To ensure plausibility, counterfactuals should yield output distribution similar to real instances of the target class. [Plumb et al. (2020)] evaluate whether each counterfactual $z$ matches the output activation of at least one training sample, i.e.: $\exists x' \in \mathcal{X}_{y^*_z} ~:~ \delta\big(\theta(x'), \theta(z)\big) < \epsilon$
This confirms that the counterfactual aligns with typical model behavior for that class.