Neural network pruning techniques reduce the number of parameters without compromising predicting ability of a network. Many algorithms have been developed for pruning both over-parameterized fully-connected networks (FCNs) and convolutional neural networks (CNNs), but analytical studies of capabilities and compression ratios of such pruned sub-networks are lacking. We theoretically study the performance of two pruning techniques (random and magnitude-based) on FCNs and CNNs. Given a target network {whose weights are independently sampled from appropriate distributions}, we provide a universal approach to bound the gap between a pruned and the target network in a probabilistic sense. The results establish that there exist pruned networks with expressive power within any specified bound from the target network.
@article{arxiv.2105.10065,
title = {A Probabilistic Approach to Neural Network Pruning},
author = {Xin Qian and Diego Klabjan},
journal= {arXiv preprint arXiv:2105.10065},
year = {2021}
}