6 problems

Let $n\geq 1$, $L\geq 1$, and let $f:[0,1]^n\to\mathbb{R}$ or $f:[0,1]^n\to\mathbb{R}^m$ be continuous. Consider a Sprecher Network with architecture $n\to[d_1,\dots,d_L]\to 1$ or…

Let $n,m\in\mathbb{N}$ with $m>1$, and let $f:[0,1]^n\to\mathbb{R}^m$ be continuous. A Sprecher Network has architecture $n\to[d_1]\to m$ with one hidden block of width…

An elementary universal formula without integration is an elementary formula intended to achieve uniform approximation of continuous functions on $[0,1]$, without using integration…

Let $\mathcal G_1$ denote the class of formula families achieving approximation on arbitrary finite subsets of $[0,1]$, and let $\mathcal G_2$ denote the class of families achievin…

Let $\mathcal G_1$ denote the class of formula families achieving approximation on arbitrary finite subsets of $[0,1]$, and let $\mathcal G_2$ denote the class of families achievin…

Non-universality conjecture. Since the step functions used to establish $L^p$-universality bypass the uniformity of the transformation by affine coupling flows, the difficulty is i…