Related papers: The Linear Algebra Mapping Problem. Current state …
This survey highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compresses it to a much smaller matrix by multiplying it by a…
This study presents a novel benchmark for evaluating Large Language Models (LLMs) using challenges derived from the Financial Modeling World Cup (FMWC) Excel competitions. We introduce a methodology for converting 113 existing FMWC…
MATLAB has emerged as one of the languages most commonly used by scientists and engineers for technical computing, with ~1,000,000 users worldwide. The compute intensive nature of technical computing means that many MATLAB users have codes…
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…
Mathematical reasoning is essential for problem-solving in education, science, and industry, serving as a crucial benchmark for evaluating artificial intelligence systems. As Large Language Models (LLMs) improve their reasoning…
This paper advocates for an intertwined design of the dense linear algebra software stack that breaks down the strict barriers between the high-level, blocked algorithms in LAPACK (Linear Algebra PACKage) and the low-level,…
Large Language Models (LLMs) have achieved remarkable success in code generation, and the race to improve their performance has become a central focus of AI research. Benchmarks and leaderboards are increasingly popular, offering…
Mathematical programming -- the task of expressing operations and decision-making problems in precise mathematical language -- is fundamental across domains, yet remains a skill-intensive process requiring operations research expertise.…
Designing and implementing efficient, provably correct parallel machine learning (ML) algorithms is challenging. Existing high-level parallel abstractions like MapReduce are insufficiently expressive while low-level tools like MPI and…
The explosion of Big Data was followed by the proliferation of numerous complex parallel software stacks whose aim is to tackle the challenges of data deluge. A drawback of a such multi-layered hierarchical deployment is the inability to…
In this paper, we present Ginkgo, a modern C++ math library for scientific high performance computing. While classical linear algebra libraries act on matrix and vector objects, Ginkgo's design principle abstracts all functionality as…
This paper presents a comparative study aimed at optimizing Llama2 inference, a critical aspect of machine learning and natural language processing (NLP). We evaluate various programming languages and frameworks, including TensorFlow,…
Many scientific discoveries are made through, or aided by, the use of simulation software. These sophisticated software applications are not built from the ground up, instead they rely on smaller parts for specific use cases, usually from…
We describe the Bandicoot GPU linear algebra toolkit, a C++ based library that prioritises ease of use without compromising efficiency. Bandicoot's API is compatible with the popular Armadillo CPU linear algebra library, enabling easy…
Evaluating Large Language Models (LLMs) with respect to real-world code complexity is essential. Otherwise, there is a risk of overestimating LLMs' programming abilities based on simplistic benchmarks, only to be disappointed when using…
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…
Designing and implementing efficient, provably correct parallel machine learning (ML) algorithms is challenging. Existing high-level parallel abstractions like MapReduce are insufficiently expressive while low-level tools like MPI and…
The rapid progress in the field of natural language processing (NLP) systems and the expansion of large language models (LLMs) have opened up numerous opportunities in the field of education and instructional methods. These advancements…
Parallel programming remains a daunting challenge, from the struggle to express a parallel algorithm without cluttering the underlying synchronous logic, to describing which devices to employ in a calculation, to correctness. Over the…
The classical linear ordering problem seeks a single ranking representing a given preference matrix. While suitable for homogeneous populations, it fails when observed preferences arise from several latent groups with distinct ranking…