7 problems

Hertrich et al.'s geometric conjecture. There do not exist polytopes $P,Q\in\Delta(m)$ such that

Hertrich et al.'s equivalent conjecture. The function

Let $f$ be a continuous piecewise linear function, and consider shallow ReLU neural networks, allowing either finite width or infinite width with a representation cost. Ongie et al…

Piecewise linearity conjecture. The Seshadri function of $A$ is piecewise linear precisely in these cases.

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,…

Two-slope extremality conjecture. If the function has no uncovered components, then it is extreme.

Let $\mu_{1}(m,n)$ be the maximum multiplicity of $z=0$ when $B(t)$ and $A(t)$ are polynomial functions of degrees $m$ and $n$, respectively. Let $\mu_{2}(m,n)$ be the maximum mult…