I don't want to be dismissive since this is pretty cool, but from just skimming the page it seems like this is basically a version to neural nets that is roughly equivalent to genetic programming?
Genetic programming is just one way to optimize candidates embedded in a high-dimensional space. Neural network research has been using population-based optimization techniques for a long time, that's not the innovation here.
This is an extension of NEAT (from 2002), which evolved neural network architectures and weights simultaneously. The interesting thing is by having a shared weight, they appear to be finding much more minimal networks, which can still be trained to have results close to the state of the art.
