7 problems

Robust eigenvectors conjecture. The robust eigenvectors of a regular simplex tensor are precisely the vectors in the frame.

Let $m_k$ be the regularized Taylor model at iterate $\bm{x}_k$, let $\bm{x}_*$ be the limit minimizer, and call a local minimizer of $m_k$ persistent if it can be continuously tra…

Let $p$ be the tensor order, let $n$ be the dimension, let $\theta_0$ denote the planted signal, and let $\theta_0$ be recovered from the observed spiked-tensor model with signal-t…

Statistical-computational gap conjecture. The algorithmic threshold scales as

In numerical experiments with tensor and accelerated tensor methods, let $M_p$ denote the Lipschitz constant of the $p$-th derivative used in the complexity bounds. The experiments…

Upper-bound improvement conjecture. The upper bound for this class of convex tensor methods can be improved. The conjecture concerns the gap between the known accelerated upper bou…

Computational hardness assumptions such as planted clique detection and Boolean satisfiability concern decision problems for which one seeks an efficient algorithm. Computational h…