  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.

Machine Learning;Machine Learning