I think it was in the warehouse/HQ scene where they explained to Ariadne the use of the dream-sharing tech in the military to train soldiers. But it got scrapped for a reason I forget. Or maybe the tech was merely leaked/stolen.

As for Professor Miles and Ariadne, I would need to watch the movie again, especially the college scenes to see if they are indeed student/teacher of the psyche or just architecture. I'm positive it's the latter because dream shaping in Inception is not about abstracts but of geometric shapes, sizes, and building an artificial reality of such realism that it would fool the mind of the Dreamer.

Also, keep in mind that Cobb, Mal, Arthur, and Ariadne each revealed more than passing knowledge of buildings, stairways, bridges, etc. Remember Ariadne with the mock labyrinths and Arthur with his Penrose stairs? Architecture and psychology are intrinsically linked in that architects deal with not just building design, but also taking into account how people will react to their artifice.