Recursive neural programs: A differentiable framework for learning compositional part-whole hierarchies and image grammars.

Human vision, thought, and planning involve parsing and representing objects and scenes using structured representations based on part-whole hierarchies. Computer vision and machine learning researchers have recently sought to emulate this capability using neural networks, but a generative model formulation has been lacking. Generative models that leverage compositionality, recursion, and part-whole hierarchies are thought to underlie human concept learning and the ability to construct and represent flexible mental concepts. We introduce Recursive Neural Programs (RNPs), a neural generative model that addresses the part-whole hierarchy learning problem by modeling images as hierarchical trees of probabilistic sensory-motor programs. These programs recursively reuse learned sensory-motor primitives to model an image within different spatial reference frames, enabling hierarchical composition of objects from parts and implementing a grammar for images. We show that RNPs can learn part-whole hierarchies for a variety of image datasets, allowing rich compositionality and intuitive parts-based explanations of objects. Our model also suggests a cognitive framework for understanding how human brains can potentially learn and represent concepts in terms of recursively defined primitives and their relations with each other.