  We propose a metric -- Projection Norm -- to predict a model's performance on
out-of-distribution (OOD) data without access to ground truth labels.
Projection Norm first uses model predictions to pseudo-label test samples and
then trains a new model on the pseudo-labels. The more the new model's
parameters differ from an in-distribution model, the greater the predicted OOD
error. Empirically, our approach outperforms existing methods on both image and
text classification tasks and across different network architectures.
Theoretically, we connect our approach to a bound on the test error for
overparameterized linear models. Furthermore, we find that Projection Norm is
the only approach that achieves non-trivial detection performance on
adversarial examples. Our code is available at
https://github.com/yaodongyu/ProjNorm.
