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We study the few-shot learning (FSL) problem, where a model learns to recognize new objects with extremely few labeled training data per category. Most of previous FSL approaches resort to the meta-learning paradigm, where the model…

Longitudinal Dispersion(LD) is the dominant process of scalar transport in natural streams. An accurate prediction on LD coefficient(Dl) can produce a performance leap in related simulation. The emerging machine learning(ML) techniques…

In this paper, we present a new method, Transductive Multi-Head Few-Shot learning (TMHFS), to address the Cross-Domain Few-Shot Learning (CD-FSL) challenge. The TMHFS method extends the Meta-Confidence Transduction (MCT) and Dense…

Riemannian flow matching (RFM) extends flow-based generative modeling to data supported on manifolds by learning a time-dependent tangent vector field whose flow-ODE transports a simple base distribution to the data law. We develop a…

The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating…

This paper studies sampling error bounds for denoising diffusion probabilistic models (DDPMs) in the 2-Wasserstein distance. Our contributions are threefold. (i) Under general Lipschitz-type conditions on the score function and for a broad…

Proper scoring rules evaluate the quality of probabilistic predictions, playing an essential role in the pursuit of accurate and well-calibrated models. Every proper score decomposes into two fundamental components -- proper calibration…

We consider the estimation and inference of graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we…

Score-based diffusion models are a recently developed framework for posterior sampling in Bayesian inverse problems with a state-of-the-art performance for severely ill-posed problems by leveraging a powerful prior distribution learned from…

The total variation (TV) regularization has phenomenally boosted various variational models for image processing tasks. We propose to combine the backward diffusion process in the earlier literature of image enhancement with the TV…

Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their…

A refined model of an extreme ultraviolet (EUV) mask stack consisting of the Mo/Si multilayer coated by a Ru protective layer and a TaBN/TaBO absorber layer was developed to facilitate accurate simulations of EUV mask performance for…

Imaging through scattering is an important, yet challenging problem. Tremendous progress has been made by exploiting the deterministic input-output "transmission matrix" for a fixed medium. However, this "one-to-one" mapping is highly…

Generative models that maximize model likelihood have gained traction in many practical settings. Among them, perturbation based approaches underpin many strong likelihood estimation models, yet they often face slow convergence and limited…

Distribution matching (DM) is a versatile domain-invariant representation learning technique that has been applied to tasks such as fair classification, domain adaptation, and domain translation. Non-parametric DM methods struggle with…

Diffusion models are known to be vulnerable to outliers in training data. In this paper we study an alternative diffusion loss function, which can preserve the high quality of generated data like the original squared $L_{2}$ loss while at…

A semi-implicit in time, entropy stable finite volume scheme for the compressible barotropic Euler system is designed and analyzed and its weak convergence to a dissipative measure-valued (DMV) solution [E. Feireisl et al., Dissipative…

The purpose of this paper is to examine the sampling problem through Euler discretization, where the potential function is assumed to be a mixture of locally smooth distributions and weakly dissipative. We introduce $\alpha_{G}$-mixture…

We study the transfer learning (TL) for the functional linear regression (FLR) under the Reproducing Kernel Hilbert Space (RKHS) framework, observing that the TL techniques in existing high-dimensional linear regression are not compatible…

Deep distance metric learning (DDML), which is proposed to learn image similarity metrics in an end-to-end manner based on the convolution neural network, has achieved encouraging results in many computer vision tasks.$L2$-normalization in…