  Leveraging the compositional nature of our world to expedite learning and
facilitate generalization is a hallmark of human perception. In machine
learning, on the other hand, achieving compositional generalization has proven
to be an elusive goal, even for models with explicit compositional priors. To
get a better handle on compositional generalization, we here approach it from
the bottom up: Inspired by identifiable representation learning, we investigate
compositionality as a property of the data-generating process rather than the
data itself. This reformulation enables us to derive mild conditions on only
the support of the training distribution and the model architecture, which are
sufficient for compositional generalization. We further demonstrate how our
theoretical framework applies to real-world scenarios and validate our findings
empirically. Our results set the stage for a principled theoretical study of
compositional generalization.
