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.

翻译：基于Terence Tao十五个月前发起的协作方程理论项目，并结合机器学习和有限模型理论的思想，我们构建了一个方程理论的潜在空间，其中每个方程理论都位于特定位置，该位置由其相对于有限幺半群大样本的统计行为决定。该实验使我们首次能够观察到推理流如何在方程理论的潜在空间中产生具有惊人方向性和良好结构的逻辑蕴含链。