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Inparticular,thestudyofLocatello19 etal., ICML 2019 was inconclusivein this regard, see their Section 5.5. This paper fills this gap by investigating20 whether disentanglement is useful for improving fairness of downstream predictions. Thetheoremprovesapoint: theBayes39 optimal classifier does not imply fairness on an entangled representation. The proof is by counterexample. We40 further support this claim with Figure 2, showing that this isapractical issue that arises on trained classifiers and41 not simply atheoretical corner case.