Noncommutative $C^*$-algebra Net: Learning Neural Networks with Powerful Product Structure in $C^*$-algebra
This work addresses the need for more powerful neural network architectures with rich product structures, potentially benefiting researchers in machine learning and related fields, though it appears incremental as it builds on existing algebraic concepts.
The authors tackled the problem of enhancing neural network learning by generalizing parameter spaces with noncommutative C*-algebra structures, resulting in a framework that enables learning multiple related networks with interactions and equivariant features, as validated by numerical experiments.
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.