  Neural networks offer good approximation to many tasks but consistently fail
to reach perfect generalization, even when theoretical work shows that such
perfect solutions can be expressed by certain architectures. Using the task of
formal language learning, we focus on one simple formal language and show that
the theoretically correct solution is in fact not an optimum of commonly used
objectives -- even with regularization techniques that according to common
wisdom should lead to simple weights and good generalization (L1, L2) or other
meta-heuristics (early-stopping, dropout). On the other hand, replacing
standard targets with the Minimum Description Length objective (MDL) results in
the correct solution being an optimum.
