Related papers: Application-tailored Linear Algebra Algorithms: A …
Evolutionary algorithms are wildly used in unmanned aerial vehicle path planning for their flexibility and effectiveness. Nevertheless, they are so sensitive to the change of environment that can't adapt to all scenarios. Due to this…
Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here, we demonstrate a method for solving a particular system of equations by using the concept…
Despite large incentives, ecorrectness in software remains an elusive goal. Declarative programming techniques, where algorithms are derived from a specification of the desired behavior, offer hope to address this problem, since there is a…
Numerous math benchmarks exist to evaluate LLMs' mathematical capabilities. However, most involve extensive manual effort and are difficult to scale. Consequently, they cannot keep pace with LLM development or easily provide new instances…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By "accurate" we mean that the computed…
We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…
Ever increasing computational power will require methods for automatic programming. We present an alternative to genetic programming, based on a general model of thinking and learning. The advantage is that evolution takes place in the…
Modern computationally-intensive applications often operate under time constraints, necessitating acceleration methods and distribution of computational workloads across multiple entities. However, the outcome is either achieved within the…
Academic Search is a search task aimed to manage and retrieve scientific documents like journal articles and conference papers. Personalization in this context meets individual researchers' needs by leveraging, through user profiles, the…
In the last decade, a considerable research effort has been devoted to developing adaptive algorithms based on kernel functions. One of the main features of these algorithms is that they form a family of universal approximation techniques,…
Modern compilers rely on hand-crafted heuristics to guide optimization passes. These human-designed rules often struggle to adapt to the complexity of modern software and hardware and lead to high maintenance burden. To address this…
The present paper gives a review of our recent progress and latest results for novel linear-algebraic algorithms and its application to large-scale quantum material simulations or electronic structure calculations. The algorithms are…
The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by deep generative networks). In this work, we study the…
We proposed a framework for solving inverse problems in differential equations based on neural networks and automatic differentiation. Neural networks are used to approximate hidden fields. We analyze the source of errors in the framework…
Autoregressive models (ARMs) have become the workhorse for sequence generation tasks, since many problems can be modeled as next-token prediction. While there appears to be a natural ordering for text (i.e., left-to-right), for many data…
We present a new method for scaling automatic configuration of computer networks. The key idea is to relax the computationally hard search problem of finding a configuration that satisfies a given specification into an approximate objective…
In this paper, we propose to consider various models of pattern recognition. At the same time, it is proposed to consider models in the form of two operators: a recognizing operator and a decision rule. Algebraic operations are introduced…
We present a technique for automatically generating features for data-driven program analyses. Recently data-driven approaches for building a program analysis have been proposed, which mine existing codebases and automatically learn…
There is enormous growth in various fields of research. This development is accompanied by new problems. To solve these problems efficiently and in an optimized manner, algorithms are created and described by researchers in the scientific…