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We provide the first global model recovery results for the IRLS (iteratively reweighted least squares) heuristic for robust regression problems. IRLS is known to offer excellent performance, despite bad initializations and data corruption,…
We introduce eigenpruning, a method that removes singular values from weight matrices in an LLM to improve its performance in a particular task. This method is inspired by interpretability methods designed to automatically find subnetworks…
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
We present a numerical method for the minimization of objectives that are augmented with large quadratic penalties of overdetermined inconsistent equality constraints. Such objectives arise from quadratic integral penalty methods for the…
Inverse problems arise in various scientific and engineering applications, necessitating robust numerical methods for their solution. In this work, we consider the effectiveness of Krylov subspace iterative methods, including GMRES, QMR,…
Image reconstruction by Algebraic Methods (AM) outperforms the transform methods in situations where the data collection procedure is constrained by time, space, and radiation dose. AM algorithms can also be applied for the cases where…
Large Language Models (LLMs) face deployment challenges due to high computational costs, and while Post-Training Quantization (PTQ) offers a solution, existing rotation-based methods struggle at very low bit-widths like 2-bit. We introduce…
In this study, we present a low-cost and unified framework for vectorized road mapping leveraging enhanced inverse perspective mapping (IPM). In this framework, Catmull-Rom splines are utilized to characterize lane lines, and all the other…
Algebraic Multigrid (AMG) methods are often robust and effective solvers for solving the large and sparse linear systems that arise from discretized PDEs and other problems, relying on heuristic graph algorithms to achieve their…
The matrix factor model has drawn growing attention for its advantage in achieving two-directional dimension reduction simultaneously for matrix-structured observations. In this paper, we propose a simple iterative least squares algorithm…
The ELM method has become widely used for classification and regressions problems as a result of its accuracy, simplicity and ease of use. The solution of the hidden layer weights by means of a matrix pseudoinverse operation is a…
We introduce an iterative method named GPMR for solving 2x2 block unsymmetric linear systems. GPMR is based on a new process that reduces simultaneously two rectangular matrices to upper Hessenberg form and that is closely related to the…
An implicit neural representation (INR) is a neural network that approximates a spatiotemporal function. Many memory-intensive visualization tasks, including modern 4D CT scanning methods, represent data natively as INRs. While INRs are…
The alignment of two similar graphs from different domains is a well-studied problem. In many practical usages, there is no reliable information or labels over the vertices or edges, leaving structural similarity as the only information…
Low-rank matrix completion has achieved great success in many real-world data applications. A matrix factorization model that learns latent features is usually employed and, to improve prediction performance, the similarities between latent…
The Augmented Lagrangian Method (ALM) is an iterative method for the solution of equality-constrained non-linear programming problems. In contrast to the quadratic penalty method, the ALM can satisfy equality constraints in an exact way.…
The Nystr\"om method is a convenient heuristic method to obtain low-rank approximations to kernel matrices in nearly linear complexity. Existing studies typically use the method to approximate positive semidefinite matrices with low or…
Direct preference optimization methods have emerged as a computationally efficient alternative to Reinforcement Learning from Human Feedback (RLHF) for aligning Large Language Models (LLMs). Latest approaches have streamlined the alignment…
The goal of this paper is to develop a novel numerical method for efficient multiplicative noise removal. The nonlocal self-similarity of natural images implies that the matrices formed by their nonlocal similar patches are low-rank. By…
A new approach for signal parametrization, which consists of a specific regression model incorporating a discrete hidden logistic process, is proposed. The model parameters are estimated by the maximum likelihood method performed by a…