  We compare classification and regression tasks in an overparameterized linear
model with Gaussian features. On the one hand, we show that with sufficient
overparameterization all training points are support vectors: solutions
obtained by least-squares minimum-norm interpolation, typically used for
regression, are identical to those produced by the hard-margin support vector
machine (SVM) that minimizes the hinge loss, typically used for training
classifiers. On the other hand, we show that there exist regimes where these
interpolating solutions generalize well when evaluated by the 0-1 test loss
function, but do not generalize if evaluated by the square loss function, i.e.
they approach the null risk. Our results demonstrate the very different roles
and properties of loss functions used at the training phase (optimization) and
the testing phase (generalization).
