# Steinmetz Neural Networks for Complex-Valued Data

arXiv: https://arxiv.org/abs/2409.10075 · HTML: https://mlsanity.com/paper/2409.10075/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 36 references that are in the map.
- First posted on arXiv 16 Sep 2024.

## Builds on (most cited first, 17 of 17)

- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Learning Robust Representations via Multi-View Information Bottleneck](https://mlsanity.com/paper/2002.07017/) (2020)
- [A Survey on Multi-view Learning](https://mlsanity.com/paper/1304.5634/) (2013)
- [Continual Learning in Low-rank Orthogonal Subspaces](https://mlsanity.com/paper/2010.11635/) (2020)
- [How Does Information Bottleneck Help Deep Learning?](https://mlsanity.com/paper/2305.18887/) (2023)
- [The Conditional Entropy Bottleneck](https://mlsanity.com/paper/2002.05379/) (2020)
- [A Survey of Complex-Valued Neural Networks](https://mlsanity.com/paper/2101.12249/) (2021)
- [Compressive Visual Representations](https://mlsanity.com/paper/2109.12909/) (2021)
- [Better than Real: Complex-valued Neural Nets for MRI Fingerprinting](https://mlsanity.com/paper/1707.00070/) (2017)
- [On Complex Valued Convolutional Neural Networks](https://mlsanity.com/paper/1602.09046/) (2016)
- [Complex-valued Neural Networks with Non-parametric Activation Functions](https://mlsanity.com/paper/1802.08026/) (2018)
- [Enhanced Radar Imaging Using a Complex-valued Convolutional Neural Network](https://mlsanity.com/paper/1712.10096/) (2017)
- [Complex-Valued vs. Real-Valued Neural Networks for Classification Perspectives: An Example on Non-Circular Data](https://mlsanity.com/paper/2009.08340/) (2020)
- [Complex Evolution Recurrent Neural Networks (ceRNNs)](https://mlsanity.com/paper/1906.02246/) (2019)
- [Complex Support Vector Machines for Regression and Quaternary Classification](https://mlsanity.com/paper/1303.2184/) (2013)
- [RASPNet: A Benchmark Dataset for Radar Adaptive Signal Processing Applications](https://mlsanity.com/paper/2406.09638/) (2024)

## Built on by (most cited first, 2 of 2)

- [Holographic Transformers for Complex-Valued Signal Processing: Integrating Phase Interference into Self-Attention](https://mlsanity.com/paper/2509.19331/) (2025)
- [Interaction as Interference: A Quantum-Inspired Aggregation Approach](https://mlsanity.com/paper/2511.10018/) (2025)

## Abstract (arXiv)

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.