6.4 Active identification and separating probes

Let \(\pi _0\mathcal F_t\) denote the current observational-equivalence classes. A probe \(p\) is separating for \(M,N\in \mathcal F_t\) if some possible response gives different query answers for the two classes. A probe policy is fairly separating when it eventually issues such a probe for every pair that remains observationally distinct and viable.

This makes active learning categorical: the learner does not merely seek a large scalar information gain. It chooses a morphism that refines a hypothesis fiber relative to the declared queries. Numerical utilities may rank such probes, but they are observers of the refinement, not its definition.