@Article{CiCP-28-1671,
author = {Lu , LuShin , YeonjongSu , Yanhui and Em Karniadakis , George},
title = {Dying ReLU and Initialization: Theory and Numerical Examples},
journal = {Communications in Computational Physics},
year = {2020},
volume = {28},
number = {5},
pages = {1671--1706},
abstract = {<p style="text-align: justify;">The dying ReLU refers to the problem when ReLU neurons become inactive
and only output 0 for any input. There are many empirical and heuristic explanations
of why ReLU neurons die. However, little is known about its theoretical analysis. In
this paper, we rigorously prove that a deep ReLU network will eventually die in probability as the depth goes to infinite. Several methods have been proposed to alleviate
the dying ReLU. Perhaps, one of the simplest treatments is to modify the initialization procedure. One common way of initializing weights and biases uses symmetric
probability distributions, which suffers from the dying ReLU. We thus propose a new
initialization procedure, namely, a randomized asymmetric initialization. We show
that the new initialization can effectively prevent the dying ReLU. All parameters required for the new initialization are theoretically designed. Numerical examples are
provided to demonstrate the effectiveness of the new initialization procedure.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2020-0165},
url = {http://global-sci.org/intro/article_detail/cicp/18393.html}
}