Related papers: An objective-adaptive refinement criterion based o…

This paper presents an accelerated proximal gradient method for multiobjective optimization, in which each objective function is the sum of a continuously differentiable, convex function and a closed, proper, convex function. Extending…

Rational approximation recently emerged as an efficient numerical tool for the solution of exterior wave propagation problems. Currently, this technique is limited to wave media which are invariant along the main propagation direction. We…

The problem of phase space transport which is of interest both theoretically and from the point of view of applications has been investigated extensively using geometric and probabilistic methods. Two of the important tools for this that…

Maximum Likelihood Estimation (MLE) and Likelihood Ratio Test (LRT) are widely used methods for estimating the transition probability matrix in Markov chains and identifying significant relationships between transitions, such as equality.…

Supervised fine-tuning (SFT) is the predominant method for adapting large language models (LLMs), yet it often struggles with generalization compared to reinforcement learning (RL). In this work, we posit that this performance disparity…

Without sufficient data, the quantity of information available for supervised training is constrained, as obtaining sufficient synthetic aperture radar (SAR) training data in practice is frequently challenging. Therefore, current SAR…

This paper proposes a novel approach to improve the training efficiency and the generalization performance of Feed Forward Neural Networks (FFNNs) resorting to an optimal rescaling of input features (OFR) carried out by a Genetic Algorithm…

Large-scale finite element simulations of complex physical systems governed by partial differential equations (PDE) crucially depend on adaptive mesh refinement (AMR) to allocate computational budget to regions where higher resolution is…

Learning-based optical flow estimation has been dominated with the pipeline of cost volume with convolutions for flow regression, which is inherently limited to local correlations and thus is hard to address the long-standing challenge of…

This paper proposes an efficient algorithm for solving the Hartree--Fock equation combining a multilevel correction scheme with an adaptive refinement technique to improve computational efficiency. The algorithm integrates a multilevel…

This paper aims to develop an efficient adaptive finite element method for the second-order elliptic problem. Although the theory for adaptive finite element methods based on residual-type a posteriori error estimator and bisection…

Parameter-efficient fine-tuning(PEFT) has largely focused on LoRA and its accuracy-oriented variants, leaving the original goal of reducing trainable parameters has receivedcomparatively little attention. We introduce FoRA, which revisits…

This paper presents an Euler--Lagrange system for a continuous-time model of the accelerated gradient methods in smooth convex optimization and proposes an associated Lyapunov-function-based convergence analysis framework. Recently,…

We present a classification method with incremental capabilities based on the Optimum-Path Forest classifier (OPF). The OPF considers instances as nodes of a fully-connected training graph, arc weights represent distances between two…

Parameter estimation of mixture regression model using the expectation maximization (EM) algorithm is highly sensitive to outliers. Here we propose a fast and efficient robust mixture regression algorithm, called Component-wise Adaptive…

This paper studies the continuous-time dynamics of primal-dual algorithms for linearly constrained convex optimization problems and provides a quantitative convergence analysis using the Lyapunov functions. With the growing prevalence of…

Fine-tuning all parameters of Large Language Models (LLMs) is computationally expensive. Parameter-Efficient Fine-Tuning (PEFT) methods address this by selectively fine-tuning specific parameters. Most of the parameter efficient fine-tuning…

We propose a new Eulerian numerical approach for constructing the forward flow maps in continuous dynamical systems. The new algorithm improves the original formulation developed in [23, 24] so that the associated partial differential…

We present a convergence analysis of a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fatemi model. We devise an iterative algorithm to compute the solution of…

Penalized selection criteria like AIC or BIC are among the most popular methods for variable selection. Their theoretical properties have been studied intensively and are well understood, but making use of them in case of high-dimensional…