Related papers: A Simple and Practical Linear Algebra Library Inte…
Linear algebra expressions, which play a central role in countless scientific computations, are often computed via a sequence of calls to existing libraries of building blocks (such as those provided by BLAS and LAPACK). A sequence…
This is an exercise based approach to matrix groups. The idea is to collect a bunch of exercises at one place which anyone with basic knowledge of linear algebra can attempt to solve and learn matrix groups and algebraic groups.
This book is a continuation of the book n-linear algebra of type I and its applications. Most of the properties that could not be derived or defined for n-linear algebra of type I is made possible in this new structure: n-linear algebra of…
Large language models (LLMs) have significantly transformed the educational landscape. As current plagiarism detection tools struggle to keep pace with LLMs' rapid advancements, the educational community faces the challenge of assessing…
The performance portability of OpenCL kernel implementations for common memory bandwidth limited linear algebra operations across different hardware generations of the same vendor as well as across vendors is studied. Certain combinations…
The two major systems of formal verification are model checking and algebraic model-based testing. Model checking is based on some form of temporal logic such as linear temporal logic (LTL) or computation tree logic (CTL). One powerful and…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
Pattern matching is a powerful tool which is part of many functional programming languages as well as computer algebra systems such as Mathematica. Among the existing systems, Mathematica offers the most expressive pattern matching.…
Automated unit test generation is critical for software quality but traditional structure-driven methods often lack the semantic understanding required to produce realistic inputs and oracles. Large language models (LLMs) address this…
Linear mixture models have proven very useful in a plethora of applications, e.g., topic modeling, clustering, and source separation. As a critical aspect of the linear mixture models, identifiability of the model parameters is…
This paper presents an in-depth analysis of Large Language Models (LLMs), focusing on LLaMA, a prominent open-source foundational model in natural language processing. Instead of assessing LLaMA through its generative output, we design…
Multi-task learning is a powerful method for solving several tasks jointly by learning robust representation. Optimization of the multi-task learning model is a more complex task than a single-task due to task conflict. Based on theoretical…
Large Language Model (LLM)-based applications are increasingly deployed across various domains, including customer service, education, and mobility. However, these systems are prone to inaccurate, fictitious, or harmful responses, and their…
Static analysis is the analysis of a program without executing it, usually carried out by an automated tool. Symbolic execution is a popular static analysis technique used both in program verification and in bug detection software. It works…
Type soundness is an important property of modern programming languages. In this paper we explore the idea that "well-typed languages are sound": the idea that the appropriate typing discipline over language specifications guarantees that…
Formal methods for verification of programs are extended to testing of programs. Their combination is intended to lead to benefits in reliable program development, testing, and evolution. Our geometric theory of testing is intended to serve…
As libraries explore large language models (LLMs) as a scalable layer for reference services, a core fairness question follows: can LLM-based services support all patrons fairly, regardless of demographic identity? While LLMs offer great…
Programs written in C/C++ often include inline assembly: a snippet of architecture-specific assembly code used to access low-level functionalities that are impossible or expensive to simulate in the source language. Although inline assembly…
Countless applications cast their computational core in terms of dense linear algebra operations. These operations can usually be implemented by combining the routines offered by standard linear algebra libraries such as BLAS and LAPACK,…
MatchingTools is a Python library for doing symbolic calculations in effective field theory. It provides the tools to construct general models by defining their field content and their interaction Lagrangian. Once a model is given, the…