相关论文: Projection, Degeneracy, and Singularity Degree for…

Let $X$ be a smooth projective hypersurface over a finite field $k$ of characteristic $p$. We address the problem of practically computing the zeta function $Z(X,T)$ of $X$ (equivalently, the point counts $\#X(\mathbb{F}_q)$, where $q =…

Face recognition (FR) methods report significant performance by adopting the convolutional neural network (CNN) based learning methods. Although CNNs are mostly trained by optimizing the softmax loss, the recent trend shows an improvement…

Newton's method for polynomial root finding is one of mathematics' most well-known algorithms. The method also has its shortcomings: it is undefined at critical points, it could exhibit chaotic behavior and is only guaranteed to converge…

This paper considers a conceptual version of a convex optimization algorithm whic is based on replacing a convex optimization problem with the root-finding problem for the approximate sub-differential mapping which is solved by repeated…

Smooth convex minimization over the unit trace-norm ball is an important optimization problem in machine learning, signal processing, statistics and other fields, that underlies many tasks in which one wishes to recover a low-rank matrix…

We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…

Face super-resolution (FSR), also known as face hallucination, which is aimed at enhancing the resolution of low-resolution (LR) face images to generate high-resolution (HR) face images, is a domain-specific image super-resolution problem.…

We consider the problem of projecting a vector onto the so-called k-capped simplex, which is a hyper-cube cut by a hyperplane. For an n-dimensional input vector with bounded elements, we found that a simple algorithm based on Newton's…

Superlinear convergence has been an elusive goal for black-box nonsmooth optimization. Even in the convex case, the subgradient method is very slow, and while some cutting plane algorithms, including traditional bundle methods, are popular…

We present a closed-form finite-dimensional projection method for regularizing a function defined by a discrete set of measurement data, which have been contaminated by random, zero mean errors, and for estimating the derivative and…

In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…

Optimization is important in machine learning problems, and quasi-Newton methods have a reputation as the most efficient numerical schemes for smooth unconstrained optimization. In this paper, we consider the explicit superlinear…

The properties of gradient techniques for the phase retrieval problem have received a considerable attention in recent years. In almost all applications, however, the phase retrieval problem is solved using a family of algorithms that can…

Heterogeneous Face Recognition (HFR) is a task that matches faces across two different domains such as visible light (VIS), near-infrared (NIR), or the sketch domain. Due to the lack of databases, HFR methods usually exploit the pre-trained…

We develop a decomposition method based on the augmented Lagrangian framework to solve a broad family of semidefinite programming problems, possibly with nonlinear objective functions, nonsmooth regularization, and general linear…

Face Super-Resolution (SR) is a subfield of the SR domain that specifically targets the reconstruction of face images. The main challenge of face SR is to restore essential facial features without distortion. We propose a novel face SR…

We investigate the concept of Best Approximation for Feedforward Neural Networks (FNN) and explore their convergence properties through the lens of Random Projection (RPNNs). RPNNs have predetermined and fixed, once and for all, internal…

We are concerned with structured $\ell_0$-norms regularization problems, with a twice continuously differentiable loss function and a box constraint. This class of problems have a wide range of applications in statistics, machine learning…

Reinforcement Fine-Tuning (RFT) on flow-based models is crucial for preference alignment. However, they often introduce visual hallucinations like over-optimized details and semantic misalignment. This work preliminarily explores why visual…

The forward-backward splitting method (FBS) for minimizing a nonsmooth composite function can be interpreted as a (variable-metric) gradient method over a continuously differentiable function which we call forward-backward envelope (FBE).…