Learning algebraic structures: Preliminary investigations
Yang‐Hui He, Minhyong Kim
Abstract
In this paper, we employ techniques of machine learning, exemplified by support vector machines and neural classifiers, to initiate the study of whether artificial intelligence (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.
Topics & Concepts
Computer scienceMatching (statistics)Identification (biology)Simple (philosophy)Table (database)Algebra over a fieldAlgebraic numberMultiplication (music)Algebraic structureArtificial intelligenceAlgebraic operationTheoretical computer scienceAlgorithmMathematicsPure mathematicsCombinatoricsData miningBotanyBiologyEpistemologyStatisticsPhilosophyMathematical analysisHomotopy and Cohomology in Algebraic TopologyTopological and Geometric Data AnalysisAlgebraic structures and combinatorial models