  Leveraging the development of structural causal model (SCM), researchers can
establish graphical models for exploring the causal mechanisms behind machine
learning techniques. As the complexity of machine learning applications rises,
single-world interventionism causal analysis encounters theoretical adaptation
limitations. Accordingly, cross-world counterfactual approach extends our
understanding of causality beyond observed data, enabling hypothetical
reasoning about alternative scenarios. However, the joint involvement of
cross-world variables, encompassing counterfactual variables and real-world
variables, challenges the construction of the graphical model. Twin network is
a subtle attempt, establishing a symbiotic relationship, to bridge the gap
between graphical modeling and the introduction of counterfactuals albeit with
room for improvement in generalization. In this regard, we demonstrate the
theoretical breakdowns of twin networks in certain cross-world counterfactual
scenarios. To this end, we propose a novel teleporter theory to establish a
general and simple graphical representation of counterfactuals, which provides
criteria for determining teleporter variables to connect multiple worlds. In
theoretical application, we determine that introducing the proposed teleporter
theory can directly obtain the conditional independence between counterfactual
variables and real-world variables from the cross-world SCM without requiring
complex algebraic derivations. Accordingly, we can further identify
counterfactual causal effects through cross-world symbolic derivation. We
demonstrate the generality of the teleporter theory to the practical
application. Adhering to the proposed theory, we build a plug-and-play module,
and the effectiveness of which are substantiated by experiments on benchmarks.
