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Invariant representation learning (IRL) encourages the prediction frominvariant causal features to labels de-confounded from the environments,advancing the technical roadmap of out-of-distribution (OOD) generalization.Despite spotlights around, recent theoretical results verified that some causalfeatures recovered by IRLs merely pretend domain-invariantly in the trainingenvironments but fail in unseen domains. The \emph{fake invariance} severelyendangers OOD generalization since the trustful objective can not be diagnosedand existing causal surgeries are invalid to rectify. In this paper, we reviewa IRL family (InvRat) under the Partially and Fully Informative InvariantFeature Structural Causal Models (PIIF SCM /FIIF SCM) respectively, to certifytheir weaknesses in representing fake invariant features, then, unify theircausal diagrams to propose ReStructured SCM (RS-SCM). RS-SCM can ideallyrebuild the spurious and the fake invariant features simultaneously. Giventhis, we further develop an approach based on conditional mutual informationwith respect to RS-SCM, then rigorously rectify the spurious and fake invarianteffects. It can be easily implemented by a small feature selection subnetintroduced in the IRL family, which is alternatively optimized to achieve ourgoal. Experiments verified the superiority of our approach to fight against thefake invariant issue across a variety of OOD generalization benchmarks.

Diagnosing and Rectifying Fake OOD Invariance: A Restructured Causal Approach