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A new stepsize for gradient method is proposed. Combining it with the exact line search stepsizes, the gradient method achieves the optimal solution in 5 steps for 3 dimensional quadratic function minimization problem. The new stepsize is…
Robust subspace estimation is fundamental to many machine learning and data analysis tasks. Iteratively Reweighted Least Squares (IRLS) is an elegant and empirically effective approach to this problem, yet its theoretical properties remain…
We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…
This work considers stepsize schedules for gradient descent on smooth convex objectives. We extend the existing literature and propose a unified technique for constructing stepsizes with analytic bounds for an arbitrary number of…
Although input-gradients techniques have evolved to mitigate and tackle the challenges associated with gradients, modern gradient-weighted CAM approaches still rely on vanilla gradients, which are inherently susceptible to the saturation…
Recently, 3D Gaussian Splatting has emerged as a prominent research direction owing to its ultrarapid training speed and high-fidelity rendering capabilities. However, the unstructured and irregular nature of Gaussian point clouds poses…
We propose a new technique that boosts the convergence of training generative adversarial networks. Generally, the rate of training deep models reduces severely after multiple iterations. A key reason for this phenomenon is that a deep…
This paper studies adaptive first-order least-squares finite element methods for second-order elliptic partial differential equations in non-divergence form. Unlike the classical finite element method which uses weak formulations of PDEs…
We present a variant of accelerated gradient descent algorithms, adapted from Nesterov's optimal first-order methods, for weakly-quasi-convex and weakly-quasi-strongly-convex functions. We show that by tweaking the so-called estimate…
Recently, machine learning has been used to substitute parts of conventional computational fluid dynamics, e.g. the cell-face reconstruction in finite-volume solvers or the curvature computation in the Volume-of-Fluid (VOF) method. The…
We explore the application of volumetric reconstruction from structured-light sensors in cognitive neuroscience, specifically in the quantification of the size-weight illusion, whereby humans tend to systematically perceive smaller objects…
A novel uncertainty-based pressure reconstruction method is proposed to evaluate the instantaneous pressure fields from velocity fields measured using particle image velocimetry (PIV) or particle tracking velocimetry (PTV). First, the…
A novel interface reconstruction strategy for volume of fluid (VOF) methods is introduced that represents the liquid-gas interface as two planes that co-exist within a single computational cell. In comparison to the piecewise linear…
A multi-fidelity regression model is proposed for combining multiple datasets with different fidelities, particularly abundant low-fidelity data and scarce high-fidelity observations. The model builds upon recent multi-fidelity frameworks…
Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…
Implicit neural networks have emerged as a crucial technology in 3D surface reconstruction. To reconstruct continuous surfaces from discrete point clouds, encoding the input points into regular grid features (plane or volume) has been…
In this paper, we explore two fundamental first-order algorithms in convex optimization, namely, gradient descent (GD) and proximal gradient method (ProxGD). Our focus is on making these algorithms entirely adaptive by leveraging local…
As a structured prediction task, scene graph generation, given an input image, aims to explicitly model objects and their relationships by constructing a visually-grounded scene graph. In the current literature, such task is universally…
Interpreting gradient methods as fixed-point iterations, we provide a detailed analysis of those methods for minimizing convex objective functions. Due to their conceptual and algorithmic simplicity, gradient methods are widely used in…
We consider the problem of minimizing the sum of two convex functions: one is the average of a large number of smooth component functions, and the other is a general convex function that admits a simple proximal mapping. We assume the whole…