In causal inference, the "Invariance" property implies:
- The relationship $X \rightarrow Y$ remains stable or continues to hold inder interventions on $X$ and perhaps other sorts of changes.
- If intervening on $X$ is to be a way of changing $Y$ some degree of invariance of the $X \rightarrow Y$ relationship is required.
In other words, laws should exhibit a kind of independence from initial conditions. This independence is not probabilistic independence, instead, we might think about this in terms of satisfaction of an invariance condition in terms of a kind of informational independence.