  Multicalibration is a notion of fairness for predictors that requires them to
provide calibrated predictions across a large set of protected groups.
Multicalibration is known to be a distinct goal than loss minimization, even
for simple predictors such as linear functions.
  In this work, we consider the setting where the protected groups can be
represented by neural networks of size $k$, and the predictors are neural
networks of size $n > k$. We show that minimizing the squared loss over all
neural nets of size $n$ implies multicalibration for all but a bounded number
of unlucky values of $n$. We also give evidence that our bound on the number of
unlucky values is tight, given our proof technique. Previously, results of the
flavor that loss minimization yields multicalibration were known only for
predictors that were near the ground truth, hence were rather limited in
applicability. Unlike these, our results rely on the expressivity of neural
nets and utilize the representation of the predictor.
