  There is an increasing interest in algorithms to learn invariant correlations
across training environments. A big share of the current proposals find
theoretical support in the causality literature but, how useful are they in
practice? The purpose of this note is to propose six linear low-dimensional
problems -- unit tests -- to evaluate different types of out-of-distribution
generalization in a precise manner. Following initial experiments, none of the
three recently proposed alternatives passes all tests. By providing the code to
automatically replicate all the results in this manuscript
(https://www.github.com/facebookresearch/InvarianceUnitTests), we hope that our
unit tests become a standard steppingstone for researchers in
out-of-distribution generalization.
