7 problems

Width-one identifiability conjecture. 1. There exist architectures $\mathcal{A}=(n_0,\ldots,n_{L+1})$ with $n_\ell=1$ for some $\ell\leq L$ for which no identifiable parameters exi…

Shallow-network closedness conjecture. The set $\mathcal{F}_{\boldsymbol{I}}(\Omega)$ is closed in $(C^0(\Omega),\|\cdot\|_\infty)$ if and only if $\boldsymbol{I}$ satisfies the se…

Closedness-equivalence conjecture. An architecture $\boldsymbol{I}$ has a closed function space on the cube if and only if its realization set is closed on arbitrary finite domains…

Let $n=2^k$, and let $\operatorname{ReLU}_n(k)$ be the set of continuous piecewise linear functions on $\mathbb{R}^n$ computable with $k$ hidden layers. Max-function formulation of…

Let $\operatorname{ReLU}_n(k)$ denote the set of continuous piecewise linear functions defined on $\mathbb{R}^n$ and computable with $k$ hidden layers. Hertrich–Lindner–Raginsky–Ba…

Generic total H-complexity conjecture. With probability $1$, the total $H$-complexity of $F$ is less than or equal to the number of $0$-cells of $\mathcal{C}(F)$.

For $n\boxin\mathbb{N}$, let … Here, $\operatorname{ReLU}_n(k)$ denotes the class of functions representable by ReLU neural networks with $n$ input variables and $k$ hidden layers,…