相关论文: Machine learning assisted exploration for affine D…

In this paper we calculate the dimension of affine Deligne-Lusztig varieties in the affine Grassmannian of unramified groups. We also examine the irreducible components of ADLVs in the superbasic case and the $J_b(F)$-action on them.

The study of affine Deligne-Lusztig varieties originally arose from arithmetic geometry, but many problems on affine Deligne-Lusztig varieties are purely Lie-theoretic in nature. This survey deals with recent progress on several important…

We propose a novel framework, called Markov-Lipschitz deep learning (MLDL), to tackle geometric deterioration caused by collapse, twisting, or crossing in vector-based neural network transformations for manifold-based representation…

We present an adaptive multilevel Monte Carlo (AMLMC) algorithm for approximating deterministic, real-valued, bounded linear functionals that depend on the solution of a linear elliptic PDE with a lognormal diffusivity coefficient and…

The landscape of condensed matter physics is facing an unprecedented data surge driven by high-throughput ab initio workflows and rapidly expanding experimental datasets. Traditional first-principles methods such as Density Functional…

Deep embedding learning becomes more attractive for discriminative feature learning, but many methods still require hard-class mining, which is computationally complex and performance-sensitive. To this end, we propose Adaptive Large Margin…

In this paper we study the geometric structure of affine Deligne-Lusztig varieties for $GL_3$ and $b$ basic. We completely determine the irreducible components of the affine Deligne-Lusztig variety. In particular, we classify the cases…

Debiased machine learning estimators for smooth functionals in nonparametric models can exhibit substantial variability and instability, often leading practitioners to instead rely on parametric or semiparametric working models. Such…

Alternating Direction Method of Multipliers (ADMM) has been used successfully in many conventional machine learning applications and is considered to be a useful alternative to Stochastic Gradient Descent (SGD) as a deep learning optimizer.…

Federated learning (FL) aims to train machine learning (ML) models collaboratively using decentralized data, bypassing the need for centralized data aggregation. Standard FL models often assume that all data come from the same unknown…

We investigate unsupervised anomaly detection for high-dimensional data and introduce a deep metric learning (DML) based framework. In particular, we learn a distance metric through a deep neural network. Through this metric, we project the…

Deep Learning (DL) aims at learning the \emph{meaningful representations}. A meaningful representation refers to the one that gives rise to significant performance improvement of associated Machine Learning (ML) tasks by replacing the raw…

In this paper we discuss the geometry of affine Deligne Lusztig varieties with very special level structure, determining their dimension and connected and irreducible components. As application, we prove the Grothendieck conjecture for…

In this paper we study the geometric structure of affine Deligne-Lusztig varieties for $GL_n$ and $b$ basic. We introduce a new condition on $\lambda$. If this is satisfied, then the corresponding affine Deligne-Lusztig variety is the…

The alternating direction method of multipliers (ADMM) has recently sparked interest as a flexible and efficient optimization tool for imaging inverse problems, namely deconvolution and reconstruction under non-smooth convex regularization.…

Affine Lusztig varieties encode the orbital integrals of Iwahori--Hecke functions and serve as building blocks for the (conjectural) theory of affine character sheaves. We establish a close relationship between affine Lusztig varieties and…

High-quality mesh generation is the foundation of accurate finite element analysis. Due to the vast interior vertices search space and complex initial boundaries, mesh generation for complicated domains requires substantial manual…

This paper addresses the problem of efficiently classifying high-dimensional data over decentralized networks. Penalized support vector machines (SVMs) are widely used for high-dimensional classification tasks. However, the double…

As a well-known optimization framework, the Alternating Direction Method of Multipliers (ADMM) has achieved tremendous success in many classification and regression applications. Recently, it has attracted the attention of deep learning…

Manifold learning (ML) aims to seek low-dimensional embedding from high-dimensional data. The problem is challenging on real-world datasets, especially with under-sampling data, and we find that previous methods perform poorly in this case.…