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.

翻译：我们显示,具有modReLU激活功能的复杂价值神经网络 $\ sigma(z) =\ mathrm{ReLU}( ⁇ z ⁇ - 1)\ cdott z / ⁇ z ⁇ $($z ⁇ $) 的复合价值神经网络,可以统一使用常规性复杂价值功能的近似值,即$\ mathbb{C ⁇ d$,对近似率有明确的界限。