35 problems

Ramanujan's conjecture. If $a_i\to a>\frac14$, then the continued fraction diverges.

Consider the sufficient convergence bounds for loopy belief propagation (LBP) in graphical models with discrete variables and nonnegative factors, including Corollary … is stronger…

Anisotropic-kernel convergence conjecture. It should be possible to generalize the aforementioned nonlocal-to-local convergence results to anisotropic kernels.

Consider hyperbolic approximations of higher-order PDEs, with $q_0$ denoting the leading-order approximation to the original solution $u$ and $q_i$, $i\geq 1$, denoting the derivat…

Let Algorithm … will continue to be a function of the degree of each node. The surrounding analysis establishes finite-time termination in the cases considered, but the general wor…

subMIDAS convergence conjecture. The subsampling algorithm subMIDAS satisfies similar convergence properties to those described in Theorem, depending on the choice of $\lambda_n$,…

Adaptive-bias conjecture. A smaller bias might not be essential when the iterates are far away from stationarity, whereas reducing the bias becomes more critical as the iterates ap…

Global convergence conjecture. The GLPA for sigmoid networks with the quadratic loss function can converge globally under certain conditions.

Adam is an optimization algorithm whose behavior depends on its hyperparameters $(\beta_1,\beta_2)$. In convergence analyses, one may choose a problem after fixing these hyperparam…

Fastest-convergence conjecture. For every such $\mathcal{R}$ and every $\delta\in(0,\frac{1}{2})$,

Flip1 convergence conjecture. In this setting, the trajectory actually converges to $\operatorname{dest}(W)$ in the $L^1$-norm, and possibly even in the $L^\infty$-norm.

Let $q$ denote the fixed-point iteration process in Eq., and let $\Psi$ denote the Anderson-acceleration process in Eq., with asymptotic convergence factors $\rho_q$ and…

Crystallographic-packing conjecture. All the results established in this article for polyhedral packings remain true for crystallographic packings in full generality.

Let $\bm{\pi}^n_t$ and $\bm{\pi}_t$ denote the discrete and limiting trajectories, and let the required regularity assumption be the bounded-variation-type oscillation bound on the…

Consider an $N$-fold Mellin–Barnes integral with a linear combination of multiple hypergeometric series representing it, and construct the associated master series from a master se…

Let an $N$-fold Mellin–Barnes integral have a series representation, and let a master set be a set of poles that parameterizes, up to a change of variables, all poles associated wi…

Let $(x^k)$ be the sequence of weight vectors generated by iterative graph normalization. Norm-to-componentwise convergence conjecture. If the $L_1$ norms of the weight vectors con…

Let Newton-Anderson denote the iterative method studied in the paper, and call a problem degenerate when its solution does not satisfy the usual nonsingularity assumptions for quad…

Consider a surrogate-based optimization method with surrogate models and a relevator, where the relevator is the model that decides whether to evaluate a candidate solution with th…

Let $E_k(\lambda)$ denote the Euclid polynomials, and consider the series … The “cauliflower” is the region depicted in Figure. Cauliflower convergence conjecture. There is converg…

Let integrable graphons be equipped with the metrics $\delta_{\square}$ and $\delta_{\square}^{\mathsf s}$, and let $\to_{\mathsf{GP}}$ and $\to_{\mathsf{GS}}$ denote the convergen…

Quadratic interpolation convergence conjecture. One might conjecture that the resulting algorithm converges similarly to a second-order method, that is, quadratically.

Let $r>0$, let $u$ be a changepoint with prior probabilities $boldsymbol{pi}=(boldsymbol{pi}0,boldsymbol{pi}1,boldsymbol{pi}2,u2026)$, and let $lambda{k+n}^k$ denote the log-likel…

Let $\omega$ be the parameter of the generalized Butterfly subdivision scheme, with the parameter range considered in the source given by $\omega\in\left[0,\frac14\right)$. The sch…

Let $u>0$ and $\kappa>0$, let $r>1$ be an integer, and consider the master equation … Let $\bar\rho$ be a steady density operator supported on the span of the coherent states…