  This paper proposes to learn hierarchical compositional AND-OR model for
interpretable image synthesis by sparsifying the generator network. The
proposed method adopts the scene-objects-parts-subparts-primitives hierarchy in
image representation. A scene has different types (i.e., OR) each of which
consists of a number of objects (i.e., AND). This can be recursively formulated
across the scene-objects-parts-subparts hierarchy and is terminated at the
primitive level (e.g., wavelets-like basis). To realize this AND-OR hierarchy
in image synthesis, we learn a generator network that consists of the following
two components: (i) Each layer of the hierarchy is represented by an
over-complete set of convolutional basis functions. Off-the-shelf convolutional
neural architectures are exploited to implement the hierarchy. (ii)
Sparsity-inducing constraints are introduced in end-to-end training, which
induces a sparsely activated and sparsely connected AND-OR model from the
initially densely connected generator network. A straightforward
sparsity-inducing constraint is utilized, that is to only allow the top-$k$
basis functions to be activated at each layer (where $k$ is a hyper-parameter).
The learned basis functions are also capable of image reconstruction to explain
the input images. In experiments, the proposed method is tested on four
benchmark datasets. The results show that meaningful and interpretable
hierarchical representations are learned with better qualities of image
synthesis and reconstruction obtained than baselines.
