Deep Learning in High Dimension: Neural Network Approximation of Analytic Functions in $L^2({\mathbb{R}}^d,{\gamma }_d)$

Christoph Schwab, Jakob Zech

For artificial deep neural networks, we prove expression rates for analytic functions $f:{\mathbb{R}}^d\to \mathbb{R}$ in the norm of $L^2({\mathbb{R}}^d,{\gamma }_d)$ where $d\in {\mathbb{N}}\…