Related papers: A Simple and Practical Linear Algebra Library Inte…
Graphical (Linear) Algebra is a family of diagrammatic languages allowing to reason about different kinds of subsets of vector spaces compositionally. It has been used to model various application domains, from signal-flow graphs to Petri…
Formally verified compilers and formally verified static analyzers are a solution to the problem that certain industries face when they have to demonstrate to authorities that the object code they run truly corresponds to its source code…
Large language models (LLMs) have shown tremendous success in following user instructions and generating helpful responses. Nevertheless, their robustness is still far from optimal, as they may generate significantly inconsistent responses…
Numerical software in computational science and engineering often relies on highly-optimized building blocks from libraries such as BLAS and LAPACK, and while such libraries provide portable performance for a wide range of computing…
Large language models (LLMs) are a promising venue for natural language understanding and generation tasks. However, current LLMs are far from reliable: they are prone to generate non-factual information and, more crucially, to contradict…
Large Language models (LLMs) can generate complicated source code from natural language prompts. However, LLMs can generate output that deviates from what the user wants, requiring supervision and editing. To support this process, we offer…
Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…
Large language models (LLMs) achieve impressive results over various tasks, and ever-expanding public repositories contain an abundance of pre-trained models. Therefore, identifying the best-performing LLM for a given task is a significant…
Transformers can learn to perform numerical computations from examples only. I study nine problems of linear algebra, from basic matrix operations to eigenvalue decomposition and inversion, and introduce and discuss four encoding schemes to…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
Generic programming is an effective methodology for developing reusable software libraries. Many programming languages provide generics and have features for describing interfaces, but none completely support the idioms used in generic…
Large Language Models (LLMs) exhibit remarkable fluency and competence across various natural language tasks. However, recent research has highlighted their sensitivity to variations in input prompts. To deploy LLMs in a safe and reliable…
We consider the issue of calibration in large language models (LLM). Recent studies have found that common interventions such as instruction tuning often result in poorly calibrated LLMs. Although calibration is well-explored in traditional…
Nowadays both commercial and open-source academic LLM have become the mainstream models of NLP. However, there is still a lack of research on LLM consistency, meaning that throughout the various stages of LLM research and deployment, its…
Existing benchmarks for evaluating mathematical reasoning in large language models (LLMs) rely primarily on competition problems, formal proofs, or artificially challenging questions -- failing to capture the nature of mathematics…
Numerical computations involving rational matrices often benefit from preserving underlying matrix structures such as symmetry, Hermitian properties, or sparsity that reflect physical, geometric, or algebraic characteristics of the system.…
Understanding a program's runtime reasoning behavior, meaning how intermediate states and control flows lead to final execution results, is essential for reliable code generation, debugging, and automated reasoning. Although large language…
Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing…
Large Language Models (LLMs) and transformer architectures have shown impressive reasoning and generation capabilities across diverse natural language tasks. However, their reliability and robustness in real-world engineering domains remain…
Search-based test generators are effective at producing unit tests with high coverage. However, such automatically generated tests have no meaningful test and variable names, making them hard to understand and interpret by developers. On…