Potential avenues

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) https://ivi.fnwi.uva.nl/isis/publications/2017/FernandoTPAMI2017/FernandoTPAMI2017.pdf

Robustness (possibilities for reducing adversarial attacks?)

Geometric model fitting situtations (computer vision)

Control systems (hard constraints are obvious in a lot of these)