6 problems

In the setting of Theorem, concerning robustness classes of convex solids and platonic solids, let downward external robustness and downward full robustness be the corresponding do…

Bubeck–Li–Nagaraj conjecture. The stated lower bound should hold for every Lipschitz activation and arbitrary weights, with no restriction on their magnitudes. The conjecture quant…

Let $\mathcal{F}=\{f_j\}_{j=1}^{2n-1}$ be a frame with $\|f_j\|\leq L$ for all $f_j\in\mathcal{F}$, and let $\omega$ denote the robustness parameter discussed above. Exponential de…

Let $\rho_{i,j}$ denote the maximal robustness of the three-dimensional equilibrium class indexed by $(i,j)$. Equilibrium-class monotonicity conjecture. If $i\geq k$ and $j\geq l$,…

For the three-dimensional equilibrium classes indexed by pairs $(2,n)$ and $(n,2)$, let $\rho_{2,n}$ and $\rho_{n,2}$ denote their maximal full robustness, and let $\rho_n$ denote…

For $n>2$, let $\rho_n$ denote the maximal robustness among planar convex solids in the equilibrium class with $n$ points, and let $\rho($regular n-gon$)$ denote the robustnes…