  Humans leverage compositionality to efficiently learn new concepts,
understanding how familiar parts can combine together to form novel objects. In
contrast, popular computer vision models struggle to make the same types of
inferences, requiring more data and generalizing less flexibly than people do.
Here, we study these distinctively human abilities across a range of different
types of visual composition, examining how people classify and generate ``alien
figures'' with rich relational structure. We also develop a Bayesian program
induction model which searches for the best programs for generating the
candidate visual figures, utilizing a large program space containing different
compositional mechanisms and abstractions. In few shot classification tasks, we
find that people and the program induction model can make a range of meaningful
compositional generalizations, with the model providing a strong account of the
experimental data as well as interpretable parameters that reveal human
assumptions about the factors invariant to category membership (here, to
rotation and changing part attachment). In few shot generation tasks, both
people and the models are able to construct compelling novel examples, with
people behaving in additional structured ways beyond the model capabilities,
e.g. making choices that complete a set or reconfiguring existing parts in
highly novel ways. To capture these additional behavioral patterns, we develop
an alternative model based on neuro-symbolic program induction: this model also
composes new concepts from existing parts yet, distinctively, it utilizes
neural network modules to successfully capture residual statistical structure.
Together, our behavioral and computational findings show how people and models
can produce a rich variety of compositional behavior when classifying and
generating visual objects.
