$C^*$-Algebraic Machine Learning: Moving in a New Direction
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916278991585280 |
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| author | Hashimoto, Yuka Ikeda, Masahiro Kadri, Hachem |
| author_facet | Hashimoto, Yuka Ikeda, Masahiro Kadri, Hachem |
| contents | Machine learning has a long collaborative tradition with several fields of mathematics, such as statistics, probability and linear algebra. We propose a new direction for machine learning research: $C^*$-algebraic ML $-$ a cross-fertilization between $C^*$-algebra and machine learning. The mathematical concept of $C^*$-algebra is a natural generalization of the space of complex numbers. It enables us to unify existing learning strategies, and construct a new framework for more diverse and information-rich data models. We explain why and how to use $C^*$-algebras in machine learning, and provide technical considerations that go into the design of $C^*$-algebraic learning models in the contexts of kernel methods and neural networks. Furthermore, we discuss open questions and challenges in $C^*$-algebraic ML and give our thoughts for future development and applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02637 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $C^*$-Algebraic Machine Learning: Moving in a New Direction Hashimoto, Yuka Ikeda, Masahiro Kadri, Hachem Machine Learning Operator Algebras Machine learning has a long collaborative tradition with several fields of mathematics, such as statistics, probability and linear algebra. We propose a new direction for machine learning research: $C^*$-algebraic ML $-$ a cross-fertilization between $C^*$-algebra and machine learning. The mathematical concept of $C^*$-algebra is a natural generalization of the space of complex numbers. It enables us to unify existing learning strategies, and construct a new framework for more diverse and information-rich data models. We explain why and how to use $C^*$-algebras in machine learning, and provide technical considerations that go into the design of $C^*$-algebraic learning models in the contexts of kernel methods and neural networks. Furthermore, we discuss open questions and challenges in $C^*$-algebraic ML and give our thoughts for future development and applications. |
| title | $C^*$-Algebraic Machine Learning: Moving in a New Direction |
| topic | Machine Learning Operator Algebras |
| url | https://arxiv.org/abs/2402.02637 |