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.
We also show the validity of our framework numerically, which illustrates its potential power.
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: Changes are highlighted in red. Notable updates can be summarized as follows:
* We emphasized the advantage of using $C^*$-algebra in Remark 1. We also compare it with Clifford algebra.
* We explained the computational cost of Group $C^*$-algebra in Remark 4.
* We elaborated on the property of $C^*$-algebra net in Section 3.2.
* We added experimental results of ensembling in Section 4.1.1 and the permutation-equivariant DeepSet in Section 4.2.
* We additionally discussed the future direction of our work in Section 5.
Assigned Action Editor: ~Gabriel_Loaiza-Ganem1
Submission Number: 1372
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