Machine Learning Discovers Invariants of Braids and Flat Braids

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-11 DOI:10.1007/s00006-024-01349-4

Alexei Lisitsa, Mateo Salles, Alexei Vernitski

引用次数: 0

Abstract

We use machine learning to classify examples of braids (or flat braids) as trivial or non-trivial. Our machine learning takes the form of supervised learning, specifically multilayer perceptron neural networks. When they achieve good results in classification, we are able to interpret their structure as mathematical conjectures and then prove these conjectures as theorems. As a result, we find new invariants of braids and prove several theorems related to them. This work evolves from our experiments exploring how different types of AI cope with untangling braids with 3 strands, this is why we concentrate mostly on braids with 3 strands.

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机器学习发现辫子和扁平辫子的不变量

我们利用机器学习将辫子（或扁平辫子）的示例分类为琐碎或非琐碎。我们的机器学习采用监督学习的形式，特别是多层感知器神经网络。当它们在分类中取得良好结果时，我们能够将其结构解释为数学猜想，然后将这些猜想证明为定理。因此，我们找到了辫子的新不变式，并证明了与之相关的几个定理。这项工作源于我们探索不同类型的人工智能如何处理三股辫子的实验，这也是我们主要关注三股辫子的原因。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.