9 problems

MDLVQ optimality conjecture. The algorithm, with an appropriate local adjustment, is also optimal for any values of $K$ and $N$.

Universal MDLVQ index-assignment conjecture. The combined use of the greedy algorithm and local adjustment $\Rsh(a,b)$ solves the problem of optimal MDLVQ index assignment for any…

Finite-index optimality conjecture. For $K>2$, the local adjustment algorithm augmenting the greedy index assignment is conjectured to be optimal for finite $N$.

Activation-function normalization conjecture. The activation function normalizes \tilde{\underaccent{\bar}{j}} to an interval close to the latent alphabet…

Let $n=3$, and consider quantizers whose error distribution is uniform over the $n$-ball. The normalized entropy of such a quantizer is the quantity being optimized. Face-centered-…

Let $d$ and $k$ denote the dimension and the number of hyperplanes, respectively, and let $M$ range over the matrices describing how reconstruction points are obtained from a hyper…

Gersho's conjecture. As $N$ tends to infinity, most cells—namely, all cells except those close to the boundary of the considered domain—become congruent to $H_d^*$.

Variant I monotonicity conjecture. If $J>1$, then the optimal $n_i$ for Variant I CPCs increase monotonically with $i\in\mathcal{S}_1$ and decrease monotonically with…

Monotonicity conjecture. If $J>1$ and $E[\eta_\ell]$ is convex in $\ell$, then the optimal multiplicities $n_i$ for Variant II CPCs increase monotonically with $i$.