Machine learning, group theory and combinatorics

机器学习、群论和组合学

• 批准号: DP230102982
• 负责人: Prof Geordie Williamson
• 金额: $ 28.02万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2023
• 资助国家: 澳大利亚
• 起止时间: 2023-10-01 至 2026-09-30
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP230102982
• 关键词: Machine; learning; group; theory; combinatorics

This project aims to investigate group theory and combinatorics using machine learning techniques. This project expects to generate new knowledge concerning symmetric groups and symmetric functions, using an innovative approach from reinforcement learning. Expected outcomes of this project include a clarification of the types of difficult problems in pure mathematics that can be gainfully attacked via machine learning, and an understanding of the role of group theory in machine learning. This should provide significant benefits, such as progress on long standing open problems, the development of an emerging technology with significant implications for mathematics, and the training of Australian scientists in a vital area of research.

该项目旨在利用机器学习技术研究群论和组合学。该项目期望使用强化学习的创新方法生成关于对称群和对称函数的新知识。该项目的预期结果包括澄清纯数学中可以通过机器学习有效解决的难题类型，以及理解群论在机器学习中的作用。这将带来巨大的好处，比如在长期悬而未决的问题上取得进展，对数学有重大影响的新兴技术的发展，以及在一个重要的研究领域培养澳大利亚科学家。