mlsanityData to 7 Oct 2026

Noncommutative C^*-algebra Net: Learning Neural Networks with Powerful Product Structure in C^*-algebra

arXiv 2302.01191 ↗First posted 26 Jan 2023math.OA cs.LG math.FAcited by 4

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Abstract (arXiv)

We propose a new generalization of neural network parameter spaces with noncommutative C^*-algebra, which possesses a rich noncommutative structure of products. We show that this noncommutative structure induces powerful effects in learning neural networks. Our framework has a wide range of applications, such as learning multiple related neural networks simultaneously with interactions and learning equivariant features with respect to group actions. Numerical experiments illustrate the validity of our framework and its potential power.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 27 of its 53 references that are in the map. First posted on arXiv 26 Jan 2023.

Builds on

27 of 53 references.

References · 27

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15 more
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Cited by year

Citing papers per year: 2023: 2; 2024: 2.

4 papers.

  1. 2023Deep Learning with Kernels through RKHM and the Perron-Frobenius Operatorcited by 7
  2. 2024C^*-Algebraic Machine Learning: Moving in a New Directioncited by 1
  3. 2023Compact Matrix Quantum Group Equivariant Neural Networkscited by 0
  4. 2024Quantum Circuit C^*-algebra Netcited by 0