Learning Algebraic Structures: Preliminary Investigations
Learning Algebraic Structures: Preliminary Investigations
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DOI：
10.1142/s2810939222500046
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发表时间：
2019-05
期刊：
影响因子：
--
通讯作者：
Yang-Hui He;Minhyong Kim
中科院分区：
文献类型：
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作者：
Yang-Hui He;Minhyong Kim
在本文中，我们采用机器学习技术，例如支持向量机和神经分类器，开始研究人工智能（AI）是否可以“学习”代数结构。使用有限群和有限环作为一个具体的游乐场，我们发现，诸如通过“看”凯莱表或正确匹配有限环的加法和乘法表来识别简单群之类的问题，至少对于小尺寸的结构，可以由AI执行，即使只在少数情况下进行了训练。这些结果与最近关于人工智能是否可以解决代数几何中某些类别问题的研究是一致的。
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.