Learning Algebraic Structures: Preliminary Investigations

TL;DR

This paper explores whether machine learning models like SVMs and neural networks can learn to identify and match algebraic structures such as finite groups and rings, demonstrating promising results on small structures.

Contribution

It introduces a novel approach to studying algebraic structures using machine learning, showing AI can recognize and match algebraic tables for small finite structures.

Findings

AI can identify simple finite groups from Cayley tables.

AI can correctly match addition and multiplication tables for small finite rings.

Results suggest potential for AI in algebraic structure recognition.

Abstract

We employ techniques of machine-learning, exemplified by support vector machines and neural classifiers, to initiate the study of whether AI can "learn" algebraic structures. Using finite groups and finite rings as a concrete playground, we find that questions such as identification of simple groups by "looking" at the Cayley table or correctly matching addition and multiplication tables for finite rings can, at least for structures of small size, be performed by the AI, even after having been trained only on small number of cases. These results are in tandem with recent investigations on whether AI can solve certain classes of problems in algebraic geometry.