Logarithmic Pruning is All You Need
This work addresses the theoretical understanding of neural network pruning for researchers, offering a more practical bound that could influence pruning algorithms, though it is incremental in improving prior theoretical results.
The paper tackles the problem of identifying subnetworks within overparameterized neural networks that achieve comparable performance without training, by removing limiting assumptions and providing tighter bounds, specifically reducing the required overparameterization from a polynomial to a logarithmic factor in neuron count per weight.
The Lottery Ticket Hypothesis is a conjecture that every large neural network contains a subnetwork that, when trained in isolation, achieves comparable performance to the large network. An even stronger conjecture has been proven recently: Every sufficiently overparameterized network contains a subnetwork that, at random initialization, but without training, achieves comparable accuracy to the trained large network. This latter result, however, relies on a number of strong assumptions and guarantees a polynomial factor on the size of the large network compared to the target function. In this work, we remove the most limiting assumptions of this previous work while providing significantly tighter bounds:the overparameterized network only needs a logarithmic factor (in all variables but depth) number of neurons per weight of the target subnetwork.