Noncommutative $C^*$-algebra Net: Learning Neural Networks with Powerful Product Structure in $C^*$-algebra
Abstract: We propose a new generalization of neural networks with noncommutative $C^*$-algebra.
An important feature of $C^*$-algebras is their noncommutative structure of products, but the existing $C^*$-algebra net frameworks have only considered commutative $C^*$-algebras.
We show that this noncommutative structure of $C^*$-algebras 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 invariant features with respect to group actions.
The validity of our framework numerically illustrates its potential power.
Submission Length: Regular submission (no more than 12 pages of main content)
Previous TMLR Submission Url: https://openreview.net/forum?id=4glHUNZB6C
Changes Since Last Submission: * We revised the introduction for better understanding.
* We discussed the relationship with peer-to-peer learning in section 3.1.1.
* We added Section 5 (Related Works) to describe the similarities and differences between Clifford algebra and $C^*$-algebra.
* We include a discussion on computational cost in Section 6.
Assigned Action Editor: ~Gabriel_Loaiza-Ganem1
Submission Number: 1884
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