  The problem of computing minimally sparse solutions of under-determined
linear systems is $NP$ hard in general. Subsets with extra properties, may
allow efficient algorithms, most notably problems with the restricted isometry
property (RIP) can be solved by convex $\ell_1$-minimization. While these
classes have been very successful, they leave out many practical applications.
  In this paper, we consider adaptable classes that are tractable after
training on a curriculum of increasingly difficult samples. The setup is
intended as a candidate model for a human mathematician, who may not be able to
tackle an arbitrary proof right away, but may be successful in relatively
flexible subclasses, or areas of expertise, after training on a suitable
curriculum.
