  Large neural networks are heavily over-parameterized. This is done because it
improves training to optimality. However once the network is trained, this
means many parameters can be zeroed, or pruned, leaving an equivalent sparse
neural network. We propose renormalizing sparse neural networks in order to
improve accuracy. We prove that our method's error converges to zero as network
parameters cluster or concentrate. We prove that without renormalizing, the
error does not converge to zero in general. We experiment with our method on
real world datasets MNIST, Fashion MNIST, and CIFAR-10 and confirm a large
improvement in accuracy with renormalization versus standard pruning.
