Provable Compositional Generalization for Object-Centric Learning
Thaddäus Wiedemer Jack Brady Alexander Panfilov Attila Juhos Matthias Bethge Wieland Brendel
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.