Attention-sublayer increment ≤ (row ℓ₁ norm of W_o) × (value bound), for the existing architecture

For all $\htmlData{mx=1}{T, d \in \htmlData{mx=0}{\mathbb{N}}}$, $\htmlData{mx=5}{w : \htmlData{mx=2}{\htmlData{mx=0}{\operatorname{Fin}}\,\htmlData{mx=1}{T}} \mathrel{\htmlData{mx=4}{\to}} \htmlData{mx=3}{\mathbb{R}}}$, $\htmlData{mx=9}{V : \htmlData{mx=2}{\htmlData{mx=0}{\operatorname{Fin}}\,\htmlData{mx=1}{T}} \mathrel{\htmlData{mx=8}{\to}} \htmlData{mx=5}{\htmlData{mx=3}{\operatorname{Fin}}\,\htmlData{mx=4}{d}} \mathrel{\htmlData{mx=7}{\to}} \htmlData{mx=6}{\mathbb{R}}}$, $\htmlData{mx=5}{\mathit{Wo} : \htmlData{mx=2}{\htmlData{mx=0}{\operatorname{Fin}}\,\htmlData{mx=1}{d}} \mathrel{\htmlData{mx=4}{\to}} \htmlData{mx=3}{\mathbb{R}}}$ and $\htmlData{mx=1}{M \in \htmlData{mx=0}{\mathbb{R}}}$, if $\htmlData{mx=4}{\forall j,\ 0 \mathrel{\htmlData{mx=3}{\leq}} \htmlData{mx=2}{\htmlData{mx=0}{w}(\htmlData{mx=1}{j})}}$, $\htmlData{mx=3}{\sum_{j} \htmlData{mx=2}{\htmlData{mx=0}{w}(\htmlData{mx=1}{j})}} \mathrel{\htmlData{mx=4}{=}} 1$ and $\htmlData{mx=7}{\forall j, k,\ \htmlData{mx=4}{\left\lvert \htmlData{mx=3}{\htmlData{mx=0}{V}(\htmlData{mx=1}{j}, \htmlData{mx=2}{k})} \right\rvert} \mathrel{\htmlData{mx=6}{\leq}} \htmlData{mx=5}{M}}$, then