Related papers: Domain-Specific Languages of Mathematics: Presenti…
Domain-specific languages (DSLs) are routinely created to simplify difficult or specialized programming tasks. They expose useful abstractions and design patterns in the form of language constructs, provide static semantics to eagerly…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
The inception of large language models has helped advance state-of-the-art performance on numerous natural language tasks. This has also opened the door for the development of foundation models for other domains and data modalities such as…
Large Language Models (LLMs) have demonstrated remarkable proficiency in understanding and generating natural language. However, their capabilities wane in highly specialized domains underrepresented in the pretraining corpus, such as…
Datasets play a central role in the training and evaluation of machine learning (ML) models. But they are also the root cause of many undesired model behaviors, such as biased predictions. To overcome this situation, the ML community is…
Deep probabilistic programming languages try to combine the advantages of deep learning with those of probabilistic programming languages. If successful, this would be a big step forward in machine learning and programming languages.…
In this chapter, I discuss teaching mathematical tools specifically tailored for economics students. A typical one-semester course in this area seeks to blend a range of topics: from foundational elements of subjects such as linear algebra…
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…
Domain Specific Languages are used to provide a tailored modelling notation for a specific application domain. There are currently two main approaches to DSLs: standard notations that are tailored by adding simple properties; new notations…
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…
We introduce a novel task consisting in assigning a proof to a given mathematical statement. The task is designed to improve the processing of research-level mathematical texts. Applying Natural Language Processing (NLP) tools to research…
Spoken language understanding has been addressed as a supervised learning problem, where a set of training data is available for each domain. However, annotating data for each domain is both financially costly and non-scalable so we should…
A new design methodology is introduced, with some examples on building Domain Specific Languages hierarchy on top of Scheme.
Large Language Models (LLMs) have recently developed new advanced functionalities. Their effectiveness relies on statistical learning and generalization capabilities. However, they face limitations in internalizing the data they process and…
The article proposes formulating and codifying a set of applied numerical methods, coined as Deep Learning Discrete Calculus (DLDC), that uses the knowledge from discrete numerical methods to interpret the deep learning algorithms through…
This document is intended as a stand-alone textbook chapter to be used for introducing some functional programming concepts into a course in which the primary teaching language is Java. For details of the approach, please see the paper…
Programming robots is a complicated and time-consuming task. A robot is essentially a real-time, distributed embedded system. Often, control and communication paths within the system are tightly coupled to the actual physical configuration…
In this article, we will showcase some analytical concepts that can be used to tackle Functional Equations (FE) in the positive real numbers domain. Such concepts and related techniques have occasionally appeared in recent High School Math…
We study the problem of learning differentiable functions expressed as programs in a domain-specific language. Such programmatic models can offer benefits such as composability and interpretability; however, learning them requires…
A new generation of educational mathematics software is being shaped in ThEdu and other academic communities on the side of computer mathematics. Respective concepts and technologies have been clarified to an extent, which calls for…