$C^*$-Algebraic Machine Learning: Moving in a New Direction
<|reference_start|>$C^*$-Algebraic Machine Learning: Moving in a New Direction: 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.<|reference_end|>
@article{hashimoto2024$c^*$-algebraic,
    title={$C^*$-Algebraic Machine Learning: Moving in a New Direction},
    author={Yuka Hashimoto, Masahiro Ikeda, and Hachem Kadri},
    journal={ICML 2024},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.02637},
    primaryClass={cs.LG math.OA stat.ML}
}