COAT: Measuring Object Compositionality in Emergent Representations

Learning representations that can decompose a multi-object scene into its constituent objects and recompose them flexibly is desirable for objectoriented reasoning and planning. Built upon object masks in the pixel space, existing metrics for objectness can only evaluate generative models with an object-specific "slot" structure. We propose to directly measure compositionality in the representation space as a form of objectness, making such evaluations tractable for a wider class of models. Our metric, COAT (Compositional Object Algebra Test), evaluates if a generic representation exhibits certain geometric properties that underpin object compositionality beyond what is already captured by the raw pixel space. Our experiments on the popular CLEVR (Johnson et.al., 2018) domain reveal that existing disentanglement-based generative models are not as compositional as one might expect, suggesting room for further modeling improvements. We hope our work allows for a unified evaluation of object-centric representations, spanning generative as well as discriminative, self-supervised models. D K of the representation space Z to recover