Bridging the Empirical-Theoretical Gap in Neural Network Formal Language
  Learning Using Minimum Description Length
Nur Lan Emmanuel Chemla Roni Katzir
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). However, replacing standard targets
with the Minimum Description Length objective (MDL) results in the correct
solution being an optimum.