Related papers: Application-tailored Linear Algebra Algorithms: A …
Equation discovery is aimed at directly extracting physical laws from data and has emerged as a pivotal research domain. Previous methods based on symbolic mathematics have achieved substantial advancements, but often require the design of…
This report showcases the role of, and future directions for, the field of Randomized Numerical Linear Algebra (RNLA) in a selection of scientific applications. These applications span the domains of imaging, genomics and dynamical systems,…
Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…
Dedicated tensor accelerators demonstrate the importance of linear algebra in modern applications. Such accelerators have the potential for impressive performance gains, but require programmers to rewrite code using vendor APIs - a barrier…
Recent work in deep learning has opened new possibilities for solving classical algorithmic tasks using end-to-end learned models. In this work, we investigate the fundamental task of solving linear systems, particularly those that are…
Retrieval-Augmented Large Language Models (LLMs), which incorporate the non-parametric knowledge from external knowledge bases into LLMs, have emerged as a promising approach to enhancing response accuracy in several tasks, such as…
It is well known that the behavior of dense linear algebra algorithms is greatly influenced by factors like target architecture, underlying libraries and even problem size; because of this, the accurate prediction of their performance is a…
In this paper, we present a generalized version of the matrix chain algorithm to generate efficient code for linear algebra problems, a task for which human experts often invest days or even weeks of works. The standard matrix chain problem…
Interested in formalizing the generation of fast running code for linear algebra applications, the authors show how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category…
We consider partially-specified optimization problems where the goal is to actively, but efficiently, acquire missing information about the problem in order to solve it. An algorithm designer wishes to solve a linear program (LP), $\max…
This work proposes a procedure for designing algorithms for specific adaptive data collection tasks like active learning and pure-exploration multi-armed bandits. Unlike the design of traditional adaptive algorithms that rely on…
Differentiable solvers for the linear assignment problem (LAP) have attracted much research attention in recent years, which are usually embedded into learning frameworks as components. However, previous algorithms, with or without learning…
We propose a methodology, based on machine learning and optimization, for selecting a solver configuration for a given instance. First, we employ a set of solved instances and configurations in order to learn a performance function of the…
Applied research in graph algorithms and combinatorial structures needs comprehensive and versatile software libraries. However, the design and the implementation of flexible libraries are challenging activities. Among the other problems…
Recently, a number of learning-based optimization methods that combine data-driven architectures with the classical optimization algorithms have been proposed and explored, showing superior empirical performance in solving various ill-posed…
In differential equation discovery algorithms, a priori expert knowledge is mainly used implicitly to constrain the form of the expected equation, making it impossible for the algorithm to truly discover equations. Instead, most…
Optimizing compilers are mainly equipped to optimize control flow. The optimization of data structures is left to the programmer and it is the programmer's responsibility to design the data structures to suit the target hardware. Very…
Scientific programmers often turn to vendor-tuned Basic Linear Algebra Subprograms (BLAS) to obtain portable high performance. However, many numerical algorithms require several BLAS calls in sequence, and those successive calls result in…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…