# On the Computational Complexities of Complex-valued Neural Networks

arXiv: https://arxiv.org/abs/2310.13075 · HTML: https://mlsanity.com/paper/2310.13075/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 33 references that are in the map.
- First posted on arXiv 19 Oct 2023.

## Builds on (most cited first, 5 of 5)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [The universal approximation theorem for complex-valued neural networks](https://mlsanity.com/paper/2012.03351/) (2020)
- [Complex-valued Neural Networks with Non-parametric Activation Functions](https://mlsanity.com/paper/1802.08026/) (2018)
- [Towards Understanding Theoretical Advantages of Complex-Reaction Networks](https://mlsanity.com/paper/2108.06711/) (2021)

## Abstract (arXiv)

Complex-valued neural networks (CVNNs) are nonlinear filters used in the digital signal processing of complex-domain data. Compared with real-valued neural networks~(RVNNs), CVNNs can directly handle complex-valued input and output signals due to their complex domain parameters and activation functions. With the trend toward low-power systems, computational complexity analysis has become essential for measuring an algorithm's power consumption. Therefore, this paper presents both the quantitative and asymptotic computational complexities of CVNNs. This is a crucial tool in deciding which algorithm to implement. The mathematical operations are described in terms of the number of real-valued multiplications, as these are the most demanding operations. To determine which CVNN can be implemented in a low-power system, quantitative computational complexities can be used to accurately estimate the number of floating-point operations. We have also investigated the computational complexities of CVNNs discussed in some studies presented in the literature.