Quantitative approximation results for complex-valued neural networks

02/25/2021

∙

We show that complex-valued neural networks with the modReLU activation function σ(z) = ReLU(|z| - 1) · z / |z| can uniformly approximate complex-valued functions of regularity C^n on compact subsets of ℂ^d, giving explicit bounds on the approximation rate.

READ FULL TEXT

Quantitative approximation results for complex-valued neural networks

Optimal approximation of C^k-functions using shallow complex-valued neural networks

On the approximation of functions by tanh neural networks

Two-layer neural networks with values in a Banach space

Interpolation of Set-Valued Functions

Bayesian Sparsification Methods for Deep Complex-valued Networks

CNM: An Interpretable Complex-valued Network for Matching

Associative Memories Using Complex-Valued Hopfield Networks Based on Spin-Torque Oscillator Arrays

Quantitative approximation results for complex-valued neural networks

Related Research

Optimal approximation of C^k-functions using shallow complex-valued neural networks

On the approximation of functions by tanh neural networks

Two-layer neural networks with values in a Banach space

Interpolation of Set-Valued Functions

Bayesian Sparsification Methods for Deep Complex-valued Networks

CNM: An Interpretable Complex-valued Network for Matching

Associative Memories Using Complex-Valued Hopfield Networks Based on Spin-Torque Oscillator Arrays