Related papers: ZpL: a p-adic precision package
The DEViaN-LM is a R package that allows to detect the values poorly explained by a Gaussian linear model. The procedure is based on the maximum of the absolute value of the studentized residuals, which is a free statistic of the parameters…
We present an empirical investigation of a new mapping system based on a graph of panoramic depth images. Panoramic images efficiently capture range measurements taken by a spinning lidar sensor, recording fine detail on the order of a few…
We present solutions to the matrix completion problems proposed by the Alignment Research Center that have a polynomial dependence on the precision $\varepsilon$. The motivation for these problems is to enable efficient computation of…
Numerical simulations of physical systems exhibit discrepancies arising from unmodeled physics and idealizations, as well as numerical approximation errors stemming from discretization and solver tolerances. This article reviews techniques…
Within the past years, hardware vendors have started designing low precision special function units in response to the demand of the Machine Learning community and their demand for high compute power in low precision formats. Also the…
Decentralized planning in uncertain environments is a complex task generally dealt with by using a decision-theoretic approach, mainly through the framework of Decentralized Partially Observable Markov Decision Processes (DEC-POMDPs).…
Classification tasks are typically handled using Machine Learning (ML) models, which lack a balance between accuracy and interpretability. This paper introduces a new approach for classification tasks using Large Language Models (LLMs) in…
Fine-grained image classification has witnessed significant advancements with the advent of deep learning and computer vision technologies. However, the scarcity of detailed annotations remains a major challenge, especially in scenarios…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
Accurate quantification of local packing density and mixing in simulations of particulate systems is essential for many industrial applications. Traditional methods which simply count the number of particle centres within a given volume of…
We give the first approximation algorithm for mixed packing and covering semidefinite programs (SDPs) with polylogarithmic dependence on width. Mixed packing and covering SDPs constitute a fundamental algorithmic primitive with recent…
Large Language Models (LLMs) have demonstrated remarkable capabilities in various natural language processing tasks. However, their size presents significant challenges for deployment and inference. This paper investigates the quantization…
The rise of automated code generation tools, such as large language models (LLMs), has introduced new challenges in ensuring the correctness and efficiency of scientific software, particularly in complex kernels, where numerical stability,…
Spectral clustering is a popular method for effectively clustering nonlinearly separable data. However, computational limitations, memory requirements, and the inability to perform incremental learning challenge its widespread application.…
Physics-informed extreme learning machines (PIELMs) typically impose boundary and initial conditions through penalty terms, yielding only approximate satisfaction that is sensitive to user-specified weights and can propagate errors into the…
The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited and insufficient precision allied to the truncation and…
The Julia package FuzzifiED aims at simplifying the numerical calculations on the fuzzy sphere. It supports exact diagonalisation (ED) and density matrix renormalisation group (DMRG) calculations. FuzzifiED can also apply to generic…
This article introduces new acceleration methods for fixed-point iterations. Extrapolations are computed using two or three mappings alternately and a new type of step length is proposed with good properties for nonlinear applications. The…
Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes…
We present PDLP, a practical first-order method for linear programming (LP) that can solve to the high levels of accuracy that are expected in traditional LP applications. In addition, it can scale to very large problems because its core…