Besides pruning (which is what you describe) you might find the "lottery ticket hypothesis" interesting. The idea is essentially that in a randomly initialized

Besides pruning (which is what you describe) you might find the "lottery ticket hypothesis" interesting. The idea is essentially that in a randomly initialized large network there is a subset of weights that are already closeish for a given task and training helps tune that and suppress everything else, and that knowing this you can actually get better results by pruning before training.