Related papers: The Lean mathematical library
DeeProb-kit is a unified library written in Python consisting of a collection of deep probabilistic models (DPMs) that are tractable and exact representations for the modelled probability distributions. The availability of a representative…
Polylab is a MATLAB toolbox for multivariate polynomial scalars and polynomial matrices with a unified symbolic-numeric interface across CPU and GPU-oriented backends. The software exposes three aligned classes: MPOLY for CPU execution,…
In a broad sense, artificial intelligence is a service to find a solution to complex intellectual problems. In this sense, the MathPartner service provides artificial intelligence that allows us to formulate questions and receive answers to…
Large language models (LLMs) often struggle with complex logical reasoning due to logical inconsistencies and the inherent difficulty of such reasoning. We use Lean, a theorem proving framework, to address these challenges. By formalizing…
Formal theories of arithmetic have traditionally been based on either classical or intuitionistic logic, leading to the development of Peano and Heyting arithmetic, respectively. We propose to use $\mu$MALL as a formal theory of arithmetic…
Mean-field games (MFGs) are limiting models to approximate $N$-player games, with a number of applications. Despite the ever-growing numerical literature on computation of MFGs, there is no library that allows researchers and practitioners…
This thesis documents a voyage towards truth and beauty via formal verification of theorems. To this end, we develop libraries in Lean 4 that present definitions and results from diverse areas of MathematiCS (i.e., Mathematics and Computer…
LLM-generated explanations can make technical content more accessible, but there is a ceiling on what they can support interactively. Because LLM outputs are static text, they cannot be executed or stepped through. We argue that grounding…
The role of data libraries in Monte Carlo simulation is discussed. A number of data libraries currently in preparation are reviewed; their data are critically examined with respect to the state-of-the-art in the respective fields. Extensive…
The Mizar Mathematical Library (MML) is a rich database of formalized mathematical proofs (see http://mizar.org). Owing to its large size (it contains more than 1100 "articles" summing to nearly 2.5 million lines of text, expressing more…
We present a formalization, in the theorem prover Lean, of the classification of solvable Lie algebras of dimension at most three over arbitrary fields. Lie algebras are algebraic objects which encode infinitesimal symmetries, and as such…
This work describes the TrueLearn Python library, which contains a family of online learning Bayesian models for building educational (or more generally, informational) recommendation systems. This family of models was designed following…
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
Development of Interactive Theorem Provers has led to the creation of big libraries and varied infrastructures for formal proofs. However, despite (or perhaps due to) their sophistication, the re-use of libraries by non-experts or across…
The democratization of Data Mining has been widely successful thanks in part to powerful and easy-to-use Machine Learning libraries. These libraries have been particularly tailored to tackle Supervised Learning. However, strong supervision…
Algorithms that create recommendations based on observed data have significant commercial value for online retailers and many other industries. Recommender systems have a significant research community, and studying such systems is part of…
One of the main tasks of the European Digital Mathematics Library project was to define a cooperation model with a variety of stakeholders that would allow building a reliable and durable global reference library, aiming to be eventually…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
Recent advancements in the coding, reasoning, and tool-using abilities of LLMs have spurred interest in library learning (i.e., online learning through the creation, storage, and retrieval of reusable and composable functions, knowledge,…
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…