I can explain this.
(1) If you start your neural network with random or default connection weights, then train it, it ends up with some essentially unused space; then you can "prune" it to remove the junk sections. This has been known for a while.
(2) If you do this and then want to restart your neural network on a similar problem (with an all new dataset and all new training), you can start with a "pruned" network already, and the way to do this is explained in the MIT papers. It DOES have to be a sufficiently similar problem for the "pre-pruning" to work right; if it's a wildly different problem, you'll have to start fresh with a large, random network.