  Predictors map individual instances in a population to the interval $[0,1]$.
For a collection $\mathcal C$ of subsets of a population, a predictor is
multi-calibrated with respect to $\mathcal C$ if it is simultaneously
calibrated on each set in $\mathcal C$. We initiate the study of the
construction of scaffolding sets, a small collection $\mathcal S$ of sets with
the property that multi-calibration with respect to $\mathcal S$ ensures
correctness, and not just calibration, of the predictor. Our approach is
inspired by the folk wisdom that the intermediate layers of a neural net learn
a highly structured and useful data representation.
