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Human vision involves parsing and representing objects and scenes usingstructured representations based on part-whole hierarchies. Computer vision andmachine learning researchers have recently sought to emulate this capabilityusing capsule networks, reference frames and active predictive coding, but agenerative model formulation has been lacking. We introduce Recursive NeuralPrograms (RNPs), which, to our knowledge, is the first neural generative modelto address the part-whole hierarchy learning problem. RNPs model images ashierarchical trees of probabilistic sensory-motor programs that recursivelyreuse learned sensory-motor primitives to model an image within differentreference frames, forming recursive image grammars. We express RNPs asstructured variational autoencoders (sVAEs) for inference and sampling, anddemonstrate parts-based parsing, sampling and one-shot transfer learning forMNIST, Omniglot and Fashion-MNIST datasets, demonstrating the model'sexpressive power. Our results show that RNPs provide an intuitive andexplainable way of composing objects and scenes, allowing rich compositionalityand intuitive interpretations of objects in terms of part-whole hierarchies.

Recursive Neural Programs: Variational Learning of Image Grammars and Part-Whole Hierarchies