# Evaluation of Complex-Valued Neural Networks on Real-Valued Classification Tasks

arXiv: https://arxiv.org/abs/1811.12351 · HTML: https://mlsanity.com/paper/1811.12351/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2018.

## Built on by (most cited first, 9 of 9)

- [A Survey of Complex-Valued Neural Networks](https://mlsanity.com/paper/2101.12249/) (2021)
- [Theory and Implementation of Complex-Valued Neural Networks](https://mlsanity.com/paper/2302.08286/) (2023)
- [Neural network is heterogeneous: Phase matters more](https://mlsanity.com/paper/2111.02014/) (2021)
- [CoShNet: A Hybrid Complex Valued Neural Network using Shearlets](https://mlsanity.com/paper/2208.06882/) (2022)
- [Towards White-Box Deep Wireless Sensing](https://mlsanity.com/paper/2507.21799/) (2025)
- [On the Approximation and Complexity of Deep Neural Networks to Invariant Functions](https://mlsanity.com/paper/2210.15279/) (2022)
- [GASPnet: Global Agreement to Synchronize Phases](https://mlsanity.com/paper/2507.16674/) (2025)
- [Phase-Aware Deep Learning with Complex-Valued CNNs for Audio Signal Applications](https://mlsanity.com/paper/2510.09926/) (2025)
- [Shortcomings and capacities of real-constrained neural networks in complex spaces](https://mlsanity.com/paper/2606.04390/) (2026)

## Abstract (arXiv)

Complex-valued neural networks are not a new concept, however, the use of real-valued models has often been favoured over complex-valued models due to difficulties in training and performance. When comparing real-valued versus complex-valued neural networks, existing literature often ignores the number of parameters, resulting in comparisons of neural networks with vastly different sizes. We find that when real and complex neural networks of similar capacity are compared, complex models perform equal to or slightly worse than real-valued models for a range of real-valued classification tasks. The use of complex numbers allows neural networks to handle noise on the complex plane. When classifying real-valued data with a complex-valued neural network, the imaginary parts of the weights follow their real parts. This behaviour is indicative for a task that does not require a complex-valued model. We further investigated this in a synthetic classification task. We can transfer many activation functions from the real to the complex domain using different strategies. The weight initialisation of complex neural networks, however, remains a significant problem.