Potential avenues
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End-to-end permutation learning: Transport polytope problem as a layer, solving with sinkhorn using implicit differentiation for image order (puzzle solving..)
Convert an image into a shape representation (so everything is made up of primitives..) impose the primitives with declarative nodes?
Rank pooling (mentioned by stephen gould)
Robustness (possibilities for reducing adversarial attacks?)
Geometric model fitting situtations (computer vision)
Control systems (hard constraints are obvious in a lot of these)