6 problems

For the synthetic sparse-coding experiment specified by MAIS-O43, with nesting fraction $\gamma$, sparsity penalty $\lambda$, and dictionary size $M$, determine the phase diagram o…

Let $\Omega^{\mathrm{o}}=\{(\mu,\nu)\in(0,1)\times(0,1)\mid \nu<\mu\}$ be the interior of $\Omega$, and let $J$ be the Jacobian defined in Eq.. Negativity conjecture. For every…

HyperCube regularizer minimizer conjecture. The unitary group representation $A_g=B_g=C_g^\intercal=\varrho(g)$ describes the unique minimizer of $\mathcal{H}$ up to unitary basis…

Weight-feature equality conjecture. Then

Self-duality conjecture. The class feature aggregate is proportional to its corresponding classifier weight: for each $k=1,\ldots,K$, $\boldsymbol{h}_k^*=\alpha\boldsymbol{w}_k^*$…

Within-class collapsing. All features within each class are identical: for each $k=1,\ldots,K$, $\boldsymbol{h}_{k,i}^*\equiv\boldsymbol{h}_k^*$ for every $i$.