Luis Berlioz | Searcharxiv

arXiv2026

The Latent Space of Equational Theories

Building on the collaborative Equational Theories project initiated by Terence Tao fifteen months ago, and combining it with ideas coming from machine learning and finite model theory, we construct a latent space of equational theories where each equational theory is located at a specific location, determined by its statistical behavior with respect to a large sample of finite magmas. This experiment enables us to observe for the first time how reasoning flows and produces surprisingly oriented and well-structured chains of logical implications in the latent space of equational theories.

cs.LO↗

arXiv2021

ArGoT: A Glossary of Terms extracted from the arXiv

We introduce ArGoT, a data set of mathematical terms extracted from the articles hosted on the arXiv website. A term is any mathematical concept defined in an article. Using labels in the article's source code and examples from other popular math websites, we mine all the terms in the arXiv data and compile a comprehensive vocabulary of mathematical terms. Each term can be then organized in a dependency graph by using the term's definitions and the arXiv's metadata. Using both hyperbolic and standard word embeddings, we demonstrate how this structure is reflected in the text's vector representation and how they capture relations of entailment in mathematical concepts. This data set is part of an ongoing effort to align natural mathematical text with existing Interactive Theorem Prover Libraries (ITPs) of formally verified statements.

cs.DL↗