  Domain generalization (DG) enables generalizing a learning machine from
multiple seen source domains to an unseen target one. The general objective of
DG methods is to learn semantic representations that are independent of domain
labels, which is theoretically sound but empirically challenged due to the
complex mixture of common and domain-specific factors. Although disentangling
the representations into two disjoint parts has been gaining momentum in DG,
the strong presumption over the data limits its efficacy in many real-world
scenarios. In this paper, we propose Mix and Reason (\mire), a new DG framework
that learns semantic representations via enforcing the structural invariance of
semantic topology. \mire\ consists of two key components, namely,
Category-aware Data Mixing (CDM) and Adaptive Semantic Topology Refinement
(ASTR). CDM mixes two images from different domains in virtue of activation
maps generated by two complementary classification losses, making the
classifier focus on the representations of semantic objects. ASTR introduces
relation graphs to represent semantic topology, which is progressively refined
via the interactions between local feature aggregation and global cross-domain
relational reasoning. Experiments on multiple DG benchmarks validate the
effectiveness and robustness of the proposed \mire.
