  Learning representations that generalize to novel compositions of known
concepts is crucial for bridging the gap between human and machine perception.
One prominent effort is learning object-centric representations, which are
widely conjectured to enable compositional generalization. Yet, it remains
unclear when this conjecture will be true, as a principled theoretical or
empirical understanding of compositional generalization is lacking. In this
work, we investigate when compositional generalization is guaranteed for
object-centric representations through the lens of identifiability theory. We
show that autoencoders that satisfy structural assumptions on the decoder and
enforce encoder-decoder consistency will learn object-centric representations
that provably generalize compositionally. We validate our theoretical result
and highlight the practical relevance of our assumptions through experiments on
synthetic image data.
