mlsanityData to 7 Oct 2026

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

arXiv 2402.02637 ↗First posted 4 Feb 2024cs.LG math.OA stat.MLcited by 1

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Abstract (arXiv)

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.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 18 of its 46 references that are in the map. First posted on arXiv 4 Feb 2024.

Builds on

18 of 46 references.

References · 18

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  12. 2021Reproducing kernel Hilbert C*-module and kernel mean embeddingscited by 10
6 more
  1. 2022C^*-algebra Net: A New Approach Generalizing Neural Network Parameters to C^*-algebracited by 9
  2. 2022Learning in RKHM: a C^*-Algebraic Twist for Kernel Machinescited by 7
  3. 2023Deep Learning with Kernels through RKHM and the Perron-Frobenius Operatorcited by 7
  4. 2023Efficient displacement convex optimization with particle gradient descentcited by 5
  5. 2023Noncommutative C^*-algebra Net: Learning Neural Networks with Powerful Product Structure in C^*-algebracited by 4
  6. 2020Kernel Mean Embeddings of Von Neumann-Algebra-Valued Measurescited by 1

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Citing papers per year: 2024: 1.

1 paper.

  1. 2024Quantum Circuit C^*-algebra Netcited by 0