  In this paper we present a controlled study on the linearized IRM framework
(IRMv1) introduced in Arjovsky et al. (2020). We show that IRMv1 (and its
variants) framework can be potentially unstable under small changes to the
optimal regressor. This can, notably, lead to worse generalisation to new
environments, even compared with ERM which converges simply to the global
minimum for all training environments mixed up all together. We also highlight
the isseus of scaling in the the IRMv1 setup. These observations highlight the
importance of rigorous evaluation and importance of unit-testing for measuring
progress towards IRM.
