No Free Prune: Information-Theoretic Barriers to Pruning at Initialization

The existence of "lottery tickets" arXiv:1803.03635 at or near initialization raises the tantalizing question of whether large models are necessary in deep learning, or whether sparse networks can be quickly identified and trained without ever training the dense models that contain them. However, efforts to find these sparse subnetworks without training the dense model ("pruning at initialization") have been broadly unsuccessful arXiv:2009.08576. We put forward a theoretical explanation for this, based on the model's effective parameter count, $p_\text{eff}$, given by …

arxiv cs.lg deep learning free information large models near networks pruning question raises stat.ml them tickets training