  The weight initialization and the activation function of deep neural networks
have a crucial impact on the performance of the training procedure. An
inappropriate selection can lead to the loss of information of the input during
forward propagation and the exponential vanishing/exploding of gradients during
back-propagation. Understanding the theoretical properties of untrained random
networks is key to identifying which deep networks may be trained successfully
as recently demonstrated by Samuel et al (2017) who showed that for deep
feedforward neural networks only a specific choice of hyperparameters known as
the `Edge of Chaos' can lead to good performance. While the work by Samuel et
al (2017) discuss trainability issues, we focus here on training acceleration
and overall performance. We give a comprehensive theoretical analysis of the
Edge of Chaos and show that we can indeed tune the initialization parameters
and the activation function in order to accelerate the training and improve the
performance.
