15 problems

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 $f_{\Lambda}:\sigma\to\mathbb{R}$ be a feature associated with an operator $\Lambda$ acting on quantum states, let $\mathcal{D}$ be a distribution of labelled states…

Consider a family of dynamical systems sharing an interconnection structure and a property $\mathcal{P}$ of interest. The property is structural when it holds for the whole family,…

Let $w$ be an $L^p$-graphon, and let the results of Theorem cited in the source be understood as the robust Robinson-property recovery results established there for $p>5$. Robust r…

Let CODASCA denote the min-max federated deep AUC maximization algorithm, and suppose it uses the square loss, which is not symmetric: a loss is symmetric when $\ell(z)+\ell(-z)$ i…

Insertion-model conjecture. The most general insertion model that the algorithm can withstand is one in which the original color classes are respected.

Consider robustness analysis using the dissipativity-based results of Theorems and, and compare it with robustness analysis using Theorem with general O'Shea-Zames-Falb multipliers…

Let $\Omega$ be the domain, let $D_N$ be the data set of $N$ points, and let $k$ be the number of nearest neighbors. Set … Let $u$ be defined by the Laplace-learning strategy in th…

Let a generator's weak incentive to deviate mean that there exists an execution of the deviation dynamics along which … so that the generator obtains a higher payoff than…

Let $\mathbf{X}(t)$ denote the stochastic population process, and let a $\theta$-perturbation of $\mathbf{X}(t)$ be the process defined by equation. In the setting where $r<0$ and…

A pairwise loss function is a function on pairs of examples and prediction values, and its associated risk functional is obtained by integrating the loss with respect to the releva…

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 $\rho(\text{regular n-gon})$ denote the robustnes…