In causal models, a given mechanism is assumed to be invariant to changes of other mechanisms. While this principle has been utilized for inference in settings where the causal variables are observed, theoretical insights when the variables of interest are latent are largely missing. We assay the connection between invariance and causal representation learning by establishing impossibility results which show that invariance alone is insufficient to identify latent causal variables. Together with practical considerations, we use these theoretical findings to highlight the need for additional constraints in order to identify representations by exploiting invariance.

翻译：在因果模型中，特定机制被假定为对其它机制的变化具有不变性。虽然这一原理已被用于观测到因果变量的场景中的推断，但当目标变量为潜变量时，相关理论见解仍较为缺失。我们通过建立不可能性结果来探究不变性与因果表示学习之间的关联，这些结果表明仅凭不变性不足以识别潜在因果变量。结合实践考量，我们利用这些理论发现强调了需要额外约束条件才能通过利用不变性来识别表示。