Activation function design for deep networks: linearity and effective initialisation
This work addresses initialization challenges in deep learning, offering a method to enhance training stability and efficiency, though it is incremental as it builds on prior identification of these problems.
The paper tackles the problems of rapid convergence of pairwise input correlations and vanishing/exploding gradients at neural network initialization by proving that activation functions with a sufficiently large linear region around the origin can avoid these issues, leading to improved test/training accuracy and reduced training time in practice.
The activation function deployed in a deep neural network has great influence on the performance of the network at initialisation, which in turn has implications for training. In this paper we study how to avoid two problems at initialisation identified in prior works: rapid convergence of pairwise input correlations, and vanishing and exploding gradients. We prove that both these problems can be avoided by choosing an activation function possessing a sufficiently large linear region around the origin, relative to the bias variance $σ_b^2$ of the network's random initialisation. We demonstrate empirically that using such activation functions leads to tangible benefits in practice, both in terms test and training accuracy as well as training time. Furthermore, we observe that the shape of the nonlinear activation outside the linear region appears to have a relatively limited impact on training. Finally, our results also allow us to train networks in a new hyperparameter regime, with a much larger bias variance than has previously been possible.