The current standard approach for initialization of the weights of neural network layers and nodes that use the Sigmoid or TanH activation function is called “glorot” or “xavier” initialization.
It is named for Xavier Glorot, currently a research scientist at Google DeepMind, and was described in the 2010 paper by Xavier and Yoshua Bengio titled “Understanding The Difficulty Of Training Deep Feedforward Neural Networks.”
There are two versions of this weight initialization method, which we will refer to as “xavier” and “normalized xavier.”
Glorot and Bengio proposed to adopt a properly scaled uniform distribution for initialization. This is called “Xavier” initialization […] Its derivation is based on the assumption that the activations are linear. This assumption is invalid for ReLU and PReLU.
— Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification, 2015.
Both approaches were derived assuming that the activation function is linear, nevertheless, they have become the standard for nonlinear activation functions like Sigmoid and Tanh, but not ReLU.