Definition. Training prompt law and evaluated prompt slice [ftip-00AL]
Definition. Training prompt law and evaluated prompt slice [ftip-00AL]
Let \(\mathcal X\) be a task-instance set. Write \(\mu _{\rm tr}=\mathcal D_{\rm tr}\) for the training-prompt coordinate of an experiment cell in Definition [ftip-009T]. A training prompt law is this probability law on \(\mathcal X\), used to draw instances during a post-training protocol. Let \(\mu _{\rm ev}\) be an independently declared evaluation law on the same set.
An evaluated prompt slice is a measurable set \(C\subseteq \mathcal X\) with \(\mu _{\rm ev}(C)>0\). Its conditional evaluation law is
\[ \mu _{\rm ev}(A\mid C) =\frac {\mu _{\rm ev}(A\cap C)}{\mu _{\rm ev}(C)}. \]The training and evaluation laws need not agree. A slice records where an effect is measured; it does not assert that prompts inside the slice are equally difficult or represented equally in pretraining. We specialize the task-law convention of Definition [ftip-001Q].