We design the first multi-layer disentanglement metric operating at all hierarchy levels of a structured latent representation, and derive its theoretical properties. Applied to object-centric representations, our metric unifies the evaluation of both object separation between latent slots and internal slot disentanglement into a common mathematical framework. It also addresses the problematic dependence on segmentation mask sharpness of previous pixel-level segmentation metrics such as ARI. Perhaps surprisingly, our experimental results show that good ARI values do not guarantee a disentangled representation, and that the exclusive focus on this metric has led to counterproductive choices in some previous evaluations. As an additional technical contribution, we present a new algorithm for obtaining feature importances that handles slot permutation invariance in the representation.
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