There are some recent examples where people have trained a collection of large nets which are then used to teach a smaller net. The smaller net can learn more quickly and finally achieves better performance than the large collection.
The methods involve providing more detailed feedback at each example. With most training data used now, we give a 0 or 1, does this example belong to this class. In the teacher networks, they were able to teach with more subtly: this is definitely not a car, it is very lizard like and a little snake like.