Related papers: Domain-Specific Languages of Mathematics: Presenti…
Fine-tuning of Large Language Models (LLMs) for downstream tasks, performed on domain-specific data has shown significant promise. However, commercial use of such LLMs is limited by the high computational cost required for their deployment…
The ability to read, write, and speak mathematics is critical to students becoming comfortable with statistical models and skills. Faster development of those skills may act as encouragement to further engage with the discipline. Vocabulary…
Mathematical maturity is a key concept for the professional life of a mathematician. This paper is not only a brief discussion of the importance of mathematical maturity but also presents some unusual ways we can use the concept to help our…
Domain Large Language Models (LLMs) are developed for domain-specific tasks based on general LLMs. But it still requires professional knowledge to facilitate the expertise for some domain-specific tasks. In this paper, we investigate into…
Mathematics formalisation is the task of writing mathematics (i.e., definitions, theorem statements, proofs) in natural language, as found in books and papers, into a formal language that can then be checked for correctness by a program. It…
Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…
Lectures notes (in italian) of some arguments of classical analysis, with exercises. A particular emphasis to functional analysis and elementary operator algebra theory is given, by means of exercises and examples.
A domain analysis & description calculus is introduced. It is shown to alleviate the issue of implicit semantics. The claim is made that domain descriptions, whether informal, or as also here, formal, amount to an explicit semantics for…
An original approach to solving rather difficult probabilistic problems arising in studying the readout of random discrete fields and having no exact analytical solutions at the moment is proposed. Several algorithms for direct, iterative,…
AI for Mathematics (AI4Math) is not only intriguing intellectually but also crucial for AI-driven discovery in science, engineering, and beyond. Extensive efforts on AI4Math have mirrored techniques in NLP, in particular, training large…
There has been a lot of recent interest in adopting machine learning methods for scientific and engineering applications. This has in large part been inspired by recent successes and advances in the domains of Natural Language Processing…
We study the semantic foundation of expressive probabilistic programming languages, that support higher-order functions, continuous distributions, and soft constraints (such as Anglican, Church, and Venture). We define a metalanguage (an…
Model-driven software development is a promising way to cope with the complexity of system integration in advanced robotics, as it already demonstrated its benefits in domains with comparably challenging system integration requirements.…
Technical computing is a challenging application area for programming languages to address. This is evinced by the unusually large number of specialized languages in the area (e.g. MATLAB, R), and the complexity of common software stacks,…
Recent advancements in large language models (LLMs) have showcased significant improvements in mathematics. However, traditional math benchmarks like GSM8k offer a unidimensional perspective, falling short in providing a holistic assessment…
For deterministic and probabilistic programs we investigate the problem of program synthesis and program optimisation (with respect to non-functional properties) in the general setting of global optimisation. This approach is based on the…
Scientific computation is a discipline that combines numerical analysis, physical understanding, algorithm development, and structured programming. Several yottacycles per year on the world's largest computers are spent simulating problems…
Despite significant advancements in the conception of (formal) integrated development environments, applying formal methods in software industry is still perceived as a difficult task. To make the task easier, providing tools that help…
The goal of this thesis is to advance the exploration of the statistical language learning design space. In pursuit of that goal, the thesis makes two main theoretical contributions: (i) it identifies a new class of designs by specifying an…
Accurate representation of procedures in restricted scenarios, such as non-standardized scientific experiments, requires precise depiction of constraints. Unfortunately, Domain-specific Language (DSL), as an effective tool to express…