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arXiv · 2601.20759

The Latent Space of Equational Theories

Luis Berlioz·Paul-André Melliès
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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.

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Luis Berlioz, Paul-André Melliès. 2026-01-28. The Latent Space of Equational Theories. https://arxiv.org/abs/2601.20759

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