In experimenting with the power of basic neural networks to learn particular functions, I was wondering whether a neural network can learn a random neural network. That is, if we take a neural network $N_0$ of some fixed shape, and randomly initialize the parameters, and then take another neural network $N_1$ of the same shape and train $N_1$ to produce the function given by $N_0$, what happens?
I feel like this is a natural question, and predict that there are others who have tried to do the same. I'm finding it difficult to search for relevant results, though.
Can anyone tell me whether this has been tried before, and where I can find the experimenters' observations?