  Learning domain-invariant semantic representations is crucial for achieving
domain generalization (DG), where a model is required to perform well on unseen
target domains. One critical challenge is that standard training often results
in entangled semantic and domain-specific features. Previous works suggest
formulating the problem from a causal perspective and solving the entanglement
problem by enforcing marginal independence between the causal (\ie semantic)
and non-causal (\ie domain-specific) features. Despite its simplicity, the
basic marginal independent-based idea alone may be insufficient to identify the
causal feature. By d-separation, we observe that the causal feature can be
further characterized by being independent of the domain conditioned on the
object, and we propose the following two strategies as complements for the
basic framework.
  First, the observation implicitly implies that for the same object, the
causal feature should not be associated with the non-causal feature, revealing
that the common practice of obtaining the two features with a shared base
feature extractor and two lightweight prediction heads might be inappropriate.
To meet the constraint, we propose a simple early-branching structure, where
the causal and non-causal feature obtaining branches share the first few blocks
while diverging thereafter, for better structure design; Second, the
observation implies that the causal feature remains invariant across different
domains for the same object. To this end, we suggest that augmentation should
be incorporated into the framework to better characterize the causal feature,
and we further suggest an effective random domain sampling scheme to fulfill
the task. Theoretical and experimental results show that the two strategies are
beneficial for the basic marginal independent-based framework. Code is
available at \url{https://github.com/liangchen527/CausEB}.
