相关论文: A non-uniform corner-cutting subdivision scheme wi…

We propose a new method for identifying cutting locations for quantum circuit cutting, with a primary focus on partitioning circuits into three or more parts. Under the assumption that the classical postprocessing function is decomposable,…

Advanced optimization algorithms such as Newton method and AdaGrad benefit from second order derivative or second order statistics to achieve better descent directions and faster convergence rates. At their heart, such algorithms need to…

This work presents a method to adaptively refine reduced-order models \emph{a posteriori} without requiring additional full-order-model solves. The technique is analogous to mesh-adaptive $h$-refinement: it enriches the reduced-basis space…

We study finite-sum non-convex optimization $\min_{x\in\mathbb{R}^d} F(x) \;=\; \frac{1}{n}\sum_{i=1}^n f_i(x)$ and analyze a variance-reduced cubic Newton method based on EMA-smoothed SARAH estimators for both gradient and Hessian…

To enhance solution accuracy and training efficiency in neural network approximation to partial differential equations, partitioned neural networks can be used as a solution surrogate instead of a single large and deep neural network…

Gradient schemes is a framework that enables the unified convergence analysis of many numerical methods for elliptic and parabolic partial differential equations: conforming and non-conforming Finite Element, Mixed Finite Element and Finite…

Quality control (QC) of MR images is essential to ensure that downstream analyses such as segmentation can be performed successfully. Currently, QC is predominantly performed visually and subjectively, at significant time and operator cost.…

We propose a new 2D shape decomposition method based on the short-cut rule. The short-cut rule originates from cognition research, and states that the human visual system prefers to partition an object into parts using the shortest possible…

In this paper, we consider stochastic second-order methods for minimizing a finite summation of nonconvex functions. One important key is to find an ingenious but cheap scheme to incorporate local curvature information. Since the true…

Many applications of quantum computing in the near term rely on variational quantum circuits (VQCs). They have been showcased as a promising model for reaching a quantum advantage in machine learning with current noisy intermediate scale…

We develop a new least squares method for solving the second-order elliptic equations in non-divergence form. Two least-squares-type functionals are proposed for solving the equations in two steps. We first obtain a numerical approximation…

When solving numerical constraints such as nonlinear equations and inequalities, solvers often exploit pruning techniques, which remove redundant value combinations from the domains of variables, at pruning steps. To find the complete…

This paper presents and analyses a new family of linear subdivision schemes to refine noisy data given on triangular meshes. The subdivision rules consist of locally fitting and evaluating a weighted least squares approximating first-degree…

Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…

This paper provides a theoretical and numerical comparison of classical first-order splitting methods for solving smooth convex optimization problems and cocoercive equations. From a theoretical point of view, we compare convergence rates…

A refinement of manifold data is a computational process, which produces a denser set of discrete data from a given one. Such refinements are closely related to multiresolution representations of manifold data by pyramid transforms, and…

Traditional k-means clustering underperforms on non-convex shapes and requires the number of clusters k to be specified in advance. We propose a simple geometric enhancement: after standard k-means, each cluster center is assigned a radius…

As a popular channel pruning method for convolutional neural networks (CNNs), network slimming (NS) has a three-stage process: (1) it trains a CNN with $\ell_1$ regularization applied to the scaling factors of the batch normalization…

We consider minimization of a smooth nonconvex objective function using an iterative algorithm based on Newton's method and the linear conjugate gradient algorithm, with explicit detection and use of negative curvature directions for the…

We present a method to match three dimensional shapes under non-isometric deformations, topology changes and partiality. We formulate the problem as matching between a set of pair-wise and point-wise descriptors, imposing a continuity prior…