Quantitative approximation results for complex-valued neural networks

• URL: http://arxiv.org/abs/2102.13092v1
• Date: Thu, 25 Feb 2021 18:57:58 GMT
• Title: Quantitative approximation results for complex-valued neural networks
• Authors: A. Caragea, D.G. Lee, J. Maly, G. Pfander, F. Voigtlaender
• Abstract summary: We show that complex-valued neural networks with the modReLU activation function $sigma(z) = mathrmReLU(|z|) can uniformly approximate complex-valued functions of regularity $Cn$ on compact subsets of $mathbbCd$, giving explicit bounds on the approximation rate.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show that complex-valued neural networks with the modReLU activation function $\sigma(z) = \mathrm{ReLU}(|z| - 1) \cdot z / |z|$ can uniformly approximate complex-valued functions of regularity $C^n$ on compact subsets of $\mathbb{C}^d$, giving explicit bounds on the approximation rate.

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