Related papers: The Lean mathematical library
We formalize the multi-graded Proj construction in Lean4, illustrating mechanized mathematics and formalization.
A pedagogical approach of problem-based learning with embedded librarianship in several undergraduate mathematics courses is implemented in this educational research. The students are assigned to work on several projects on various…
Scientific Computing relies on executing computer algorithms coded in some programming languages. Given a particular available hardware, algorithms speed is a crucial factor. There are many scientific computing environments used to code…
To facilitate the research on large language models (LLMs), this paper presents a comprehensive and unified library, LLMBox, to ease the development, use, and evaluation of LLMs. This library is featured with three main merits: (1) a…
We describe in this paper new design techniques used in the \cpp exact linear algebra library \linbox, intended to make the library safer and easier to use, while keeping it generic and efficient. First, we review the new simplified…
Many internet applications are powered by machine learned models, which are usually trained on labeled datasets obtained through either implicit / explicit user feedback signals or human judgments. Since societal biases may be present in…
The purpose of this project is to collect symbol information in the Mizar Mathematical Library and manipulate it into practical and organized documentation. Inspired by the MathWiki project and API reference systems for computer programs,…
The task of algorithm selection involves choosing an algorithm from a set of algorithms on a per-instance basis in order to exploit the varying performance of algorithms over a set of instances. The algorithm selection problem is attracting…
The Clair library is intended to simplify a number of generic tasks in Natural Language Processing (NLP), Information Retrieval (IR), and Network Analysis. Its architecture also allows for external software to be plugged in with very little…
How can the complexity of ML-enabled systems be managed effectively? The goal of this research is to investigate how complexity affects ML-Enabled Systems (MLES). To address this question, this research aims to introduce a metrics-based…
The large language models (LLMs) might produce a persuasive argument within mathematical and logical fields, although such argument often includes some minor missteps, including the entire omission of side conditions, invalid inference…
This paper discusses digital online mathematics examinations -- a discussion ranging from high school to university level examinations. In particular, we consider the nature of mathematical writing, what is distinctive about mathematical…
A software library for constructing and learning probabilistic models is presented. The library offers a set of building blocks from which a large variety of static and dynamic models can be built. These include hierarchical models for…
Randomized numerical linear algebra - RandNLA, for short - concerns the use of randomization as a resource to develop improved algorithms for large-scale linear algebra computations. The origins of contemporary RandNLA lay in theoretical…
A theorem prover without an extensive library is much less useful to its potential users. Algebra, the study of algebraic structures, is a core component of such libraries. Algebraic theories also are themselves structured, the study of…
A large amount of data is produced every second from modern information systems such as mobile devices, the world wide web, Internet of Things, social media, etc. Analysis and mining of this massive data requires a lot of advanced tools and…
Labeled data for imitation learning of theorem proving in large libraries of formalized mathematics is scarce as such libraries require years of concentrated effort by human specialists to be built. This is particularly challenging when…
Digital mathematical libraries assemble the knowledge of years of mathematical research. Numerous disciplines (e.g., physics, engineering, pure and applied mathematics) rely heavily on compendia gathered findings. Likewise, modern research…
This paper introduces Paraconsistent-Lib, an open-source, easy-to-use Python library for building PAL2v algorithms in reasoning and decision-making systems. Paraconsistent-Lib is designed as a general-purpose library of PAL2v standard…
Matrix-matrix multiplication is a fundamental operation of great importance to scientific computing and, increasingly, machine learning. It is a simple enough concept to be introduced in a typical high school algebra course yet in practice…