Steinmetz Neural Networks for Complex-Valued Data
This work addresses a domain-specific problem in signal processing and complex-valued data analysis, representing an incremental advancement with novel architectural components.
The authors tackled the problem of processing complex-valued data with deep neural networks by introducing Steinmetz Neural Networks with parallel real-valued subnetworks and an Analytic Neural Network variant with a consistency penalty for analytic signal representations. Their approach demonstrated improved performance and robustness to additive noise on benchmark datasets and synthetic examples.
We introduce a new approach to processing complex-valued data using DNNs consisting of parallel real-valued subnetworks with coupled outputs. Our proposed class of architectures, referred to as Steinmetz Neural Networks, incorporates multi-view learning to construct more interpretable representations in the latent space. Moreover, we present the Analytic Neural Network, which incorporates a consistency penalty that encourages analytic signal representations in the latent space of the Steinmetz neural network. This penalty enforces a deterministic and orthogonal relationship between the real and imaginary components. Using an information-theoretic construction, we demonstrate that the generalization gap upper bound posited by the analytic neural network is lower than that of the general class of Steinmetz neural networks. Our numerical experiments depict the improved performance and robustness to additive noise, afforded by our proposed networks on benchmark datasets and synthetic examples.