The minimal width of universal $p$-adic ReLU neural networks

Abstract

We determine the minimal width of $p$-adic neural networks with the universal approximation property for continuous ${\mathbb{Q}}_p$-valued functions on compact open subsets with respect to the $L_q$ norms and the $C_1$ norm, where the activation function is a natural $p$-adic analogue of the ReLU function.

arXiv comment16 pages, comments welcome!