  In domain generalization, multiple labeled non-independent and
non-identically distributed source domains are available during training while
neither the data nor the labels of target domains are. Currently, learning
so-called domain invariant representations (DIRs) is the prevalent approach to
domain generalization. In this work, we define DIRs employed by existing works
in probabilistic terms and show that by learning DIRs, overly strict
requirements are imposed concerning the invariance. Particularly, DIRs aim to
perfectly align representations of different domains, i.e. their input
distributions. This is, however, not necessary for good generalization to a
target domain and may even dispose of valuable classification information. We
propose to learn so-called hypothesis invariant representations (HIRs), which
relax the invariance assumptions by merely aligning posteriors, instead of
aligning representations. We report experimental results on public domain
generalization datasets to show that learning HIRs is more effective than
learning DIRs. In fact, our approach can even compete with approaches using
prior knowledge about domains.
