  For example, in machine translation tasks, to achieve bidirectional
translation between two languages, the source corpus is often used as the
target corpus, which involves the training of two models with opposite
directions. The question of which one can adapt most quickly to a domain shift
is of significant importance in many fields. Specifically, consider an original
distribution p that changes due to an unknown intervention, resulting in a
modified distribution p*. In aligning p with p*, several factors can affect the
adaptation rate, including the causal dependencies between variables in p. In
real-life scenarios, however, we have to consider the fairness of the training
process, and it is particularly crucial to involve a sensitive variable (bias)
present between a cause and an effect variable. To explore this scenario, we
examine a simple structural causal model (SCM) with a cause-bias-effect
structure, where variable A acts as a sensitive variable between cause (X) and
effect (Y). The two models, respectively, exhibit consistent and contrary
cause-effect directions in the cause-bias-effect SCM. After conducting unknown
interventions on variables within the SCM, we can simulate some kinds of domain
shifts for analysis. We then compare the adaptation speeds of two models across
four shift scenarios. Additionally, we prove the connection between the
adaptation speeds of the two models across all interventions.
