Steinmetz Neural Networks for Complex-Valued Data

Abstract

In this work, 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, leverages multi-view learning to construct more interpretable representations within 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. Utilizing an information-theoretic construction, we demonstrate that the generalization error 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 these networks on benchmark datasets and synthetic examples.

Tasks

Reproductions