3 problems

Let $K$ be prefix Kolmogorov complexity, let $\boldsymbol{\vartheta}_0$ be the true parameter, and let $\Delta(k)$ denote the complexity difference used in the MDL setup. Strengthe…

Let $v$ be a string, let $L^m(v)$ denote the length of its shortest grammar, and let $\boldsymbol{\operatorname{MDL}}(v)$ denote the MDL code for $v$. Let $\gamma(n):=n f_1(n)$. Sy…

Let $\mathcal{M}$ be a sufficiently capable base model trained on a corpus containing code, mathematics, and structured data, and let $n^*$ be a PLT trie node with probability…