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Low precision arithmetic, in particular half precision floating point arithmetic, is now available in commercial hardware. Using lower precision can offer significant savings in computation and communication costs with proportional savings…

Large Language Models (LLMs) have made significant progress in dialogue, yet redundant memory contexts severely limit their effectiveness in long-term dialogue agents. External memory systems have been proposed to improve memory…

Imaging interferometric data in radio astronomy requires the use of non-linear algorithms that rely on different assumptions on the source structure and may produce non-unique results. This is especially true for Very Long Baseline…

We consider the robust multi-dimensional scaling (RMDS) problem in this paper. The goal is to localize point locations from pairwise distances that may be corrupted by outliers. Inspired by classic MDS theories, and nonconvex works for the…

This paper is about GMRES algorithms for the solution of nonsingular linear systems. We first consider basic algorithms and study their convergence. We then focus on acceleration strategies and parallel algorithms that are useful for…

In this paper we demonstrate a simple heuristic adaptive restart technique that can dramatically improve the convergence rate of accelerated gradient schemes. The analysis of the technique relies on the observation that these schemes…

We consider solution of multiply shifted systems of nonsymmetric linear equations, possibly also with multiple right-hand sides. First, for a single right-hand side, the matrix is shifted by several multiples of the identity. Such problems…

In this work, based on the continuous time approach, we propose an accelerated gradient method with adaptive residual restart for convex multiobjective optimization problems. For the first, we derive rigorously the continuous limit of the…

With recent advancements in Large Multimodal Models (LMMs) across various domains, a novel prompting method called visual referring prompting has emerged, showing significant potential in enhancing human-computer interaction within…

ML(n)BiCGStab is a Krylov subspace method for the solution of large, sparse and non-symmetric linear systems. In theory, it is a method that lies between the well-known BiCGStab and GMRES/FOM. In fact, when n = 1, ML(1)BiCGStab is BiCGStab…

This article introduces a novel methodology for the massive parallelization of projection-based depths, addressing the computational challenges of data depth in high-dimensional spaces. We propose an algorithmic framework based on Refined…

Reinforcement learning algorithms often suffer from slow convergence due to sparse reward signals, particularly in complex environments where feedback is delayed or infrequent. This paper introduces the Psychological Regret Model (PRM), a…

This paper introduces the Parallelized Circumcentered Reflection Method (P-CRM), a circumcentric approach that parallelizes the Circumcentered Reflection Method (CRM) for solving Convex Feasibility Problems in affine settings. Beyond…

This paper is concerned with the modeling errors appeared in the numerical methods of inverse medium scattering problems (IMSP). Optimization based iterative methods are wildly employed to solve IMSP, which are computationally intensive due…

Most existing 3D referring expression segmentation (3DRES) methods rely on dense, high-quality point clouds, while real-world agents such as robots and mobile phones operate with only a few sparse RGB views and strict latency constraints.…

This paper proposes a Riemannian Multiobjective Proximal Gradient Method (RMPGM) for composite optimization problems on manifolds. Unlike scalarization-based approaches, the proposed framework directly handles vector-valued objectives and…

Multi-step retrieval-augmented generation (RAG) has become a widely adopted strategy for enhancing large language models (LLMs) on tasks that demand global comprehension and intensive reasoning. Although many RAG systems incorporate a…

We investigate the regularizing behavior of an iterative Krylov subspace method for the solution of linear inverse problems in precisions lower than double. Recent works have considered the projection of iterated Tikhonov methods using…

A distributed algorithm for least mean square (LMS) can be used in distributed signal estimation and in distributed training for multivariate regression models. The convergence speed of an algorithm is a critical factor because a faster…

Tikhonov regularization is a widely used technique in solving inverse problems that can enforce prior properties on the desired solution. In this paper, we propose a Krylov subspace based iterative method for solving linear inverse problems…