Could this research support an approach to neural networks that start out wide and shallow, then through neuron deletion and (reluctantly) added levels, become

Could this research support an approach to neural networks that start out wide and shallow, then through neuron deletion and (reluctantly) added levels, become deeper and narrower? The network would morph from generic machinery to specialized machinery. Seems analogous to our learning, where we initially give the subject all of our attention, then infer patterns and use them.