  We study why overparameterization -- increasing model size well beyond the
point of zero training error -- can hurt test error on minority groups despite
improving average test error when there are spurious correlations in the data.
Through simulations and experiments on two image datasets, we identify two key
properties of the training data that drive this behavior: the proportions of
majority versus minority groups, and the signal-to-noise ratio of the spurious
correlations. We then analyze a linear setting and theoretically show how the
inductive bias of models towards "memorizing" fewer examples can cause
overparameterization to hurt. Our analysis leads to a counterintuitive approach
of subsampling the majority group, which empirically achieves low minority
error in the overparameterized regime, even though the standard approach of
upweighting the minority fails. Overall, our results suggest a tension between
using overparameterized models versus using all the training data for achieving
low worst-group error.
