Related papers: Machine learning algorithms for three-dimensional …

Reduced-order models based on level-set methods are widely used tools to qualitatively capture and track the nonlinear dynamics of an interface. The aim of this paper is to develop a physics-informed, data-driven, statistically rigorous…

Deep neural networks have been demonstrated to achieve phenomenal success in many domains, and yet their inner mechanisms are not well understood. In this paper, we investigate the curvature of image manifolds, i.e., the manifold deviation…

We propose an alternating subgradient method with non-constant step sizes for solving convex-concave saddle-point problems associated with general convex-concave functions. We assume that the sequence of our step sizes is not summable but…

Training neural networks for tasks such as 3D point cloud semantic segmentation demands extensive datasets, yet obtaining and annotating real-world point clouds is costly and labor-intensive. This work aims to introduce a novel pipeline for…

Training Deep Neural Networks relies on the model converging on a high-dimensional, non-convex loss landscape toward a good minimum. Yet, much of the phenomenology of training remains ill understood. We focus on three seemingly disparate…

In semi-supervised learning, methods that rely on confidence learning to generate pseudo-labels have been widely proposed. However, increasing research finds that when faced with noisy and biased data, the model's representation network is…

Over the past two decades, we have seen an exponentially increased amount of point clouds collected with irregular shapes in various areas. Motivated by the importance of solid modeling for point clouds, we develop a novel and efficient…

The immense computational cost of simulating turbulence has motivated the use of machine learning approaches for super-resolving turbulent flows. A central challenge is ensuring that learned models respect physical symmetries, such as…

3D shape analysis has been largely focused on traditional 3D representations of point clouds and meshes, but the discrete nature of these data makes the analysis susceptible to variations in input resolutions. Recent development of neural…

Federated learning is a distributed machine learning approach which enables a shared server model to learn by aggregating the locally-computed parameter updates with the training data from spatially-distributed client silos. Though…

Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…

In this work, we investigate stochastic quasi-Newton methods for minimizing a finite sum of cost functions over a decentralized network. In Part I, we develop a general algorithmic framework that incorporates stochastic quasi-Newton…

Many supervised learning tasks have intrinsic symmetries, such as translational and rotational symmetry in image classifications. These symmetries can be exploited to enhance performance. We formulate the symmetry constraints into a concise…

This paper considers and proposes some algorithms to compute the mean curvature flow under topological changes. Instead of solving the fully nonlinear partial differential equations based on the level set approach, we propose some…

Density level sets can be estimated using plug-in methods, excess mass algorithms or a hybrid of the two previous methodologies. The plug-in algorithms are based on replacing the unknown density by some nonparametric estimator, usually the…

We introduce a novel diffusion-based spectral algorithm to tackle regression analysis on high-dimensional data, particularly data embedded within lower-dimensional manifolds. Traditional spectral algorithms often fall short in such…

In the mean field regime, neural networks are appropriately scaled so that as the width tends to infinity, the learning dynamics tends to a nonlinear and nontrivial dynamical limit, known as the mean field limit. This lends a way to study…

This paper presents CALM-Net, a curvature-aware LiDAR point cloud-based multi-branch neural network for vehicle re-identification. The proposed model addresses the challenge of learning discriminative and complementary features from…

Motivated by image-on-scalar regression with data aggregated across multiple sites, we consider a setting in which multiple independent studies each collect multiple dependent vector outcomes, with potential mean model parameter homogeneity…

We contribute to the growing body of knowledge on more powerful and adaptive stepsizes for convex optimization, empowered by local curvature information. We do not go the route of fully-fledged second-order methods which require the…