# Dying ReLU and Initialization: Theory and Numerical Examples

arXiv: https://arxiv.org/abs/1903.06733 · HTML: https://mlsanity.com/paper/1903.06733/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2019.

## Built on by (most cited first, 1 of 1)

- [TeLU Activation Function for Fast and Stable Deep Learning](https://mlsanity.com/paper/2412.20269/) (2024)

## Abstract (arXiv)

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.