The Latent Space of Equational Theories

Abstract: 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.