  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
prove 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.
