GP for NNs has, but this isn't GP; "self-reproduction" (as in the original title) here means that the neural network is learning to output a copy of itself. In other words, the NN is learning to be a quine (as indicated by the current title). This is a very different than just applying genetic programming to NNs. In GP, you're updating the NN (or whatever) by copying it with mutations/recombinations. Here, the NN itself is learning to create a copy of itself.

The fact that they manage to also train to the network to simultaneously perform somewhat complicated tasks is super crazy.