Related papers: A locally gradient-preserving reinitialization for…
Many interfacial phenomena in physical and biological systems are dominated by high order geometric quantities such as curvature. Here a semi-implicit method is combined with a level set jet scheme to handle stiff nonlinear advection…
This paper considers subject level privacy in the FL setting, where a subject is an individual whose private information is embodied by several data items either confined within a single federation user or distributed across multiple…
Despite being the cornerstone of deep learning, backpropagation is criticized for its inherent sequentiality, which can limit the scalability of very deep models. Such models faced convergence issues due to vanishing gradient, later…
We propose a sequential homotopy method for the solution of mathematical programming problems formulated in abstract Hilbert spaces under the Guignard constraint qualification. The method is equivalent to performing projected backward Euler…
In GPS-denied scenarios, a robust environmental perception and localization system becomes crucial for autonomous driving. In this paper, a LiDAR-based online localization system is developed, incorporating road marking detection and…
Reinforcement learning from human feedback (RLHF) has become the dominant paradigm for aligning large language models with human preferences. However, policy gradient methods such as PPO suffer from high variance gradient estimates,…
Deep neural networks achieve state-of-the-art and sometimes super-human performance across various domains. However, when learning tasks sequentially, the networks easily forget the knowledge of previous tasks, known as "catastrophic…
In this work, we propose an efficient adaptive multilevel preconditioned Jacobi-Davidson (PJD) method for eigenvalue problems with singularity. Our multilevel method utilizes a local smoothing strategy to solve the preconditioned…
Image segmentation is an essential component in many image processing and computer vision tasks. The primary goal of image segmentation is to simplify an image for easier analysis, and there are two broad approaches for achieving this: edge…
This paper studies large-scale optimization problems on Riemannian manifolds whose objective function is a finite sum of negative log-probability losses. Such problems arise in various machine learning and signal processing applications. By…
A wide range of optimization problems arising in machine learning can be solved by gradient descent algorithms, and a central question in this area is how to efficiently compress a large-scale dataset so as to reduce the computational…
We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general…
We propose a novel distance-based regularization method for deep metric learning called Multi-level Distance Regularization (MDR). MDR explicitly disturbs a learning procedure by regularizing pairwise distances between embedding vectors…
Surface partial differential equations arise in numerous scientific and engineering applications. Their numerical solution on static and evolving surfaces remains challenging due to geometric complexity and, for evolving geometries, the…
In this paper we analyze a class of trace finite element methods (TraceFEM) for the discretization of vector-Laplace equations. A key issue in the finite element discretization of such problems is the treatment of the constraint that the…
In this paper the local iterative Lie-Schwinger block-diagonalization method, introduced in [FP], [DFPR1], and [DFPR2] for quantum chains, is extended to higher-dimensional quantum lattice systems with Hamiltonians that can be written as…
We investigate the ill-posed inverse problem of recovering unknown spatially dependent parameters in nonlinear evolution PDEs. We propose a bi-level Landweber scheme, where the upper-level parameter reconstruction embeds a lower-level state…
Solutions of partial differential equations (PDEs) on manifolds have provided important applications in different fields in science and engineering. Existing methods are majorly based on discretization of manifolds as implicit functions,…
In this paper, a self-learning approach is proposed towards solving scene-specific pedestrian detection problem without any human' annotation involved. The self-learning approach is deployed as progressive steps of object discovery, object…
In this paper, inspired by the multigrid method, we propose a multi-level deep framework for deep solvers. Overall, it divides the entire training process into different levels of training. At each level of training, an adaptive sampling…