7 problems

Let $P_{\mathcal{M}}$ be a stationary distribution with entropy $H$, let $H_N$ denote the LAWS hit rate after $N$ total queries, and let $N_{\min}$ be the per-node visit threshold.…

Let $P_{\mathcal{M}}$ range over stationary distributions with entropy $H$, and let $N$ be the number of queries. LAWS acquisition lower bound. No online inference caching algorith…

Let $\mathcal{M}_1$ be a language model and $\mathcal{M}_2$ a robotics model with a shared natural-language task representation. Let $n^*$ be a shared PLT trie node and let…

Let $t_i$ be the token at position $i$, let $H_i=H(t_i\mid t_{<i})$ be its conditional entropy, and let $\mathcal{T}$ be the LAWS trie with description length $L(\mathcal{T})$. Opt…

Consider the non-uniform centralized caching problem with two files, using the paper's general placement scheme and the lower bound developed for the delivery rate. Achievability c…

Let $N$ and $K$ denote the numbers of files and users, respectively, and let $\mathcal{W}$ and $\mathcal{Z}$ denote the corresponding collections of random variables in the caching…

In a caching system with demands grouped into demand type classes, consider the outer bounds obtained from subsets of requests. Equivalent-bounds conjecture. In some cases, the sam…