Fully Deterministic Shallow Neural Networks with Localized Activations. Part I: Construction and Optimal Sobolev Approximation

Ran Bi, Weibing Deng

We construct shallow neural networks with fixed Gaussian and tanh-difference activations on bounded Lipschitz domains $\Omega \subset {\mathbb{R}}^d$, $d\ge 2$. For each $s>0$, explicit dete…