On the Computational Complexities of Complex-valued Neural Networks
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866929463614242816 |
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| author | Mayer, Kayol Soares Soares, Jonathan Aguiar Cruz, Ariadne Arrais Arantes, Dalton Soares |
| author_facet | Mayer, Kayol Soares Soares, Jonathan Aguiar Cruz, Ariadne Arrais Arantes, Dalton Soares |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_13075 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Computational Complexities of Complex-valued Neural Networks Mayer, Kayol Soares Soares, Jonathan Aguiar Cruz, Ariadne Arrais Arantes, Dalton Soares Neural and Evolutionary Computing Machine Learning Signal Processing 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. |
| title | On the Computational Complexities of Complex-valued Neural Networks |
| topic | Neural and Evolutionary Computing Machine Learning Signal Processing |
| url | https://arxiv.org/abs/2310.13075 |