On the Impact of the Activation Function on Deep Neural Networks Training

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 (Schoenholz 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 (Schoenholz 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 performance.