flows and…

We investigate the Distributionally Robust Regret-Optimal (DR-RO) control of discrete-time linear dynamical systems with quadratic cost over an infinite horizon. Regret is the difference in cost obtained by a causal controller and a…

This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If…

Deep neural networks rely heavily on normalization methods to improve their performance and learning behavior. Although normalization methods spurred the development of increasingly deep and efficient architectures, they also increase the…

In this paper, we propose a new and unified approach for nonparametric regression and conditional distribution learning. Our approach simultaneously estimates a regression function and a conditional generator using a generative learning…

We introduce Primal-Dual Wasserstein GAN, a new learning algorithm for building latent variable models of the data distribution based on the primal and the dual formulations of the optimal transport (OT) problem. We utilize the primal…

Deep neural networks (DNNs) are known to be vulnerable to adversarial attacks that would trigger misclassification of DNNs but may be imperceptible to human perception. Adversarial defense has been an important way to improve the robustness…

This paper develops a randomized approach for incrementally building deep neural networks, where a supervisory mechanism is proposed to constrain the random assignment of the weights and biases, and all the hidden layers have direct links…

Recent results in nonparametric regression show that deep learning, i.e., neural network estimates with many hidden layers, are able to circumvent the so-called curse of dimensionality in case that suitable restrictions on the structure of…

We consider a one-hidden-layer leaky ReLU network of arbitrary width trained by stochastic gradient descent (SGD) following an arbitrary initialization. We prove that SGD produces neural networks that have classification accuracy…

Deep learning methods continue to have a decided impact on machine learning, both in theory and in practice. Statistical theoretical developments have been mostly concerned with approximability or rates of estimation when recovering…