ID: 1905.02263

Learning Algebraic Structures: Preliminary Investigations

May 2, 2019

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Yang-Hui He, Minhyong Kim
Computer Science
High Energy Physics - Theory
Mathematics
Statistics
Machine Learning
Group Theory
Rings and Algebras
Machine Learning

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.

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