On the Computational Complexities of Complex-valued Neural Networks

• Main Authors: Mayer, Kayol Soares, Soares, Jonathan Aguiar, Cruz, Ariadne Arrais, Arantes, Dalton Soares
• Format: Journal Article
• Language: English
• Published: 19-10-2023
• Subjects: Computer Science - Learning; Computer Science - Neural and Evolutionary Computing
• DOI: 10.48550/arxiv.2310.13075

IEEE Latin-American Conference on Communications (LATINCOM 2023) 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.