Position: $C^*$-Algebraic Machine Learning $-$ Moving in a New Direction

Yuka Hashimoto, Masahiro Ikeda, Hachem Kadri
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:17667-17679, 2024.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-hashimoto24a, title = {Position: $C^*$-Algebraic Machine Learning $-$ Moving in a New Direction}, author = {Hashimoto, Yuka and Ikeda, Masahiro and Kadri, Hachem}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {17667--17679}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/hashimoto24a/hashimoto24a.pdf}, url = {https://proceedings.mlr.press/v235/hashimoto24a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Position: $C^*$-Algebraic Machine Learning $-$ Moving in a New Direction %A Yuka Hashimoto %A Masahiro Ikeda %A Hachem Kadri %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-hashimoto24a %I PMLR %P 17667--17679 %U https://proceedings.mlr.press/v235/hashimoto24a.html %V 235 %X 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.
APA
Hashimoto, Y., Ikeda, M. & Kadri, H.. (2024). Position: $C^*$-Algebraic Machine Learning $-$ Moving in a New Direction. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:17667-17679 Available from https://proceedings.mlr.press/v235/hashimoto24a.html.

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